Algebra I Common Core State Standards Regents at

Algebra I Common Core State Standards Regents at
Algebra I CCSS Regents Exam Questions at Random Worksheet # 1
NAME:__________________________
www.jmap.org
Algebra I Common Core State Standards Regents at Random Worksheets
1 Write an exponential equation for the graph shown
below.
4 Which recursively defined function has a first term
equal to 10 and a common difference of 4?
1) f(1) = 10
2)
f(x) = f(x − 1) + 4
f(1) = 4
3)
f(x) = f(x − 1) + 10
f(1) = 10
4)
f(x) = 4f(x − 1)
f(1) = 4
f(x) = 10f(x − 1)
Explain how you determined the equation.
2 Which equation has the same solutions as
2x 2 + x − 3 = 0
1) (2x − 1)(x + 3) = 0
2) (2x + 1)(x − 3) = 0
3) (2x − 3)(x + 1) = 0
4) (2x + 3)(x − 1) = 0
3 David has two jobs. He earns $8 per hour
babysitting his neighbor’s children and he earns
$11 per hour working at the coffee shop. Write an
inequality to represent the number of hours, x,
babysitting and the number of hours, y, working at
the coffee shop that David will need to work to
earn a minimum of $200. David worked 15 hours
at the coffee shop. Use the inequality to find the
number of full hours he must babysit to reach his
goal of $200.
5 Rowan has $50 in a savings jar and is putting in $5
every week. Jonah has $10 in his own jar and is
putting in $15 every week. Each of them plots his
progress on a graph with time on the horizontal
axis and amount in the jar on the vertical axis.
Which statement about their graphs is true?
1) Rowan’s graph has a steeper slope than
Jonah’s.
2) Rowan’s graph always lies above Jonah’s.
3) Jonah’s graph has a steeper slope than
Rowan’s.
4) Jonah’s graph always lies above Rowan’s.
6 The length of the shortest side of a right triangle is
8 inches. The lengths of the other two sides are
represented by consecutive odd integers. Which
equation could be used to find the lengths of the
other sides of the triangle?
1) 8 2 + (x + 1) = x 2
2)
3)
4)
x 2 + 8 2 = (x + 1) 2
8 2 + (x + 2) = x 2
x 2 + 8 2 = (x + 2) 2
Algebra I CCSS Regents Exam Questions at Random Worksheet # 2
NAME:__________________________
www.jmap.org
7 Peyton is a sprinter who can run the 40-yard dash
in 4.5 seconds. He converts his speed into miles
per hour, as shown below.
40 yd 3 ft 5280 ft 60 sec 60 min
⋅
⋅
⋅
⋅
4.5 sec 1 yd 1 mi
1 min
1 hr
Which ratio is incorrectly written to convert his
speed?
3 ft
1)
1 yd
5280 ft
2)
1 mi
60 sec
3)
1 min
60 min
4)
1 hr
10 A local business was looking to hire a landscaper
to work on their property. They narrowed their
choices to two companies. Flourish Landscaping
Company charges a flat rate of $120 per hour.
Green Thumb Landscapers charges $70 per hour
plus a $1600 equipment fee. Write a system of
equations representing how much each company
charges. Determine and state the number of hours
that must be worked for the cost of each company
to be the same. [The use of the grid below is
optional.] If it is estimated to take at least 35 hours
to complete the job, which company will be less
expensive? Justify your answer.
8 Guy and Jim work at a furniture store. Guy is paid
$185 per week plus 3% of his total sales in dollars,
x, which can be represented by g(x) = 185 + 0.03x .
Jim is paid $275 per week plus 2.5% of his total
sales in dollars, x, which can be represented by
f(x) = 275 + 0.025x . Determine the value of x, in
dollars, that will make their weekly pay the same.
9 A rectangular picture measures 6 inches by 8
inches. Simon wants to build a wooden frame for
the picture so that the framed picture takes up a
maximum area of 100 square inches on his wall.
The pieces of wood that he uses to build the frame
all have the same width. Write an equation or
inequality that could be used to determine the
maximum width of the pieces of wood for the
frame Simon could create. Explain how your
equation or inequality models the situation. Solve
the equation or inequality to determine the
maximum width of the pieces of wood used for the
frame to the nearest tenth of an inch.
11 When factored completely, the expression p 4 − 81
is equivalent to
1) (p 2 + 9)(p 2 − 9)
2)
3)
4)
(p 2 − 9)(p 2 − 9)
(p 2 + 9)(p + 3)(p − 3)
(p + 3)(p − 3)(p + 3)(p − 3)
Algebra I CCSS Regents Exam Questions at Random Worksheet # 3
NAME:__________________________
www.jmap.org
12 The table below represents the function F.
x
F(x)
The equation that represents this function is
1) F(x) = 3 x
2) F(x) = 3x
3
9
3)
4)
13 Which statistic would indicate that a linear
function would not be a good fit to model a data
set?
1) r = −0.93
2) r = 1
4
17
6
65
7
129
8
257
F(x) = 2 x + 1
F(x) = 2x + 3
15 The equation to determine the weekly earnings of
an employee at The Hamburger Shack is given by
w(x), where x is the number of hours worked.

0 ≤ x ≤ 40
 10x,
w(x) = 
 15(x − 40) + 400, x > 40
Determine the difference in salary, in dollars, for
an employee who works 52 hours versus one who
works 38 hours. Determine the number of hours an
employee must work in order to earn $445.
Explain how you arrived at this answer.
3)
4)
14 If f(x) = 3 x and g(x) = 2x + 5 , at which value of x
is f(x) < g(x) ?
1) −1
2) 2
3) −3
4) 4
16 Some banks charge a fee on savings accounts that
are left inactive for an extended period of time.
The equation y = 5000(0.98) x represents the value,
y, of one account that was left inactive for a period
of x years. What is the y-intercept of this equation
and what does it represent?
1) 0.98, the percent of money in the account
initially
2) 0.98, the percent of money in the account after
x years
3) 5000, the amount of money in the account
initially
4) 5000, the amount of money in the account after
x years
Algebra I CCSS Regents Exam Questions at Random Worksheet # 4
NAME:__________________________
www.jmap.org
17 Isaiah collects data from two different companies, each with four employees. The results of the study, based on
each worker’s age and salary, are listed in the tables below.
Company 1
Worker’s
Salary
Age in
in
Years
Dollars
25
30,000
27
32,000
28
35,000
33
38,000
Company 2
Worker’s
Salary
Age in
in
Years
Dollars
25
29,000
28
35,500
29
37,000
31
65,000
Which statement is true about these data?
1) The median salaries in both companies
are greater than $37,000.
2) The mean salary in company 1 is greater
than the mean salary in company 2.
3)
4)
18 The formula for the area of a trapezoid is
1
A = h(b 1 + b 2 ). Express b 1 in terms of A, h, and
2
b 2 . The area of a trapezoid is 60 square feet, its
height is 6 ft, and one base is 12 ft. Find the
number of feet in the other base.
The salary range in company 2 is greater
than the salary range in company 1.
The mean age of workers at company 1 is
greater than the mean age of workers at
company 2.
19 Which situation could be modeled by using a linear
function?
1) a bank account balance that grows at a rate of
5% per year, compounded annually
2) a population of bacteria that doubles every 4.5
hours
3) the cost of cell phone service that charges a
base amount plus 20 cents per minute
4) the concentration of medicine in a person’s
body that decays by a factor of one-third every
hour
Algebra I CCSS Regents Exam Questions at Random Worksheet # 5
NAME:__________________________
www.jmap.org
20 Which graph shows a line where each value of y is
three more than half of x?
1)
2)
22 Connor wants to attend the town carnival. The
price of admission to the carnival is $4.50, and
each ride costs an additional 79 cents. If he can
spend at most $16.00 at the carnival, which
inequality can be used to solve for r, the number of
rides Connor can go on, and what is the maximum
number of rides he can go on?
1) 0.79 + 4.50r ≤ 16.00; 3 rides
2) 0.79 + 4.50r ≤ 16.00; 4 rides
3) 4.50 + 0.79r ≤ 16.00; 14 rides
4) 4.50 + 0.79r ≤ 16.00; 15 rides
23 A football player attempts to kick a football over a
goal post. The path of the football can be modeled
1 2 2
x + x, where x is the
by the function h(x) = −
225
3
horizontal distance from the kick, and h(x) is the
height of the football above the ground, when both
are measured in feet. On the set of axes below,
graph the function y = h(x) over the interval
0 ≤ x ≤ 150.
3)
4)
21 Fred is given a rectangular piece of paper. If the
length of Fred's piece of paper is represented by
2x − 6 and the width is represented by 3x − 5, then
the paper has a total area represented by
1) 5x − 11
2) 6x 2 − 28x + 30
3) 10x − 22
4) 6x 2 − 6x − 11
Determine the vertex of y = h(x) . Interpret the
meaning of this vertex in the context of the
problem. The goal post is 10 feet high and 45
yards away from the kick. Will the ball be high
enough to pass over the goal post? Justify your
answer.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 6
NAME:__________________________
www.jmap.org
24 Which trinomial is equivalent to
3(x − 2) 2 − 2(x − 1)?
1)
2)
3)
4)
3x 2 − 2x − 10
3x 2 − 2x − 14
3x 2 − 14x + 10
3x 2 − 14x + 14
25 Let f be a function such that f(x) = 2x − 4 is
defined on the domain 2 ≤ x ≤ 6. The range of this
function is
1) 0 ≤ y ≤ 8
2) 0 ≤ y < ∞
3) 2 ≤ y ≤ 6
4) −∞ < y < ∞
26 A company produces x units of a product per
month, where C(x) represents the total cost and
R(x) represents the total revenue for the month.
The functions are modeled by C(x) = 300x + 250
and R(x) = −0.5x 2 + 800x − 100. The profit is the
difference between revenue and cost where
P(x) = R(x) − C(x) . What is the total profit, P(x) ,
for the month?
1) P(x) = −0.5x 2 + 500x − 150
2)
3)
4)
28 If Lylah completes the square for
f(x) = x 2 − 12x + 7 in order to find the minimum,
she must write f(x) in the general form
f(x) = (x − a) 2 + b . What is the value of a for f(x) ?
1) 6
2) −6
3) 12
4) −12
29 Given: L =
2
M=3 3
N=
16
P= 9
Which expression results in a rational number?
1) L + M
2) M + N
3) N + P
4) P + L
30 The diagrams below represent the first three terms
of a sequence.
P(x) = −0.5x 2 + 500x − 350
P(x) = −0.5x 2 − 500x + 350
P(x) = −0.5x 2 + 500x + 350
27 Jackson is starting an exercise program. The first
day he will spend 30 minutes on a treadmill. He
will increase his time on the treadmill by 2 minutes
each day. Write an equation for T(d), the time, in
minutes, on the treadmill on day d. Find T(6), the
minutes he will spend on the treadmill on day 6.
Assuming the pattern continues, which formula
determines a n , the number of shaded squares in the
nth term?
1) a n = 4n + 12
2) a n = 4n + 8
3) a n = 4n + 4
4) a n = 4n + 2
Algebra I CCSS Regents Exam Questions at Random Worksheet # 7
NAME:__________________________
www.jmap.org
31 A function is shown in the table below.
x f(x)
−4 2
−1 −4
0 −2
3 16
If included in the table, which ordered pair, (−4,1) or (1,−4), would result in a relation that is no longer a function?
Explain your answer.
32 During a snowstorm, a meteorologist tracks the
amount of accumulating snow. For the first three
hours of the storm, the snow fell at a constant rate
of one inch per hour. The storm then stopped for
two hours and then started again at a constant rate
of one-half inch per hour for the next four hours.
a) On the grid below, draw and label a graph that
models the accumulation of snow over time using
the data the meteorologist collected.
33 On the set of axes below, draw the graph of the
3
equation y = − x + 3.
4
Is the point (3,2) a solution to the equation?
Explain your answer based on the graph drawn.
b) If the snowstorm started at 6 p.m., how much
snow had accumulated by midnight?
Algebra I CCSS Regents Exam Questions at Random Worksheet # 8
NAME:__________________________
www.jmap.org
34 The table below lists the total cost for parking for a period of time on a street in Albany, N.Y. The total cost is for
any length of time up to and including the hours parked. For example, parking for up to and including 1 hour
would cost $1.25; parking for 3.5 hours would cost $5.75.
Hours Total
Parked Cost
1
1.25
2
2.50
3
4.00
4
5.75
5
7.75
6
10.00
Graph the step function that represents the cost for the number of hours parked.
Explain how the cost per hour to park changes over the six-hour period.
35 The zeros of the function f(x) = 3x 2 − 3x − 6 are
1) −1 and −2
2) 1 and −2
3) 1 and 2
4) −1 and 2
36 Given the graph of the line represented by the
equation f(x) = −2x + b , if b is increased by 4 units,
the graph of the new line would be shifted 4 units
1) right
2) up
3) left
4) down
Algebra I CCSS Regents Exam Questions at Random Worksheet # 9
NAME:__________________________
www.jmap.org
37 Each day Toni records the height of a plant for her science lab. Her data are shown in the table below.
Day (n)
Height (cm)
1
3.0
2
4.5
3
6.0
4
7.5
5
9.0
The plant continues to grow at a constant daily rate. Write an equation to represent h(n), the height of the plant on
the nth day.
38 If a sequence is defined recursively by f(0) = 2 and
f(n + 1) = −2f(n) + 3 for n ≥ 0, then f(2) is equal to
1) 1
2) −11
3) 5
4) 17
39 The inequality 7 −
1)
x>9
2)
x>−
3)
x<9
4)
x<−
42 On the set of axes below, graph the function
y = |x + 1 | .
2
x < x − 8 is equivalent to
3
3
5
3
5
40 Rhonda deposited $3000 in an account in the
Merrick National Bank, earning 4.2% interest,
compounded annually. She made no deposits or
withdrawals. Write an equation that can be used to
find B, her account balance after t years.
41 Solve the inequality below to determine and state
the smallest possible value for x in the solution set.
3(x + 3) ≤ 5x − 3
State the range of the function. State the domain
over which the function is increasing.
43 If the quadratic formula is used to find the roots of
the equation x 2 − 6x − 19 = 0, the correct roots are
1) 3 ± 2 7
2)
3)
4)
−3 ± 2 7
3 ± 4 14
−3 ± 4 14
Algebra I CCSS Regents Exam Questions at Random Worksheet # 10
NAME:__________________________
www.jmap.org
44 Which equation has the same solution as
x 2 − 6x − 12 = 0?
1) (x + 3) 2 = 21
2)
3)
4)
46 Which inequality is represented in the graph
below?
(x − 3) 2 = 21
(x + 3) 2 = 3
(x − 3) 2 = 3
45 Which table of values represents a linear
relationship?
1)
2)
1)
2)
3)
4)
y ≥ −3x + 4
y ≤ −3x + 4
y ≥ −4x − 3
y ≤ −4x − 3
47 Sam and Jeremy have ages that are consecutive odd
integers. The product of their ages is 783. Which
equation could be used to find Jeremy’s age, j, if he
is the younger man?
1) j 2 + 2 = 783
2)
3)
4)
j 2 − 2 = 783
j 2 + 2j = 783
j 2 − 2j = 783
3)
4)
48 Which domain would be the most appropriate set to
use for a function that predicts the number of
household online-devices in terms of the number of
people in the household?
1) integers
2) whole numbers
3) irrational numbers
4) rational numbers
Algebra I CCSS Regents Exam Questions at Random Worksheet # 11
NAME:__________________________
www.jmap.org
49 How does the graph of f(x) = 3(x − 2) 2 + 1
compare to the graph of g(x) = x ?
1) The graph of f(x) is wider than the graph of
g(x) , and its vertex is moved to the left 2 units
and up 1 unit.
2) The graph of f(x) is narrower than the graph of
g(x) , and its vertex is moved to the right 2 units
and up 1 unit.
3) The graph of f(x) is narrower than the graph of
g(x) , and its vertex is moved to the left 2 units
and up 1 unit.
4) The graph of f(x) is wider than the graph of
g(x) , and its vertex is moved to the right 2 units
and up 1 unit.
2
52 Which graph represents the solution of y ≤ x + 3
and y ≥ −2x − 2?
1)
2)
50 The cost of airing a commercial on television is
modeled by the function C(n) = 110n + 900, where
n is the number of times the commercial is aired.
Based on this model, which statement is true?
1) The commercial costs $0 to produce and $110
per airing up to $900.
2) The commercial costs $110 to produce and
$900 each time it is aired.
3) The commercial costs $900 to produce and
$110 each time it is aired.
4) The commercial costs $1010 to produce and
can air an unlimited number of times.
51 When solving the equation 4(3x 2 + 2) − 9 = 8x 2 + 7,
Emily wrote 4(3x 2 + 2) = 8x 2 + 16 as her first step.
Which property justifies Emily's first step?
1) addition property of equality
2) commutative property of addition
3) multiplication property of equality
4) distributive property of multiplication over
addition
3)
4)
53 Alex is selling tickets to a school play. An adult
ticket costs $6.50 and a student ticket costs $4.00.
Alex sells x adult tickets and 12 student tickets.
Write a function, f(x) , to represent how much
money Alex collected from selling tickets.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 12
NAME:__________________________
www.jmap.org
54 Given: y + x > 2
y ≤ 3x − 2
Which graph shows the solution of the given set of
inequalities?
56 The Jamison family kept a log of the distance they
traveled during a trip, as represented by the graph
below.
1)
2)
During which interval was their average speed the
greatest?
1) the first hour to the second hour
2) the second hour to the fourth hour
3) the sixth hour to the eighth hour
4) the eighth hour to the tenth hour
3)
57 Which system of equations has the same solution
as the system below?
2x + 2y = 16
4)
55 The zeros of the function f(x) = (x + 2) 2 − 25 are
1) −2 and 5
2) −3 and 7
3) −5 and 2
4) −7 and 3
3x − y = 4
1)
2x + 2y = 16
2)
6x − 2y = 4
2x + 2y = 16
3)
6x − 2y = 8
x + y = 16
4)
3x − y = 4
6x + 6y = 48
6x + 2y = 8
Algebra I CCSS Regents Exam Questions at Random Worksheet # 13
NAME:__________________________
www.jmap.org
58 How many real solutions does the equation
x 2 − 2x + 5 = 0 have? Justify your answer.
61 A student is asked to solve the equation
4(3x − 1) 2 − 17 = 83. The student's solution to the
problem starts as 4(3x − 1) 2 = 100
59 John and Sarah are each saving money for a car.
The total amount of money John will save is given
by the function f(x) = 60 + 5x . The total amount of
money Sarah will save is given by the function
g(x) = x 2 + 46 . After how many weeks, x, will they
have the same amount of money saved? Explain
how you arrived at your answer.
(3x − 1) 2 = 25
A correct next step in the solution of the problem is
1) 3x − 1 = ±5
2) 3x − 1 = ±25
3) 9x 2 − 1 = 25
4) 9x 2 − 6x + 1 = 5
62 For which function defined by a polynomial are the
zeros of the polynomial −4 and −6?
1) y = x 2 − 10x − 24
60 Caitlin has a movie rental card worth $175. After
she rents the first movie, the card’s value is
$172.25. After she rents the second movie, its value
is $169.50. After she rents the third movie, the
card is worth $166.75. Assuming the pattern
continues, write an equation to define A(n), the
amount of money on the rental card after n rentals.
Caitlin rents a movie every Friday night. How
many weeks in a row can she afford to rent a
movie, using her rental card only? Explain how
you arrived at your answer.
2)
3)
4)
y = x 2 + 10x + 24
y = x 2 + 10x − 24
y = x 2 − 10x + 24
63 John has four more nickels than dimes in his
pocket, for a total of $1.25. Which equation could
be used to determine the number of dimes, x, in his
pocket?
1) 0.10(x + 4) + 0.05(x) = $1.25
2) 0.05(x + 4) + 0.10(x) = $1.25
3) 0.10(4x) + 0.05(x) = $1.25
4) 0.05(4x) + 0.10(x) = $1.25
64 Rachel and Marc were given the information shown below about the bacteria growing in a Petri dish in their
biology class.
Number of Hours, x
Number of Bacteria, B(x)
1
2
3
4
5
6
7
8
9
10
220 280 350 440 550 690 860 1070 1340 1680
Rachel wants to model this information with a linear function. Marc wants to use an exponential function. Which
model is the better choice? Explain why you chose this model.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 14
NAME:__________________________
www.jmap.org
65 At an office supply store, if a customer purchases
fewer than 10 pencils, the cost of each pencil is
$1.75. If a customer purchases 10 or more pencils,
the cost of each pencil is $1.25. Let c be a function
for which c (x) is the cost of purchasing x pencils,
where x is a whole number.

 1.75x, if 0 ≤ x ≤ 9
c (x) = 
 1.25x, if x ≥ 10
66 Which equation has the same solutions as
x 2 + 6x − 7 = 0?
1) (x + 3) 2 = 2
2)
3)
4)
(x − 3) 2 = 2
(x − 3) 2 = 16
(x + 3) 2 = 16
Create a graph of c on the axes below.
67 New Clarendon Park is undergoing renovations to
its gardens. One garden that was originally a
square is being adjusted so that one side is doubled
in length, while the other side is decreased by three
meters. The new rectangular garden will have an
area that is 25% more than the original square
garden. Write an equation that could be used to
determine the length of a side of the original square
garden. Explain how your equation models the
situation. Determine the area, in square meters, of
the new rectangular garden.
68 The graph below represents a jogger's speed during
her 20-minute jog around her neighborhood.
A customer brings 8 pencils to the cashier. The
cashier suggests that the total cost to purchase 10
pencils would be less expensive. State whether the
cashier is correct or incorrect. Justify your answer.
Which statement best describes what the jogger
was doing during the 9 − 12 minute interval of her
jog?
1) She was standing still.
2) She was increasing her speed.
3) She was decreasing her speed.
4) She was jogging at a constant rate.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 15
NAME:__________________________
www.jmap.org
69 About a year ago, Joey watched an online video of a band and noticed that it had been viewed only 843 times.
One month later, Joey noticed that the band’s video had 1708 views. Joey made the table below to keep track of
the cumulative number of views the video was getting online.
Months Since First Viewing
0
1
2
3
4
5
6
Total Views
843
1708
forgot to record
7124
14,684
29,787
62,381
a) Write a regression equation that best models these data. Round all values to the nearest hundredth. Justify
your choice of regression equation. b) As shown in the table, Joey forgot to record the number of views after the
second month. Use the equation from part a to estimate the number of full views of the online video that Joey
forgot to record.
70 A high school drama club is putting on their annual
theater production. There is a maximum of 800
tickets for the show. The costs of the tickets are $6
before the day of the show and $9 on the day of the
show. To meet the expenses of the show, the club
must sell at least $5,000 worth of tickets.
a) Write a system of inequalities that represent this
situation.
b) The club sells 440 tickets before the day of the
show. Is it possible to sell enough additional
tickets on the day of the show to at least meet the
expenses of the show? Justify your answer.
71 A gardener is planting two types of trees:
Type A is three feet tall and grows at a rate
of 15 inches per year.
Type B is four feet tall and grows at a rate
of 10 inches per year.
Algebraically determine exactly how many years it
will take for these trees to be the same height.
72 The graph of y = f(x) is shown below.
Which point could be used to find f(2) ?
1) A
2) B
3) C
4) D
Algebra I CCSS Regents Exam Questions at Random Worksheet # 16
NAME:__________________________
www.jmap.org
73 The table below shows the average diameter of a pupil in a person’s eye as he or she grows older.
Age
(years)
20
30
40
50
60
70
80
Average Pupil
Diameter (mm)
4.7
4.3
3.9
3.5
3.1
2.7
2.3
What is the average rate of change, in millimeters per year, of a person’s pupil diameter from age 20 to age 80?
1) 2.4
3) −2.4
2) 0.04
4) −0.04
74 Two functions, y = |x − 3 | and 3x + 3y = 27, are
graphed on the same set of axes. Which statement
is true about the solution to the system of
equations?
1) (3,0) is the solution to the system because it
satisfies the equation y = |x − 3 | .
2) (9,0) is the solution to the system because it
satisfies the equation 3x + 3y = 27.
3) (6,3) is the solution to the system because it
satisfies both equations.
4) (3,0), (9,0), and (6,3) are the solutions to the
system of equations because they all satisfy at
least one of the equations.
75 Solve for x algebraically:
7x − 3(4x − 8) ≤ 6x + 12 − 9x
If x is a number in the interval [4,8], state all
integers that satisfy the given inequality. Explain
how you determined these values.
76 If f(x) = x 2 − 2x − 8 and g(x) =
value of x is f(x) = g(x) ?
1) −1.75 and −1.438
2) −1.75 and 4
3) −1.438 and 0
4) 4 and 0
1
x − 1, for which
4
77 Christopher looked at his quiz scores shown below
for the first and second semester of his Algebra
class.
Semester 1: 78, 91, 88, 83, 94
Semester 2: 91, 96, 80, 77, 88, 85, 92
Which statement about Christopher's performance
is correct?
1) The interquartile range for semester 1 is greater
than the interquartile range for semester 2.
2) The median score for semester 1 is greater than
the median score for semester 2.
3) The mean score for semester 2 is greater than
the mean score for semester 1.
4) The third quartile for semester 2 is greater than
the third quartile for semester 1.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 17
NAME:__________________________
www.jmap.org
78 Determine the smallest integer that makes
−3x + 7 − 5x < 15 true.
81 Graph f(x) = x 2 and g(x) = 2 x for x ≥ 0 on the set
of axes below.
79 On the axes below, graph f(x) = |3x| .
State which function, f(x) or g(x) , has a greater
value when x = 20. Justify your reasoning.
If g(x) = f(x) − 2, how is the graph of f(x)
translated to form the graph of g(x) ? If
h(x) = f(x − 4), how is the graph of f(x) translated
to form the graph of h(x)?
80 The breakdown of a sample of a chemical
compound is represented by the function
p(t) = 300(0.5) t , where p(t) represents the number
of milligrams of the substance and t represents the
time, in years. In the function p(t), explain what
0.5 and 300 represent.
82 If f(x) =
1)
2)
3)
4)
1
−2
−1
13
−
3
2x + 3
, then
6x − 5
 1 
f   =
 2 
Algebra I CCSS Regents Exam Questions at Random Worksheet # 18
NAME:__________________________
www.jmap.org
83 Albert says that the two systems of equations shown below have the same solutions.
First System
8x + 9y = 48
Second System
8x + 9y = 48
12x + 5y = 21
−8.5y = −51
Determine and state whether you agree with Albert. Justify your answer.
84 Which point is not on the graph represented by
y = x 2 + 3x − 6 ?
1) (−6,12)
2) (−4,−2)
3) (2,4)
4) (3,−6)
85 A satellite television company charges a one-time
installation fee and a monthly service charge. The
total cost is modeled by the function y = 40 + 90x .
Which statement represents the meaning of each
part of the function?
1) y is the total cost, x is the number of months of
service, $90 is the installation fee, and $40 is
the service charge per month.
2) y is the total cost, x is the number of months of
service, $40 is the installation fee, and $90 is
the service charge per month.
3) x is the total cost, y is the number of months of
service, $40 is the installation fee, and $90 is
the service charge per month.
4) x is the total cost, y is the number of months of
service, $90 is the installation fee, and $40 is
the service charge per month.
86 Solve the equation 4x 2 − 12x = 7 algebraically for
x.
87 Morgan can start wrestling at age 5 in Division 1.
He remains in that division until his next odd
birthday when he is required to move up to the next
division level. Which graph correctly represents
this information?
1)
2)
3)
4)
Algebra I CCSS Regents Exam Questions at Random Worksheet # 19
NAME:__________________________
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88 Given the functions g(x), f(x), and h(x) shown below:
g(x) = x 2 − 2x
x
0
1
2
3
f(x)
1
2
5
7
The correct list of functions ordered from greatest to least by average rate of change over the interval 0 ≤ x ≤ 3 is
1) f(x), g(x), h(x)
3) g(x), f(x), h(x)
2) h(x) , g(x), f(x)
4) h(x) , f(x), g(x)
89 A sunflower is 3 inches tall at week 0 and grows 2
inches each week. Which function(s) shown below
can be used to determine the height, f(n) , of the
sunflower in n weeks?
I. f(n) = 2n + 3
II. f(n) = 2n + 3(n − 1)
III. f(n) = f(n − 1) + 2 where f(0) = 3
1) I and II
2) II, only
3) III, only
4) I and III
90 A landscaper is creating a rectangular flower bed
such that the width is half of the length. The area
of the flower bed is 34 square feet. Write and solve
an equation to determine the width of the flower
bed, to the nearest tenth of a foot.
91 Express the product of 2x 2 + 7x − 10 and x + 5 in
standard form.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 20
NAME:__________________________
www.jmap.org
92 The table below shows the number of grams of carbohydrates, x, and the number of Calories, y, of six different
foods.
Carbohydrates (x)
8
9.5
10
6
7
4
Calories (y)
120
138
147
88
108
62
Which equation best represents the line of best fit for this set of data?
1) y = 15x
3) y = 0.1x − 0.4
2) y = 0.07x
4) y = 14.1x + 5.8
93 The country of Benin in West Africa has a
population of 9.05 million people. The population
is growing at a rate of 3.1% each year. Which
function can be used to find the population 7 years
from now?
1) f(t) = (9.05 × 10 6 )(1 − 0.31) 7
2)
3)
4)
f(t) = (9.05 × 10 6 )(1 + 0.31) 7
f(t) = (9.05 × 10 6 )(1 + 0.031) 7
f(t) = (9.05 × 10 6 )(1 − 0.031) 7
96 A school is building a rectangular soccer field that
has an area of 6000 square yards. The soccer field
must be 40 yards longer than its width. Determine
algebraically the dimensions of the soccer field, in
yards.
97 The graph of the function f(x) =
below.
94 What are the roots of the equation x 2 + 4x − 16 = 0?
1) 2 ± 2 5
2)
3)
4)
−2 ± 2 5
2±4 5
−2 ± 4 5
95 The function f has a domain of {1,3,5,7} and a
range of {2,4,6}. Could f be represented by
{(1,2),(3,4),(5,6),(7,2)}? Justify your answer.
The domain of the function is
1) {x | x > 0}
2) {x | x ≥ 0}
3) {x | x > −4}
4) {x | x ≥ −4}
x + 4 is shown
Algebra I CCSS Regents Exam Questions at Random Worksheet # 21
NAME:__________________________
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98 The solution of the equation (x + 3) 2 = 7 is
1)
2)
3)
4)
3± 7
7± 3
−3 ± 7
−7 ± 3
99 Next weekend Marnie wants to attend either
carnival A or carnival B. Carnival A charges $6 for
admission and an additional $1.50 per ride.
Carnival B charges $2.50 for admission and an
additional $2 per ride.
a) In function notation, write A(x) to represent the
total cost of attending carnival A and going on x
rides. In function notation, write B(x) to represent
the total cost of attending carnival B and going on x
rides.
b) Determine the number of rides Marnie can go on
such that the total cost of attending each carnival is
the same. [Use of the set of axes below is
optional.]
c) Marnie wants to go on five rides. Determine
which carnival would have the lower total cost.
Justify your answer.
100 Beverly did a study this past spring using data she
collected from a cafeteria. She recorded data
weekly for ice cream sales and soda sales. Beverly
found the line of best fit and the correlation
coefficient, as shown in the diagram below.
Given this information, which statement(s) can
correctly be concluded?
I. Eating more ice cream causes a person to
become thirsty.
II. Drinking more soda causes a person to become
hungry.
III. There is a strong correlation between ice cream
sales and soda sales.
1) I, only
2) III, only
3) I and III
4) II and III
101 Mo's farm stand sold a total of 165 pounds of
apples and peaches. She sold apples for $1.75 per
pound and peaches for $2.50 per pound. If she
made $337.50, how many pounds of peaches did
she sell?
1) 11
2) 18
3) 65
4) 100
Algebra I CCSS Regents Exam Questions at Random Worksheet # 22
NAME:__________________________
www.jmap.org
102 Draw the graph of y =
below.
x − 1 on the set of axes
104 The graphs below represent functions defined by
polynomials. For which function are the zeros of
the polynomials 2 and −3?
1)
2)
103 A polynomial function contains the factors x, x − 2,
and x + 5 . Which graph(s) below could represent
the graph of this function?
3)
1)
2)
3)
4)
I, only
II, only
I and III
I, II, and III
4)
Algebra I CCSS Regents Exam Questions at Random Worksheet # 23
NAME:__________________________
www.jmap.org
105 Natasha is planning a school celebration and wants
to have live music and food for everyone who
attends. She has found a band that will charge her
$750 and a caterer who will provide snacks and
drinks for $2.25 per person. If her goal is to keep
the average cost per person between $2.75 and
$3.25, how many people, p, must attend?
1) 225 < p < 325
2) 325 < p < 750
3) 500 < p < 1000
4) 750 < p < 1500
106 What is one point that lies in the solution set of the
system of inequalities graphed below?
108 Given 2x + ax − 7 > −12, determine the largest
integer value of a when x = −1.
109 The equation for the volume of a cylinder is
V = π r 2 h . The positive value of r, in terms of h
and V, is
V
1)
r=
2)
3)
r = Vπ h
r = 2Vπ h
V
r=
2π
4)
πh
110 The graph of the equation y = ax 2 is shown below.
1)
2)
3)
4)
(7,0)
(3,0)
(0,7)
(−3,5)
107 Factor the expression x 4 + 6x 2 − 7 completely.
1
If a is multiplied by − , the graph of the new
2
equation is
1) wider and opens downward
2) wider and opens upward
3) narrower and opens downward
4) narrower and opens upward
111 Write an equation that defines m(x) as a trinomial
where m(x) = (3x − 1)(3 − x) + 4x 2 + 19. Solve for x
when m(x) = 0.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 24
NAME:__________________________
www.jmap.org
112 Robin collected data on the number of hours she watched television on Sunday through Thursday nights for a
period of 3 weeks. The data are shown in the table below.
Week 1
Week 2
Week 3
Sun
4
4.5
4
Mon
3
5
3
Tues
3.5
2.5
1
Wed Thurs
2
2
3
1.5
1.5
2.5
Using an appropriate scale on the number line below, construct a box plot for the 15 values.
113 Krystal was given $3000 when she turned 2 years
old. Her parents invested it at a 2% interest rate
compounded annually. No deposits or withdrawals
were made. Which expression can be used to
determine how much money Krystal had in the
account when she turned 18?
1) 3000(1 + 0.02) 16
2)
3)
4)
3000(1 − 0.02) 16
3000(1 + 0.02) 18
3000(1 − 0.02) 18
114 Four expressions are shown below.
2(2x 2 − 2x − 60)
I
4(x 2 − x − 30)
4(x + 6)(x − 5)
4x(x − 1) − 120
The expression 4x 2 − 4x − 120 is equivalent to
1) I and II, only
2) II and IV, only
3) I, II, and IV
4) II, III, and IV
II
III
IV
115 The vertex of the parabola represented by
f(x) = x 2 − 4x + 3 has coordinates (2,−1). Find the
coordinates of the vertex of the parabola defined by
g(x) = f(x − 2) . Explain how you arrived at your
answer. [The use of the set of axes below is
optional.]
Algebra I CCSS Regents Exam Questions at Random Worksheet # 25
NAME:__________________________
www.jmap.org
116 The volume of a large can of tuna fish can be
calculated using the formula V = π r 2 h. Write an
equation to find the radius, r, in terms of V and h.
Determine the diameter, to the nearest inch, of a
large can of tuna fish that has a volume of 66 cubic
inches and a height of 3.3 inches.
117 The number of carbon atoms in a fossil is given by
the function y = 5100(0.95) x , where x represents
the number of years since being discovered. What
is the percent of change each year? Explain how
you arrived at your answer.
118 A rectangular garden measuring 12 meters by 16
meters is to have a walkway installed around it
with a width of x meters, as shown in the diagram
below. Together, the walkway and the garden have
an area of 396 square meters.
Write an equation that can be used to find x, the
width of the walkway. Describe how your equation
models the situation. Determine and state the
width of the walkway, in meters.
119 Which statement is not always true?
1) The product of two irrational numbers is
irrational.
2) The product of two rational numbers is
rational.
3) The sum of two rational numbers is rational.
4) The sum of a rational number and an irrational
number is irrational.
120 In the equation x 2 + 10x + 24 = (x + a)(x + b) , b is
an integer. Find algebraically all possible values of
b.
121 Graph the function y = |x − 3 | on the set of axes
below.
Explain how the graph of y = |x − 3 | has changed
from the related graph y = |x | .
Algebra I CCSS Regents Exam Questions at Random Worksheet # 26
NAME:__________________________
www.jmap.org
 |x | x < 1

122 Which graph represents f(x) = 
?

 x x ≥ 1
124 The residual plots from two different sets of
bivariate data are graphed below.
1)
2)
3)
Explain, using evidence from graph A and graph B,
which graph indicates that the model for the data is
a good fit.
125 The distance a free falling object has traveled can
1
be modeled by the equation d = at 2 , where a is
2
acceleration due to gravity and t is the amount of
time the object has fallen. What is t in terms of a
and d?
1)
2)
4)
3)
4)
123 Solve 8m2 + 20m = 12 for m by factoring.
t=
da
2
2d
a
 da  2
t =  
 d 
t=
t=
 2d

 a

 2



Algebra I CCSS Regents Exam Questions at Random Worksheet # 27
NAME:__________________________
www.jmap.org
126 A function is graphed on the set of axes below.
Which function is related to the graph?
 2
 x , x < 1
1) f(x) = 

 x − 2, x > 1
 2
 x , x < 1

2) f(x) = 
 1 x + 1 , x > 1
 2
2
 2
 x , x < 1
3) f(x) = 

 2x − 7, x > 1
 2
 x , x < 1

4) f(x) = 
9
 3
 x − , x > 1
2
2

127 Jacob and Zachary go to the movie theater and
purchase refreshments for their friends. Jacob
spends a total of $18.25 on two bags of popcorn
and three drinks. Zachary spends a total of $27.50
for four bags of popcorn and two drinks. Write a
system of equations that can be used to find the
price of one bag of popcorn and the price of one
drink. Using these equations, determine and state
the price of a bag of popcorn and the price of a
drink, to the nearest cent.
128 Which function has the same y-intercept as the
graph below?
1)
2)
3)
4)
12 − 6x
4
27 + 3y = 6x
6y + x = 18
y + 3 = 6x
y=
129 On the set of axes below, graph the function
represented by y = 3 x − 2 for the domain
−6 ≤ x ≤ 10.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 28
NAME:__________________________
www.jmap.org
130 A nutritionist collected information about different brands of beef hot dogs. She made a table showing the number
of Calories and the amount of sodium in each hot dog.
Calories per
Beef Hot Dog
186
181
176
149
184
190
158
139
Milligrams of Sodium
per Beef Hot Dog
495
477
425
322
482
587
370
322
a) Write the correlation coefficient for the line of best fit. Round your answer to the nearest hundredth.
b) Explain what the correlation coefficient suggests in the context of this problem.
131 The table below shows the average yearly balance in a savings account where interest is compounded annually.
No money is deposited or withdrawn after the initial amount is deposited.
Year
0
10
20
30
40
50
Balance, in Dollars
380.00
562.49
832.63
1232.49
1824.39
2700.54
Which type of function best models the given data?
1) linear function with a negative rate of
3) exponential decay function
change
2) linear function with a positive rate of
4) exponential growth function
change
132 The owner of a small computer repair business has one employee, who is paid an hourly rate of $22. The owner
estimates his weekly profit using the function P(x) = 8600 − 22x . In this function, x represents the number of
1) computers repaired per week
3) customers served per week
2) hours worked per week
4) days worked per week
Algebra I CCSS Regents Exam Questions at Random Worksheet # 29
NAME:__________________________
www.jmap.org
133 Use the data below to write the regression equation ( y = ax + b ) for the raw test score based on the hours tutored.
Round all values to the nearest hundredth.
Tutor
Hours, x
1
2
3
4
5
6
7
Raw Test
Score
30
37
35
47
56
67
62
Residual
(Actual-Predicted)
1.3
1.9
−6.4
−0.7
2.0
6.6
−4.7
Equation: ___________________________
Create a residual plot on the axes below, using the residual scores in the table above.
Based on the residual plot, state whether the equation is a good fit for the data. Justify your answer.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 30
NAME:__________________________
www.jmap.org
134 A laboratory technician studied the population growth of a colony of bacteria. He recorded the number of bacteria
every other day, as shown in the partial table below.
t (time, in days)
f(t) (bacteria)
0
2
4
25 15,625 9,765,625
Which function would accurately model the technician's data?
3) f(t) = 25t
1) f(t) = 25 t
2)
f(t) = 25 t + 1
4)
135 Max purchased a box of green tea mints. The
nutrition label on the box stated that a serving of
three mints contains a total of 10 Calories. On the
axes below, graph the function, C, where C (x)
represents the number of Calories in x mints.
Write an equation that represents C (x). A full box
of mints contains 180 Calories. Use the equation to
determine the total number of mints in the box.
136 If f(1) = 3 and f(n) = −2f(n − 1) + 1, then f(5) =
1) −5
2) 11
3) 21
4) 43
f(t) = 25(t + 1)
137 Firing a piece of pottery in a kiln takes place at
different temperatures for different amounts of
time. The graph below shows the temperatures in a
kiln while firing a piece of pottery after the kiln is
preheated to 200ºF.
During which time interval did the temperature in
the kiln show the greatest average rate of change?
1) 0 to 1 hour
2) 1 hour to 1.5 hours
3) 2.5 hours to 5 hours
4) 5 hours to 8 hours
Algebra I CCSS Regents Exam Questions at Random Worksheet # 31
NAME:__________________________
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138 Graph the following function on the set of axes
below.

 |x |, − 3 ≤ x < 1
f(x) = 
 4,
1≤x≤8
140 The function V(t) = 1350(1.017) t represents the
value V(t), in dollars, of a comic book t years after
its purchase. The yearly rate of appreciation of the
comic book is
1) 17%
2) 1.7%
3) 1.017%
4) 0.017%
141 Ryker is given the graph of the function
1
y = x 2 − 4 . He wants to find the zeros of the
2
function, but is unable to read them exactly from
the graph.
139 Alicia has invented a new app for smart phones that
two companies are interested in purchasing for a
2-year contract. Company A is offering her
$10,000 for the first month and will increase the
amount each month by $5000. Company B is
offering $500 for the first month and will double
their payment each month from the previous
month. Monthly payments are made at the end of
each month. For which monthly payment will
company B’s payment first exceed company A’s
payment?
1) 6
2) 7
3) 8
4) 9
Find the zeros in simplest radical form.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 32
NAME:__________________________
www.jmap.org
142 Donna wants to make trail mix made up of
almonds, walnuts and raisins. She wants to mix
one part almonds, two parts walnuts, and three
parts raisins. Almonds cost $12 per pound, walnuts
cost $9 per pound, and raisins cost $5 per pound.
Donna has $15 to spend on the trail mix.
Determine how many pounds of trail mix she can
make. [Only an algebraic solution can receive full
credit.]
144 The value in dollars, v(x), of a certain car after x
years is represented by the equation
v(x) = 25,000(0.86) x . To the nearest dollar, how
much more is the car worth after 2 years than after
3 years?
1) 2589
2) 6510
3) 15,901
4) 18,490
143 Which quadratic function has the largest
maximum?
1) h(x) = (3 − x)(2 + x)
145 If the area of a rectangle is expressed as x 4 − 9y 2 ,
then the product of the length and the width of the
rectangle could be expressed as
1) (x − 3y)(x + 3y)
2)
3)
4)
2)
3)
k(x) = −5x 2 − 12x + 4
(x 2 − 3y)(x 2 + 3y)
(x 2 − 3y)(x 2 − 3y)
(x 4 + y)(x − 9y)
146 What is the correlation coefficient of the linear fit
of the data shown below, to the nearest hundredth?
4)
1)
2)
3)
4)
1.00
0.93
−0.93
−1.00
Algebra I CCSS Regents Exam Questions at Random Worksheet # 33
NAME:__________________________
www.jmap.org
147 The cost of a pack of chewing gum in a vending
machine is $0.75. The cost of a bottle of juice in
the same machine is $1.25. Julia has $22.00 to
spend on chewing gum and bottles of juice for her
team and she must buy seven packs of chewing
gum. If b represents the number of bottles of juice,
which inequality represents the maximum number
of bottles she can buy?
1) 0.75b + 1.25(7) ≥ 22
2) 0.75b + 1.25(7) ≤ 22
3) 0.75(7) + 1.25b ≥ 22
4) 0.75(7) + 1.25b ≤ 22
148 The two sets of data below represent the number of
runs scored by two different youth baseball teams
over the course of a season.
Team A: 4, 8, 5, 12, 3, 9, 5, 2
Team B: 5, 9, 11, 4, 6, 11, 2, 7
Which set of statements about the mean and
standard deviation is true?
1) mean A < mean B
standard deviation A > standard deviation B
2) mean A > mean B
standard deviation A < standard deviation B
3) mean A < mean B
standard deviation A < standard deviation B
4) mean A > mean B
standard deviation A > standard deviation B
149 The value of the x-intercept for the graph of
4x − 5y = 40 is
1) 10
4
2)
5
4
3) −
5
4) −8
150 To watch a varsity basketball game, spectators
must buy a ticket at the door. The cost of an adult
ticket is $3.00 and the cost of a student ticket is
$1.50. If the number of adult tickets sold is
represented by a and student tickets sold by s,
which expression represents the amount of money
collected at the door from the ticket sales?
1) 4.50as
2) 4.50(a + s)
3) (3.00a)(1.50s)
4) 3.00a + 1.50s
151 A driver leaves home for a business trip and drives
at a constant speed of 60 miles per hour for 2
hours. Her car gets a flat tire, and she spends 30
minutes changing the tire. She resumes driving and
drives at 30 miles per hour for the remaining one
hour until she reaches her destination. On the set
of axes below, draw a graph that models the
driver’s distance from home.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 34
NAME:__________________________
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152 The school newspaper surveyed the student body for an article about club membership. The table below shows
the number of students in each grade level who belong to one or more clubs.
9th
10th
11th
12th
1 Club
90
125
87
75
2 Clubs
33
12
22
27
3 or More Clubs
12
15
18
23
If there are 180 students in ninth grade, what percentage of the ninth grade students belong to more than one club?
153 The graph of f(x) is shown below.
154 Which representations are functions?
1)
2)
3)
4)
I and II
II and IV
III, only
IV, only
Which function could represent the graph of f(x) ?
1)
2)
3)
4)
f(x) = (x + 2)(x 2 + 3x − 4)
f(x) = (x − 2)(x 2 + 3x − 4)
f(x) = (x + 2)(x 2 + 3x + 4)
f(x) = (x − 2)(x 2 + 3x + 4)
155 In 2013, the United States Postal Service charged
$0.46 to mail a letter weighing up to 1 oz. and
$0.20 per ounce for each additional ounce. Which
function would determine the cost, in dollars, c(z),
of mailing a letter weighing z ounces where z is an
integer greater than 1?
1) c(z) = 0.46z + 0.20
2) c(z) = 0.20z + 0.46
3) c(z) = 0.46(z − 1) + 0.20
4) c(z) = 0.20(z − 1) + 0.46
Algebra I CCSS Regents Exam Questions at Random Worksheet # 35
NAME:__________________________
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156 A company is considering building a
manufacturing plant. They determine the weekly
production cost at site A to be A(x) = 3x 2 while the
production cost at site B is B(x) = 8x + 3, where x
represents the number of products, in hundreds,
and A(x) and B(x) are the production costs, in
hundreds of dollars. Graph the production cost
functions on the set of axes below and label them
site A and site B.
158 An astronaut drops a rock off the edge of a cliff on
the Moon. The distance, d(t), in meters, the rock
travels after t seconds can be modeled by the
function d(t) = 0.8t 2 . What is the average speed, in
meters per second, of the rock between 5 and 10
seconds after it was dropped?
1) 12
2) 20
3) 60
4) 80
159 When directed to solve a quadratic equation by
completing the square, Sam arrived at the equation

2
 x − 5  = 13 . Which equation could have been

2 
4

the original equation given to Sam?
1) x 2 + 5x + 7 = 0
2) x 2 + 5x + 3 = 0
3) x 2 − 5x + 7 = 0
4) x 2 − 5x + 3 = 0
State the positive value(s) of x for which the
production costs at the two sites are equal. Explain
how you determined your answer. If the company
plans on manufacturing 200 products per week,
which site should they use? Justify your answer.
157 The graph of a linear equation contains the points
(3,11) and (−2,1). Which point also lies on the
graph?
1) (2,1)
2) (2,4)
3) (2,6)
4) (2,9)
160 a) Given the function f(x) = −x 2 + 8x + 9 , state
whether the vertex represents a maximum or
minimum point for the function. Explain your
answer.
b) Rewrite f(x) in vertex form by completing the
square.
161 A toy rocket is launched from the ground straight
upward. The height of the rocket above the
ground, in feet, is given by the equation
h(t) = −16t 2 + 64t , where t is the time in seconds.
Determine the domain for this function in the given
context. Explain your reasoning.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 36
NAME:__________________________
www.jmap.org
162 An application developer released a new app to be downloaded. The table below gives the number of downloads
for the first four weeks after the launch of the app.
Number of Weeks
Number of Downloads
1
2
3
4
120 180 270 405
Write an exponential equation that models these data. Use this model to predict how many downloads the
developer would expect in the 26th week if this trend continues. Round your answer to the nearest download.
Would it be reasonable to use this model to predict the number of downloads past one year? Explain your
reasoning.
163 On the set of axes below, graph the inequality
2x + y > 1.
165 Ms. Fox asked her class "Is the sum of 4.2 and 2
rational or irrational?" Patrick answered that the
sum would be irrational. State whether Patrick is
correct or incorrect. Justify your reasoning.
166 The graph of an inequality is shown below.
164 Which value of x satisfies the equation
9 
7 
x+
= 20?


28 
3
1)
2)
3)
4)
8.25
8.89
19.25
44.92
a) Write the inequality represented by the graph.
b) On the same set of axes, graph the inequality
x + 2y < 4.
c) The two inequalities graphed on the set of axes
form a system. Oscar thinks that the point (2,1) is
in the solution set for this system of inequalities.
Determine and state whether you agree with Oscar.
Explain your reasoning.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 37
NAME:__________________________
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167 Edith babysits for x hours a week after school at a
job that pays $4 an hour. She has accepted a job
that pays $8 an hour as a library assistant working y
hours a week. She will work both jobs. She is able
to work no more than 15 hours a week, due to
school commitments. Edith wants to earn at least
$80 a week, working a combination of both jobs.
Write a system of inequalities that can be used to
represent the situation. Graph these inequalities on
the set of axes below.
169 A population that initially has 20 birds
approximately doubles every 10 years. Which
graph represents this population growth?
1)
2)
Determine and state one combination of hours that
will allow Edith to earn at least $80 per week while
working no more than 15 hours.
168 What are the zeros of the function
f(x) = x 2 − 13x − 30?
1) −10 and 3
2) 10 and −3
3) −15 and 2
4) 15 and −2
3)
4)
170 If the difference (3x 2 − 2x + 5) − (x 2 + 3x − 2) is
1
multiplied by x 2 , what is the result, written in
2
standard form?
Algebra I CCSS Regents Exam Questions at Random Worksheet # 38
NAME:__________________________
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171 Which equation(s) represent the graph below?
y = (x + 2)(x 2 − 4x − 12)
I
II
III
1)
2)
3)
4)
y = (x − 3)(x 2 + x − 2)
y = (x − 1)(x 2 − 5x − 6)
I, only
II, only
I and II
II and III
172 Officials in a town use a function, C, to analyze
traffic patterns. C(n) represents the rate of traffic
through an intersection where n is the number of
observed vehicles in a specified time interval.
What would be the most appropriate domain for the
function?
1) {. . .− 2,−1,0,1,2,3,. . . }
2) {−2,−1,0,1,2,3}
1
1
1
3) {0, ,1,1 ,2,2 }
2
2
2
4) {0,1,2,3,. . . }
173 An on-line electronics store must sell at least $2500
worth of printers and computers per day. Each
printer costs $50 and each computer costs $500.
The store can ship a maximum of 15 items per day.
On the set of axes below, graph a system of
inequalities that models these constraints.
Determine a combination of printers and computers
that would allow the electronics store to meet all of
the constraints. Explain how you obtained your
answer.
174 Which table represents a function?
1)
2)
3)
4)
Algebra I CCSS Regents Exam Questions at Random Worksheet # 39
NAME:__________________________
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175 Emma recently purchased a new car. She decided to keep track of how many gallons of gas she used on five of
her business trips. The results are shown in the table below.
Miles Driven
150
200
400
600
1000
Number of
Gallons Used
7
10
19
29
51
Write the linear regression equation for these data where miles driven is the independent variable. (Round all
values to the nearest hundredth.)
176 The table below shows the attendance at a museum in select years from 2007 to 2013.
Attendance at Museum
2007 2008 2009 2011 2013
Year
8.3
8.5
8.5
8.8
9.3
Attendance (millions)
State the linear regression equation represented by the data table when x = 0 is used to represent the year 2007 and
y is used to represent the attendance. Round all values to the nearest hundredth. State the correlation coefficient
to the nearest hundredth and determine whether the data suggest a strong or weak association.
177 A cell phone company charges $60.00 a month for
up to 1 gigabyte of data. The cost of additional
data is $0.05 per megabyte. If d represents the
number of additional megabytes used and c
represents the total charges at the end of the month,
which linear equation can be used to determine a
user's monthly bill?
1) c = 60 − 0.05d
2) c = 60.05d
3) c = 60d − 0.05
4) c = 60 + 0.05d
178 Miriam and Jessica are growing bacteria in a
laboratory. Miriam uses the growth function
f(t) = n 2t while Jessica uses the function
g(t) = n 4t , where n represents the initial number of
bacteria and t is the time, in hours. If Miriam starts
with 16 bacteria, how many bacteria should Jessica
start with to achieve the same growth over time?
1) 32
2) 16
3) 8
4) 4
Algebra I CCSS Regents Exam Questions at Random Worksheet # 40
NAME:__________________________
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179 Let f be the function represented by the graph
below.
1
Let g be a function such that g(x) = − x 2 + 4x + 3.
2
Determine which function has the larger maximum
value. Justify your answer.
181 Corinne is planning a beach vacation in July and is
analyzing the daily high temperatures for her
potential destination. She would like to choose a
destination with a high median temperature and a
small interquartile range. She constructed box
plots shown in the diagram below.
Which destination has a median temperature above
80 degrees and the smallest interquartile range?
1) Ocean Beach
2) Whispering Palms
3) Serene Shores
4) Pelican Beach
182 Which expression is equivalent to x 4 − 12x 2 + 36 ?
1) (x 2 − 6)(x 2 − 6)
180 During the 2010 season, football player McGee’s
earnings, m, were 0.005 million dollars more than
those of his teammate Fitzpatrick’s earnings, f.
The two players earned a total of 3.95 million
dollars. Which system of equations could be used
to determine the amount each player earned, in
millions of dollars?
1) m + f = 3.95
2)
m + 0.005 = f
m − 3.95 = f
3)
f + 0.005 = m
f − 3.95 = m
4)
m + 0.005 = f
m + f = 3.95
f + 0.005 = m
2)
3)
4)
(x 2 + 6)(x 2 + 6)
(6 − x 2 )(6 + x 2 )
(x 2 + 6)(x 2 − 6)
183 Last week, a candle store received $355.60 for
selling 20 candles. Small candles sell for $10.98
and large candles sell for $27.98. How many large
candles did the store sell?
1) 6
2) 8
3) 10
4) 12
Algebra I CCSS Regents Exam Questions at Random Worksheet # 41
NAME:__________________________
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184 The table below shows the annual salaries for the 24 members of a professional sports team in terms of millions of
dollars.
0.5
1.0
1.4
4.2
0.5
1.0
1.8
4.6
0.6
1.1
2.5
5.1
0.7
1.25
3.7
6
0.75
1.3
3.8
6.3
0.8
1.4
4
7.2
The team signs an additional player to a contract worth 10 million dollars per year. Which statement about the
median and mean is true?
1) Both will increase.
3) Only the mean will increase.
2) Only the median will increase.
4) Neither will change.
185 The table below represents the residuals for a line of best fit.
x
Residual
2
2
3
1
3
−1
4
6
7
8
−2 −3 −2 −1
9
2
9
0
Plot these residuals on the set of axes below.
Using the plot, assess the fit of the line for these residuals and justify your answer.
10
3
Algebra I CCSS Regents Exam Questions at Random Worksheet # 42
NAME:__________________________
www.jmap.org
186 A pattern of blocks is shown below.
If the pattern of blocks continues, which formula(s) could be used to determine the number of blocks in the nth
term?
I
an = n + 4
1)
2)
I and II
I and III
II
a1 = 2
an = an − 1 + 4
3)
4)
187 A company that manufactures radios first pays a
start-up cost, and then spends a certain amount of
money to manufacture each radio. If the cost of
manufacturing r radios is given by the function
c(r) = 5.25r + 125, then the value 5.25 best
represents
1) the start-up cost
2) the profit earned from the sale of one radio
3) the amount spent to manufacture each radio
4) the average number of radios manufactured
188 What are the solutions to the equation
x 2 − 8x = 24 ?
1) x = 4 ± 2 10
2)
3)
4)
x = −4 ± 2 10
x = 4±2 2
x = −4 ± 2 2
III
a n = 4n − 2
II and III
III, only
189 The function h(t) = −16t 2 + 144 represents the
height, h(t), in feet, of an object from the ground at
t seconds after it is dropped. A realistic domain for
this function is
1) −3 ≤ t ≤ 3
2) 0 ≤ t ≤ 3
3) 0 ≤ h(t) ≤ 144
4) all real numbers
190 A student was given the equation x 2 + 6x − 13 = 0
to solve by completing the square. The first step
that was written is shown below.
x 2 + 6x = 13
The next step in the student’s process was
x 2 + 6x + c = 13 + c . State the value of c that
creates a perfect square trinomial. Explain how the
value of c is determined.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 43
NAME:__________________________
www.jmap.org
191 A typical cell phone plan has a fixed base fee that
includes a certain amount of data and an overage
charge for data use beyond the plan. A cell phone
plan charges a base fee of $62 and an overage
charge of $30 per gigabyte of data that exceed 2
gigabytes. If C represents the cost and g represents
the total number of gigabytes of data, which
equation could represent this plan when more than
2 gigabytes are used?
1) C = 30 + 62(2 − g)
2) C = 30 + 62(g − 2)
3) C = 62 + 30(2 − g)
4) C = 62 + 30(g − 2)
192 If 4x 2 − 100 = 0, the roots of the equation are
1) −25 and 25
2) −25, only
3) −5 and 5
4) −5, only
193 Which statement is not always true?
1) The sum of two rational numbers is rational.
2) The product of two irrational numbers is
rational.
3) The sum of a rational number and an irrational
number is irrational.
4) The product of a nonzero rational number and
an irrational number is irrational.
194 The third term in an arithmetic sequence is 10 and
the fifth term is 26. If the first term is a 1 , which is
an equation for the nth term of this sequence?
1) a n = 8n + 10
2) a n = 8n − 14
3) a n = 16n + 10
4) a n = 16n − 38
195 A ball is thrown into the air from the edge of a
48-foot-high cliff so that it eventually lands on the
ground. The graph below shows the height, y, of
the ball from the ground after x seconds.
For which interval is the ball's height always
decreasing?
1) 0 ≤ x ≤ 2.5
2) 0 < x < 5.5
3) 2.5 < x < 5.5
4) x ≥ 2
1
x + 9, which statement is always true?
3
f(x) < 0
f(x) > 0
If x < 0 , then f(x) < 0.
If x > 0 , then f(x) > 0.
196 If f(x) =
1)
2)
3)
4)
197 Dylan invested $600 in a savings account at a 1.6%
annual interest rate. He made no deposits or
withdrawals on the account for 2 years. The
interest was compounded annually. Find, to the
nearest cent, the balance in the account after 2
years.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 44
NAME:__________________________
www.jmap.org
198 Joey enlarged a 3-inch by 5-inch photograph on a copy machine. He enlarged it four times. The table below
shows the area of the photograph after each enlargement.
Enlargement
Area (square inches)
0
15
1
18.8
2
23.4
3
29.3
4
36.6
What is the average rate of change of the area from the original photograph to the fourth enlargement, to the
nearest tenth?
1) 4.3
3) 5.4
2) 4.5
4) 6.0
199 Let f(x) = −2x 2 and g(x) = 2x − 4 . On the set of
axes below, draw the graphs of y = f(x) and
y = g(x) .
Using this graph, determine and state all values of
x for which f(x) = g(x) .
200 Subtract 5x 2 + 2x − 11 from 3x 2 + 8x − 7. Express
the result as a trinomial.
201 An animal shelter spends $2.35 per day to care for
each cat and $5.50 per day to care for each dog.
Pat noticed that the shelter spent $89.50 caring for
cats and dogs on Wednesday. Write an equation to
represent the possible numbers of cats and dogs
that could have been at the shelter on Wednesday.
Pat said that there might have been 8 cats and 14
dogs at the shelter on Wednesday. Are Pat’s
numbers possible? Use your equation to justify
your answer. Later, Pat found a record showing
that there were a total of 22 cats and dogs at the
shelter on Wednesday. How many cats were at the
shelter on Wednesday?
202 For which value of P and W is P + W a rational
number?
1
1
and W =
1) P =
3
6
1
1
2) P =
and W =
4
9
1
1
3) P =
and W =
6
10
1
1
4) P =
and W =
25
2
Algebra I CCSS Regents Exam Questions at Random Worksheet # 45
NAME:__________________________
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203 Given the following quadratic functions:
x
n(x)
−3
−7
g(x) = −x 2 − x + 6
and
−2 −1 0 1 2
0
5 8 9 8
Which statement about these functions is true?
1) Over the interval −1 ≤ x ≤ 1, the average 3)
rate of change for n(x) is less than that
for g(x) .
2) The y-intercept of g(x) is greater than the 4)
y-intercept for n(x).
204 Which ordered pair is not in the solution set of
1
y > − x + 5 and y ≤ 3x − 2?
2
1) (5,3)
2) (4,3)
3) (3,4)
4) (4,4)
205 Keith determines the zeros of the function f(x) to
be −6 and 5. What could be Keith's function?
1) f(x) = (x + 5)(x + 6)
2) f(x) = (x + 5)(x − 6)
3) f(x) = (x − 5)(x + 6)
4) f(x) = (x − 5)(x − 6)
206 If A = 3x 2 + 5x − 6 and B = −2x 2 − 6x + 7, then
A − B equals
1) −5x 2 − 11x + 13
2) 5x 2 + 11x − 13
3) −5x 2 − x + 1
4) 5x 2 − x + 1
3
5
4
0
5
−7
The function g(x) has a greater
maximum value than n(x).
The sum of the roots of n(x) = 0 is
greater than the sum of the roots of
g(x) = 0 .
207 The formula for the volume of a cone is
1
V = π r 2 h . The radius, r, of the cone may be
3
expressed as
1)
3V
πh
2)
V
3π h
3)
3
4)
1
3
V
πh
V
πh
208 What is the value of x in the equation
x−2 1 5
+ = ?
6 6
3
1) 4
2) 6
3) 8
4) 11
Algebra I CCSS Regents Exam Questions at Random Worksheet # 46
NAME:__________________________
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Algebra I Common Core State Standards Regents at Random Worksheets
209 An online company lets you download songs for
$0.99 each after you have paid a $5 membership
fee. Which domain would be most appropriate to
calculate the cost to download songs?
1) rational numbers greater than zero
2) whole numbers greater than or equal to one
3) integers less than or equal to zero
4) whole numbers less than or equal to one
210 The growth of a certain organism can be modeled
by C(t) = 10(1.029) 24t , where C(t) is the total
number of cells after t hours. Which function is
approximately equivalent to C(t)?
1)
2)
3)
4)
C(t) = 240(.083) 24t
C(t) = 10(.083) t
C(t) = 10(1.986) t
C(t) = 240(1.986)
t
24
211 The dot plot shown below represents the number of
pets owned by students in a class.
212 Given the following expressions:
5 3

 

III.  5  ⋅  5 
I. − +
8 5

 

1


II. + 2
IV. 3 ⋅  49 
2


Which expression(s) result in an irrational number?
1) II, only
2) III, only
3) I, III, IV
4) II, III, IV
213 What is the largest integer, x, for which the value
of f(x) = 5x 4 + 30x 2 + 9 will be greater than the
value of g(x) = 3 x ?
1) 7
2) 8
3) 9
4) 10
214 The range of the function f(x) = x 2 + 2x − 8 is all
real numbers
1) less than or equal to −9
2) greater than or equal to −9
3) less than or equal to −1
4) greater than or equal to −1
215 The value, v(t), of a car depreciates according to
Which statement about the data is not true?
1) The median is 3.
2) The interquartile range is 2.
3) The mean is 3.
4) The data contain no outliers.
the function v(t) = P(.85) t , where P is the purchase
price of the car and t is the time, in years, since the
car was purchased. State the percent that the value
of the car decreases by each year. Justify your
answer.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 47
NAME:__________________________
www.jmap.org
216 A statistics class surveyed some students during one lunch period to obtain opinions about television programming
preferences. The results of the survey are summarized in the table below.
Programming Preferences
Comedy Drama
70
35
Male
48
42
Female
Based on the sample, predict how many of the school's 351 males would prefer comedy. Justify your answer.
217 Which statement is true about the quadratic functions g(x) , shown in the table below, and f(x) = (x − 3) 2 + 2?
x
0
1
2
3
4
5
6
1)
2)
They have the same vertex.
They have the same zeros.
3)
4)
g(x)
4
−1
−4
−5
−4
−1
4
They have the same axis of symmetry.
They intersect at two points.
218 The function, t(x), is shown in the table below.
x t(x)
−3 10
−1 7.5
1
5
3 2.5
5
0
Determine whether t(x) is linear or exponential. Explain your answer.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 48
NAME:__________________________
www.jmap.org
219 A sequence of blocks is shown in the diagram
below.
This sequence can be defined by the recursive
function a 1 = 1 and a n = a n − 1 + n. Assuming the
pattern continues, how many blocks will there be
when n = 7?
1) 13
2) 21
3) 28
4) 36
222 Zeke and six of his friends are going to a baseball
game. Their combined money totals $28.50. At
the game, hot dogs cost $1.25 each, hamburgers
cost $2.50 each, and sodas cost $0.50 each. Each
person buys one soda. They spend all $28.50 on
food and soda. Write an equation that can
determine the number of hot dogs, x, and
hamburgers, y, Zeke and his friends can buy.
Graph your equation on the grid below.
220 Mario's $15,000 car depreciates in value at a rate of
19% per year. The value, V, after t years can be
modeled by the function V = 15,000(0.81) t . Which
function is equivalent to the original function?
1) V = 15,000(0.9) 9t
2)
3)
4)
V = 15,000(0.9) 2t
V = 15,000(0.9)
V = 15,000(0.9)
t
9
t
2
221 A typical marathon is 26.2 miles. Allan averages
12 kilometers per hour when running in marathons.
Determine how long it would take Allan to
complete a marathon, to the nearest tenth of an
hour. Justify your answer.
Determine how many different combinations,
including those combinations containing zero, of
hot dogs and hamburgers Zeke and his friends can
buy, spending all $28.50. Explain your answer.
223 Fred's teacher gave the class the quadratic function
f(x) = 4x 2 + 16x + 9.
a) State two different methods Fred could use to
solve the equation f(x) = 0 .
b) Using one of the methods stated in part a, solve
f(x) = 0 for x, to the nearest tenth.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 49
NAME:__________________________
www.jmap.org
224 A student invests $500 for 3 years in a savings
account that earns 4% interest per year. No further
deposits or withdrawals are made during this time.
Which statement does not yield the correct balance
in the account at the end of 3 years?
1) 500(1.04) 3
2)
3)
4)
228 The scatterplot below compares the number of bags
of popcorn and the number of sodas sold at each
performance of the circus over one week.
500(1 −.04) 3
500(1 +.04)(1 +.04)(1 +.04)
500 + 500(.04) + 520(.04) + 540.8(.04)
225 Which polynomial function has zeros at -3, 0, and
4?
1) f(x) = (x + 3)(x 2 + 4)
2)
3)
4)
f(x) = (x 2 − 3)(x − 4)
f(x) = x(x + 3)(x − 4)
f(x) = x(x − 3)(x + 4)
226 Which equation and ordered pair represent the
correct vertex form and vertex for
j(x) = x 2 − 12x + 7?
1)
2)
3)
4)
j(x) = (x − 6) 2 + 43,
j(x) = (x − 6) 2 + 43,
j(x) = (x − 6) 2 − 29,
j(x) = (x − 6) 2 − 29,
(6,43)
(−6,43)
(6,−29)
(−6,−29)
227 Sara was asked to solve this word problem: "The
product of two consecutive integers is 156. What
are the integers?" What type of equation should
she create to solve this problem?
1) linear
2) quadratic
3) exponential
4) absolute value
Which conclusion can be drawn from the
scatterplot?
1) There is a negative correlation between
popcorn sales and soda sales.
2) There is a positive correlation between popcorn
sales and soda sales.
3) There is no correlation between popcorn sales
and soda sales.
4) Buying popcorn causes people to buy soda.
229 When the function f(x) = x 2 is multiplied by the
value a, where a > 1, the graph of the new function,
g(x) = ax 2
1) opens upward and is wider
2) opens upward and is narrower
3) opens downward and is wider
4) opens downward and is narrower
Algebra I CCSS Regents Exam Questions at Random Worksheet # 50
NAME:__________________________
www.jmap.org
230 A parking garage charges a base rate of $3.50 for up to 2 hours, and an hourly rate for each additional hour. The
sign below gives the prices for up to 5 hours of parking.
Parking Rates
2 hours
$3.50
3 hours
$9.00
4 hours $14.50
5 hours $20.00
Which linear equation can be used to find x, the additional hourly parking rate?
1) 9.00 + 3x = 20.00
3) 2x + 3.50 = 14.50
2) 9.00 + 3.50x = 20.00
4) 2x + 9.00 = 14.50
231 The table below shows the cost of mailing a postcard in different years. During which time interval did the cost
increase at the greatest average rate?
1898 1971 1985 2006 2012
Year
1
6
14
24
35
Cost (¢)
1)
2)
1898-1971
1971-1985
3)
4)
232 The function f(x) = 3x 2 + 12x + 11 can be written
in vertex form as
1) f(x) = (3x + 6) 2 − 25
2)
3)
4)
f(x) = 3(x + 6) 2 − 25
f(x) = 3(x + 2) 2 − 1
f(x) = 3(x + 2) 2 + 7
233 Is the sum of 3 2 and 4 2 rational or irrational?
Explain your answer.
1985-2006
2006-2012
234 Solve the equation below for x in terms of a.
4(ax + 3) − 3ax = 25 + 3a
235 A plumber has a set fee for a house call and
charges by the hour for repairs. The total cost of
her services can be modeled by c(t) = 125t + 95.
Which statements about this function are true?
I. A house call fee costs $95.
II. The plumber charges $125 per hour.
III. The number of hours the job takes is
represented by t.
1) I and II, only
2) I and III, only
3) II and III, only
4) I, II, and III
Algebra I CCSS Regents Exam Questions at Random Worksheet # 51
NAME:__________________________
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236 If f(x) = x 2 and g(x) = x , determine the value(s) of
x that satisfy the equation f(x) = g(x) .
239 The expression x 4 − 16 is equivalent to
1) (x 2 + 8)(x 2 − 8)
2)
3)
237 In the diagram below, f(x) = x 3 + 2x 2 is graphed.
Also graphed is g(x) , the result of a translation of
f(x) .
4)
(x 2 − 8)(x 2 − 8)
(x 2 + 4)(x 2 − 4)
(x 2 − 4)(x 2 − 4)
240 In 2014, the cost to mail a letter was 49¢ for up to
one ounce. Every additional ounce cost 21¢.
Which recursive function could be used to
determine the cost of a 3-ounce letter, in cents?
1) a 1 = 49; a n = a n − 1 + 21
2) a 1 = 0; a n = 49a n − 1 + 21
3) a 1 = 21; a n = a n − 1 + 49
4) a 1 = 0; a n = 21a n − 1 + 49
241 Which inequality is represented by the graph
below?
Determine an equation of g(x) . Explain your
reasoning.
238 A store sells self-serve frozen yogurt sundaes. The
function C(w) represents the cost, in dollars, of a
sundae weighing w ounces. An appropriate domain
for the function would be
1) integers
2) rational numbers
3) nonnegative integers
4) nonnegative rational numbers
1)
2)
3)
4)
y ≤ 2x − 3
y ≥ 2x − 3
y ≤ −3x + 2
y ≥ −3x + 2
Algebra I CCSS Regents Exam Questions at Random Worksheet # 52
NAME:__________________________
www.jmap.org
242 The cost of belonging to a gym can be modeled by
C(m) = 50m + 79.50, where C(m) is the total cost
for m months of membership. State the meaning of
the slope and y-intercept of this function with
respect to the costs associated with the gym
membership.
245 What are the solutions to the equation
x 2 − 8x = 10 ?
1) 4 ± 10
2)
3)
4)
4 ± 26
−4 ± 10
−4 ± 26
243 The graph representing a function is shown below.
246 A car leaves Albany, NY, and travels west toward
Buffalo, NY. The equation D = 280 − 59t can be
used to represent the distance, D, from Buffalo
after t hours. In this equation, the 59 represents the
1) car's distance from Albany
2) speed of the car
3) distance between Buffalo and Albany
4) number of hours driving
Which function has a minimum that is less than the
one shown in the graph?
1) y = x 2 − 6x + 7
2) y = |x + 3 | − 6
3)
4)
y = x 2 − 2x − 10
y = |x − 8 | + 2
244 The zeros of the function f(x) = x 2 − 5x − 6 are
1) −1 and 6
2) 1 and −6
3) 2 and −3
4) −2 and 3
247 The 2014 winner of the Boston Marathon runs as
many as 120 miles per week. During the last few
weeks of his training for an event, his mileage can
be modeled by M(w) = 120(.90) w − 1, where w
represents the number of weeks since training
began. Which statement is true about the model
M(w)?
1) The number of miles he runs will increase by
90% each week.
2) The number of miles he runs will be 10% of
the previous week.
3) M(w) represents the total mileage run in a
given week.
4) w represents the number of weeks left until his
marathon.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 53
NAME:__________________________
www.jmap.org
248 The table below shows the temperature, T(m), of a cup of hot chocolate that is allowed to chill over several
minutes, m.
Time, m (minutes)
Temperature, T(m)
(ºF)
0
150
2
4
108 78
6
56
8
41
Which expression best fits the data for T(m)?
1)
2)
150(0.85) m
150(1.15) m
3)
4)
150(0.85) m − 1
150(1.15) m − 1
249 A family is traveling from their home to a vacation resort hotel. The table below shows their distance from home
as a function of time.
Time (hrs)
Distance (mi)
0
0
2
5
7
140 375 480
Determine the average rate of change between hour 2 and hour 7, including units.
250 Which expression is equivalent to 16x 2 − 36?
1) 4(2x − 3)(2x − 3)
2) 4(2x + 3)(2x − 3)
3) (4x − 6)(4x − 6)
4) (4x + 6)(4x + 6)
251 Which situation does not describe a causal
relationship?
1) The higher the volume on a radio, the louder
the sound will be.
2) The faster a student types a research paper, the
more pages the paper will have.
3) The shorter the distance driven, the less
gasoline that will be used.
4) The slower the pace of a runner, the longer it
will take the runner to finish the race.
252 A drama club is selling tickets to the spring
musical. The auditorium holds 200 people.
Tickets cost $12 at the door and $8.50 if purchased
in advance. The drama club has a goal of selling at
least $1000 worth of tickets to Saturday's show.
Write a system of inequalities that can be used to
model this scenario. If 50 tickets are sold in
advance, what is the minimum number of tickets
that must be sold at the door so that the club meets
its goal? Justify your answer.
253 As x increases beyond 25, which function will have
the largest value?
1) f(x) = 1.5x
2) g(x) = 1.5x + 3
3)
4)
h(x) = 1.5x 2
k(x) = 1.5x 3 + 1.5x 2
Algebra I CCSS Regents Exam Questions at Random Worksheet # 54
NAME:__________________________
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254 The Reel Good Cinema is conducting a mathematical study. In its theater, there are 200 seats. Adult tickets cost
$12.50 and child tickets cost $6.25. The cinema's goal is to sell at least $1500 worth of tickets for the theater.
Write a system of linear inequalities that can be used to find the possible combinations of adult tickets, x, and
child tickets, y, that would satisfy the cinema's goal. Graph the solution to this system of inequalities on the set of
axes below. Label the solution with an S. Marta claims that selling 30 adult tickets and 80 child tickets will result
in meeting the cinema's goal. Explain whether she is correct or incorrect, based on the graph drawn.
255 Write the expression 5x + 4x 2 (2x + 7) − 6x 2 − 9x as
a polynomial in standard form.
256 Amy solved the equation 2x 2 + 5x − 42 = 0. She
7
stated that the solutions to the equation were and
2
−6. Do you agree with Amy's solutions? Explain
why or why not.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 55
NAME:__________________________
www.jmap.org
257 Which system of equations does not have the same
solution as the system below?
4x + 3y = 10
1)
−6x − 5y = −16
−12x − 9y = −30
2)
12x + 10y = 32
20x + 15y = 50
3)
−18x − 15y = −48
24x + 18y = 60
4)
−24x − 20y = −64
40x + 30y = 100
259 The formula for the sum of the degree measures of
the interior angles of a polygon is S = 180(n − 2).
Solve for n, the number of sides of the polygon, in
terms of S.
260 Shawn incorrectly graphed the inequality
−x − 2y ≥ 8 as shown below.
36x + 30y = −96
258 Graph the inequality y + 4 < −2(x − 4) on the set of
axes below.
Explain Shawn's mistake. Graph the inequality
correctly on the set of axes below.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 56
NAME:__________________________
www.jmap.org
261 An expression of the fifth degree is written with a
leading coefficient of seven and a constant of six.
Which expression is correctly written for these
conditions?
1) 6x 5 + x 4 + 7
2) 7x 6 − 6x 4 + 5
3) 6x 7 − x 5 + 5
4) 7x 5 + 2x 2 + 6
262 A mapping is shown in the diagram below.
264 The Celluloid Cinema sold 150 tickets to a movie.
Some of these were child tickets and the rest were
adult tickets. A child ticket cost $7.75 and an adult
ticket cost $10.25. If the cinema sold $1470 worth
of tickets, which system of equations could be used
to determine how many adult tickets, a, and how
many child tickets, c, were sold?
1) a + c = 150
2)
10.25a + 7.75c = 1470
a + c = 1470
3)
10.25a + 7.75c = 150
a + c = 150
4)
7.75a + 10.25c = 1470
a + c = 1470
7.75a + 10.25c = 150
This mapping is
1) a function, because Feb has two outputs, 28
and 29
2) a function, because two inputs, Jan and Mar,
result in the output 31
3) not a function, because Feb has two outputs, 28
and 29
4) not a function, because two inputs, Jan and
Mar, result in the output 31
265 A construction worker needs to move 120 ft3 of dirt
by using a wheelbarrow. One wheelbarrow load
holds 8 ft3 of dirt and each load takes him 10
minutes to complete. One correct way to figure out
the number of hours he would need to complete
this job is
120 ft 3 10 min 60 min 1 load
1)
•
•
•
1 load
1 hr
1
8 ft 3
2)
3)
263 Kendal bought x boxes of cookies to bring to a
party. Each box contains 12 cookies. She decides
to keep two boxes for herself. She brings 60
cookies to the party. Which equation can be used
to find the number of boxes, x, Kendal bought?
1) 2x − 12 = 60
2) 12x − 2 = 60
3) 12x − 24 = 60
4) 24 − 12x = 60
4)
8 ft 3
1
120 ft 3 60 min
•
•
•
1 hr
1
10 min 1 load
3
1 load
8 ft 3
1 hr
120 ft
•
•
•
10 min 1 load 60 min
1
1 hr
120 ft 3 1 load 10 min
•
•
•
1 load 60 min
1
8 ft 3
Algebra I CCSS Regents Exam Questions at Random Worksheet # 57
NAME:__________________________
www.jmap.org
266 Solve the following system of inequalities
graphically on the grid below and label the solution
S.
3x + 4y > 20
268 The sum of two numbers, x and y, is more than 8.
When you double x and add it to y, the sum is less
than 14. Graph the inequalities that represent this
scenario on the set of axes below.
x < 3y − 18
Is the point (3,7) in the solution set? Explain your
answer.
267 A part of Jennifer's work to solve the equation
2(6x 2 − 3) = 11x 2 − x is shown below.
Given: 2(6x 2 − 3) = 11x 2 − x
Step 1: 12x 2 − 6 = 11x 2 − x
Which property justifies her first step?
1) identity property of multiplication
2) multiplication property of equality
3) commutative property of multiplication
4) distributive property of multiplication over
subtraction
Kai says that the point (6,2) is a solution to this
system. Determine if he is correct and explain your
reasoning.
269 A computer application generates a sequence of
musical notes using the function f(n) = 6(16) n ,
where n is the number of the note in the sequence
and f(n) is the note frequency in hertz. Which
function will generate the same note sequence as
f(n) ?
1)
2)
3)
4)
g(n) = 12(2) 4n
h(n) = 6(2) 4n
p(n) = 12(4) 2n
k(n) = 6(8) 2n
Algebra I CCSS Regents Exam Questions at Random Worksheet # 58
NAME:__________________________
www.jmap.org
270 Samantha purchases a package of sugar cookies.
The nutrition label states that each serving size of 3
cookies contains 160 Calories. Samantha creates
the graph below showing the number of cookies
eaten and the number of Calories consumed.
Explain why it is appropriate for Samantha to draw
a line through the points on the graph.
271 Which statistic can not be determined from a box
plot representing the scores on a math test in Mrs.
DeRidder's algebra class?
1) the lowest score
2) the median score
3) the highest score
4) the score that occurs most frequently
272 In the function f(x) = (x − 2) 2 + 4, the minimum
value occurs when x is
1) −2
2) 2
3) −4
4) 4
273 The graph below was created by an employee at a
gas station.
Which statement can be justified by using the
graph?
1) If 10 gallons of gas was purchased, $35 was
paid.
2) For every gallon of gas purchased, $3.75 was
paid.
3) For every 2 gallons of gas purchased, $5.00
was paid.
4) If zero gallons of gas were purchased, zero
miles were driven.
274 Konnor wants to burn 250 Calories while
exercising for 45 minutes at the gym. On the
treadmill, he can burn 6 Cal/min. On the stationary
bike, he can burn 5 Cal/min. If t represents the
number of minutes on the treadmill and b
represents the number of minutes on the stationary
bike, which expression represents the number of
Calories that Konnor can burn on the stationary
bike?
1) b
2) 5b
3) 45 − b
4) 250 − 5b
Algebra I CCSS Regents Exam Questions at Random Worksheet # 59
NAME:__________________________
www.jmap.org
275 A radio station did a survey to determine what kind of music to play by taking a sample of middle school, high
school, and college students. They were asked which of three different types of music they prefer on the radio:
hip-hop, alternative, or classic rock. The results are summarized in the table below.
Middle School
High School
College
Hip-Hop
28
22
16
Alternative
18
22
20
Classic Rock
4
6
14
What percentage of college students prefer classic rock?
1) 14%
3) 33%
2) 28%
4) 58%
276 Wenona sketched the polynomial P(x) as shown on
the axes below.
278 The height, H, in feet, of an object dropped from
the top of a building after t seconds is given by
H(t) = −16t 2 + 144. How many feet did the object
fall between one and two seconds after it was
dropped? Determine, algebraically, how many
seconds it will take for the object to reach the
ground.
279 A system of equations is given below.
x + 2y = 5
2x + y = 4
Which system of equations does not have the same
solution?
1) 3x + 6y = 15
2)
2x + y = 4
4x + 8y = 20
3)
2x + y = 4
x + 2y = 5
4)
6x + 3y = 12
x + 2y = 5
Which equation could represent P(x) ?
1)
2)
3)
4)
P(x) = (x + 1)(x − 2)
P(x) = (x − 1)(x + 2) 2
P(x) = (x + 1)(x − 2)
P(x) = (x − 1)(x + 2)
2
4x + 2y = 12
277 Solve the equation for y: (y − 3) = 4y − 12
2
Algebra I CCSS Regents Exam Questions at Random Worksheet # 60
NAME:__________________________
www.jmap.org
280 Which function is shown in the table below?
x
f(x)
1
−2
9
1
−1
3
0
1
1
3
2
9
3 27
1)
f(x) = 3x
3)
2)
f(x) = x + 3
4)
281 The graph below shows two functions, f(x) and
g(x) . State all the values of x for which
f(x) = g(x) .
f(x) = −x 3
f(x) = 3 x
283 Which point is a solution to the system below?
2y < −12x + 4
y < −6x + 4
1)
2)
282 What is the domain of the relation shown below?
{(4,2),(1,1),(0,0),(1,−1),(4,−2)}
1) {0,1,4}
2) {−2,−1,0,1,2}
3) {−2,−1,0,1,2,4}
4) {−2,−1,0,0,1,1,1,2,4,4}
 1 
 1, 
 2 


3)
(0,6)
 1 
 − ,5 
 2 


4)
(−3,2)
284 Janice is asked to solve 0 = 64x 2 + 16x − 3. She
begins the problem by writing the following steps:
Line 1 0 = 64x 2 + 16x − 3
Line 2 0 = B 2 + 2B − 3
Line 3 0 = (B + 3)(B − 1)
Use Janice's procedure to solve the equation for x.
Explain the method Janice used to solve the
quadratic equation.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 61
NAME:__________________________
www.jmap.org
285 Determine if the product of 3 2 and 8 18 is
rational or irrational. Explain your answer.
290 Marcel claims that the graph below represents a
function.
286 If a population of 100 cells triples every hour,
which function represents p(t), the population after
t hours?
1) p(t) = 3(100) t
2)
3)
4)
p(t) = 100(3) t
p(t) = 3t + 100
p(t) = 100t + 3
287 When factored completely, x 3 − 13x 2 − 30x is
1) x(x + 3)(x − 10)
2) x(x − 3)(x − 10)
3) x(x + 2)(x − 15)
4) x(x − 2)(x + 15)
288 Joe has a rectangular patio that measures 10 feet by
12 feet. He wants to increase the area by 50% and
plans to increase each dimension by equal lengths,
x. Which equation could be used to determine x?
1) (10 + x)(12 + x) = 120
2) (10 + x)(12 + x) = 180
3) (15 + x)(18 + x) = 180
4)
(15)(18) = 120 + x 2
289 What is the solution of the equation
2(x + 2) 2 − 4 = 28?
1) 6, only
2) 2, only
3) 2 and −6
4) 6 and −2
State whether Marcel is correct. Justify your
answer.
291 Graph the inequality y > 2x − 5 on the set of axes
below. State the coordinates of a point in its
solution.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 62
NAME:__________________________
www.jmap.org
292 The solution of an equation with two variables, x
and y, is
1) the set of all x values that make y = 0
2) the set of all y values that make x = 0
3) the set of all ordered pairs, (x,y), that make the
equation true
4) the set of all ordered pairs, (x,y), where the
graph of the equation crosses the y-axis
295 Given the function f(n) defined by the following:
f(1) = 2
f(n) = −5f(n − 1) + 2
Which set could represent the range of the
function?
1) {2,4,6,8,. . . }
2) {2,−8,42,−208,. . . }
3) {−8,−42,−208,1042,. . . }
4) {−10,50,−250,1250,. . . }
293 The graph below shows the distance in miles, m,
hiked from a camp in h hours.
296 Based on the graph below, which expression is a
possible factorization of p(x)?
Which hourly interval had the greatest rate of
change?
1) hour 0 to hour 1
2) hour 1 to hour 2
3) hour 2 to hour 3
4) hour 3 to hour 4
294 The range of the function defined as y = 5 x is
1) y < 0
2) y > 0
3) y ≤ 0
4) y ≥ 0
1)
2)
3)
4)
(x + 3)(x − 2)(x − 4)
(x − 3)(x + 2)(x + 4)
(x + 3)(x − 5)(x − 2)(x − 4)
(x − 3)(x + 5)(x + 2)(x + 4)
297 During a recent snowstorm in Red Hook, NY,
Jaime noted that there were 4 inches of snow on the
ground at 3:00 p.m., and there were 6 inches of
snow on the ground at 7:00 p.m. If she were to
graph these data, what does the slope of the line
connecting these two points represent in the
context of this problem?
Algebra I CCSS Regents Exam Questions at Random Worksheet # 63
NAME:__________________________
www.jmap.org
298 A graph of average resting heart rates is shown
below. The average resting heart rate for adults is
72 beats per minute, but doctors consider resting
rates from 60-100 beats per minute within normal
range.
300 An Air Force pilot is flying at a cruising altitude of
9000 feet and is forced to eject from her aircraft.
The function h(t) = −16t 2 + 128t + 9000 models the
height, in feet, of the pilot above the ground, where
t is the time, in seconds, after she is ejected from
the aircraft. Determine and state the vertex of h(t).
Explain what the second coordinate of the vertex
represents in the context of the problem. After the
pilot was ejected, what is the maximum number of
feet she was above the aircraft's cruising altitude?
Justify your answer.
301 Boyle's Law involves the pressure and volume of
gas in a container. It can be represented by the
formula P 1 V 1 = P 2 V 2 . When the formula is solved
for P 2 , the result is
1) P 1 V 1 V 2
V2
2)
P1 V1
Which statement about average resting heart rates
is not supported by the graph?
1) A 10-year-old has the same average resting
heart rate as a 20-year-old.
2) A 20-year-old has the same average resting
heart rate as a 30-year-old.
3) A 40-year-old may have the same average
resting heart rate for ten years.
4) The average resting heart rate for teenagers
steadily decreases.
299 A contractor has 48 meters of fencing that he is
going to use as the perimeter of a rectangular
garden. The length of one side of the garden is
represented by x, and the area of the garden is 108
square meters. Determine, algebraically, the
dimensions of the garden in meters.
3)
P1 V1
V2
4)
P1 V2
V1
302 Describe the effect that each transformation below
has on the function f(x) = |x | , where a > 0.
g(x) = |x − a |
h(x) = |x | − a
303 The function r(x) is defined by the expression
x 2 + 3x − 18. Use factoring to determine the zeros
of r(x). Explain what the zeros represent on the
graph of r(x).
Algebra I CCSS Regents Exam Questions at Random Worksheet # 64
NAME:__________________________
www.jmap.org
304 On the set of axes below, graph
1
g(x) = x + 1
2
and
 2x + 1, x ≤ −1

f(x) = 

2
 2 − x , x > −1
306 Ian is borrowing $1000 from his parents to buy a
notebook computer. He plans to pay them back at
the rate of $60 per month. Ken is borrowing $600
from his parents to purchase a snowboard. He
plans to pay his parents back at the rate of $20 per
month. Write an equation that can be used to
determine after how many months the boys will
owe the same amount. Determine algebraically and
state in how many months the two boys will owe
the same amount. State the amount they will owe
at this time. Ian claims that he will have his loan
paid off 6 months after he and Ken owe the same
amount. Determine and state if Ian is correct.
Explain your reasoning.
307 State whether 7 − 2 is rational or irrational.
Explain your answer.
1
x + 3 and j(x) = |x | ,
2
which value of x makes h(x) = j(x)?
1) −2
2) 2
3) 3
4) −6
308 Given the functions h(x) =
How many values of x satisfy the equation
f(x) = g(x) ? Explain your answer, using evidence
from your graphs.
305 The graphs of the functions f(x) = |x − 3 | + 1 and
g(x) = 2x + 1 are drawn. Which statement about
these functions is true?
1) The solution to f(x) = g(x) is 3.
2) The solution to f(x) = g(x) is 1.
3) The graphs intersect when y = 1 .
4) The graphs intersect when x = 3 .
309 Michael has $10 in his savings account. Option 1
will add $100 to his account each week. Option 2
will double the amount in his account at the end of
each week. Write a function in terms of x to model
each option of saving. Michael wants to have at
least $700 in his account at the end of 7 weeks to
buy a mountain bike. Determine which option(s)
will enable him to reach his goal. Justify your
answer.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 65
NAME:__________________________
www.jmap.org
310 The data table below shows the median diameter of grains of sand and the slope of the beach for 9 naturally
occurring ocean beaches.
Median Diameter of
Grains of Sand,
in Millimeters (x)
Slope of Beach,
in Degrees (y)
0.17
0.19
0.22
0.235
0.235
0.3
0.35
0.42
0.85
0.63
0.7
0.82
0.88
1.15
1.5
4.4
7.3
11.3
Write the linear regression equation for this set of data, rounding all values to the nearest thousandth. Using this
equation, predict the slope of a beach, to the nearest tenth of a degree, on a beach with grains of sand having a
median diameter of 0.65 mm.
311 The graph below shows the variation in the average
temperature of Earth's surface from 1950-2000,
according to one source.
312 Sandy programmed a website's checkout process
with an equation to calculate the amount customers
will be charged when they download songs. The
website offers a discount. If one song is bought at
the full price of $1.29, then each additional song is
$.99. State an equation that represents the cost, C,
when s songs are downloaded. Sandy figured she
would be charged $52.77 for 52 songs. Is this the
correct amount? Justify your answer.
313 When multiplying polynomials for a math
assignment, Pat found the product to be
−4x + 8x 2 − 2x 3 + 5. He then had to state the
leading coefficient of this polynomial. Pat wrote
down −4. Do you agree with Pat's answer?
Explain your reasoning.
314 Using the formula for the volume of a cone,
express r in terms of V, h, and π .
During which years did the temperature variation
change the most per unit time? Explain how you
determined your answer.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 66
NAME:__________________________
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315 The line represented by the equation 4y + 2x = 33.6 shares a solution point with the line represented by the table
below.
x
−5
−2
2
4
11
The solution for this system is
1) (−14.0,−1.4)
2) (−6.8,5.0)
3)
4)
316 Which scenario represents exponential growth?
1) A water tank is filled at a rate of 2
gallons/minute.
2) A vine grows 6 inches every week.
3) A species of fly doubles its population every
month during the summer.
4) A car increases its distance from a garage as it
travels at a constant speed of 25 miles per hour.
317 Which pair of equations could not be used to solve
the following equations for x and y?
4x + 2y = 22
−2x + 2y = −8
1)
4x + 2y = 22
2)
2x − 2y = 8
4x + 2y = 22
3)
−4x + 4y = −16
12x + 6y = 66
4)
6x − 6y = 24
8x + 4y = 44
−8x + 8y = −8
y
3.2
3.8
4.6
5
6.4
(1.9,4.6)
(6.0,5.4)
318 A teacher wrote the following set of numbers on
the board:
a = 20 b = 2.5 c = 225
Explain why a + b is irrational, but b + c is rational.
319 The formula for the surface area of a right
rectangular prism is A = 2lw + 2hw + 2lh, where l,
w, and h represent the length, width, and height,
respectively. Which term of this formula is not
dependent on the height?
1) A
2) 2lw
3) 2hw
4) 2lh
320 Which expression is equivalent to
2(3g − 4) − (8g + 3)?
1) −2g − 1
2) −2g − 5
3) −2g − 7
4) −2g − 11
Algebra I CCSS Regents Exam Questions at Random Worksheet # 67
NAME:__________________________
www.jmap.org
321 To keep track of his profits, the owner of a carnival
booth decided to model his ticket sales on a graph.
He found that his profits only declined when he
sold between 10 and 40 tickets. Which graph could
represent his profits?
322 Given that f(x) = 2x + 1 , find g(x) if
g(x) = 2[f(x)] 2 − 1.
323 The zeros of the function f(x) = 2x 2 − 4x − 6 are
1) 3 and −1
2) 3 and 1
3) −3 and 1
4) −3 and −1
1)
324 Abigail's and Gina's ages are consecutive integers.
Abigail is younger than Gina and Gina's age is
represented by x. If the difference of the square of
Gina's age and eight times Abigail's age is 17,
which equation could be used to find Gina's age?
1) (x + 1) 2 − 8x = 17
2)
2)
3)
4)
3)
4)
(x − 1) 2 − 8x = 17
x 2 − 8(x + 1) = 17
x 2 − 8(x − 1) = 17
325 One characteristic of all linear functions is that
they change by
1) equal factors over equal intervals
2) unequal factors over equal intervals
3) equal differences over equal intervals
4) unequal differences over equal intervals
Algebra I CCSS Regents Exam Questions at Random Worksheet # 68
NAME:__________________________
www.jmap.org
326 Jacob and Jessica are studying the spread of
dandelions. Jacob discovers that the growth over t
weeks can be defined by the function f(t) = (8) ⋅ 2 t .
Jessica finds that the growth function over t weeks
is g(t) = 2 t + 3 . Calculate the number of dandelions
that Jacob and Jessica will each have after 5 weeks.
Based on the growth from both functions, explain
the relationship between f(t) and g(t) .
327 Central High School had five members on their
swim team in 2010. Over the next several years,
the team increased by an average of 10 members
per year. The same school had 35 members in their
chorus in 2010. The chorus saw an increase of 5
members per year. Write a system of equations to
model this situation, where x represents the number
of years since 2010. Graph this system of
equations on the set of axes below.
328 Sue and Kathy were doing their algebra homework.
They were asked to write the equation of the line
that passes through the points (−3,4) and (6,1). Sue
1
wrote y − 4 = − (x + 3) and Kathy wrote
3
1
y = − x + 3 . Justify why both students are correct.
3
329 Which expression is equivalent to 36x 2 − 100?
1) 4(3x − 5)(3x − 5)
2) 4(3x + 5)(3x − 5)
3) 2(9x − 25)(9x − 25)
4) 2(9x + 25)(9x − 25)
330 What is the solution to the system of equations
below?
y = 2x + 8
1)
2)
3)
4)
3(−2x + y) = 12
no solution
infinite solutions
(−1,6)
 1 
 ,9 
2 


331 What is the product of 2x + 3 and 4x 2 − 5x + 6?
1) 8x 3 − 2x 2 + 3x + 18
2) 8x 3 − 2x 2 − 3x + 18
3) 8x 3 + 2x 2 − 3x + 18
4) 8x 3 + 2x 2 + 3x + 18
Explain in detail what each coordinate of the point
of intersection of these equations means in the
context of this problem.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 69
NAME:__________________________
www.jmap.org
332 The expression 3(x 2 − 1) − (x 2 − 7x + 10) is
equivalent to
1) 2x 2 − 7x + 7
2) 2x 2 + 7x − 13
3) 2x 2 − 7x + 9
4) 2x 2 + 7x − 11
333 The formula for blood flow rate is given by
p1 − p2
F=
, where F is the flow rate, p 1 the
r
initial pressure, p 2 the final pressure, and r the
resistance created by blood vessel size. Which
formula can not be derived from the given formula?
1) p 1 = Fr + p 2
2) p 2 = p 1 − Fr
3) r = F  p 2 − p 1 
p1 − p2
4) r =
F
334 How many of the equations listed below represent
the line passing through the points (2,3) and
(4,−7)?
5x + y = 13
y + 7 = −5(x − 4)
y = −5x + 13
y − 7 = 5(x − 4)
1)
2)
3)
4)
1
2
3
4
335 Analysis of data from a statistical study shows a
linear relationship in the data with a correlation
coefficient of -0.524. Which statement best
summarizes this result?
1) There is a strong positive correlation between
the variables.
2) There is a strong negative correlation between
the variables.
3) There is a moderate positive correlation
between the variables.
4) There is a moderate negative correlation
between the variables.
336 What is the solution set of the equation
(x − 2)(x − a) = 0?
1) -2 and a
2) -2 and -a
3) 2 and a
4) 2 and -a
337 Graph f(x) = |x | and g(x) = −x 2 + 6 on the grid
below. Does f(−2) = g(−2) ? Use your graph to
explain why or why not.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 70
NAME:__________________________
www.jmap.org
338 The Ebola virus has an infection rate of 11% per
day as compared to the SARS virus, which has a
rate of 4% per day. If there were one case of Ebola
and 30 cases of SARS initially reported to
authorities and cases are reported each day, which
statement is true?
1) At day 10 and day 53 there are more Ebola
cases.
2) At day 10 and day 53 there are more SARS
cases.
3) At day 10 there are more SARS cases, but at
day 53 there are more Ebola cases.
4) At day 10 there are more Ebola cases, but at
day 53 there are more SARS cases.
339 In the functions f(x) = kx 2 and g(x) = |kx | , k is a
1
positive integer. If k is replaced by , which
2
statement about these new functions is true?
1) The graphs of both f(x) and g(x) become
wider.
2) The graph of f(x) becomes narrower and the
graph of g(x) shifts left.
3) The graphs of both f(x) and g(x) shift
vertically.
4) The graph of f(x) shifts left and the graph of
g(x) becomes wider.
340 Andy has $310 in his account. Each week, w, he
withdraws $30 for his expenses. Which expression
could be used if he wanted to find out how much
money he had left after 8 weeks?
1) 310 − 8w
2) 280 + 30(w − 1)
3) 310w − 30
4) 280 − 30(w − 1)
341 Alex launched a ball into the air. The height of the
ball can be represented by the equation
h = −8t 2 + 40t + 5, where h is the height, in units,
and t is the time, in seconds, after the ball was
launched. Graph the equation from t = 0 to t = 5
seconds.
State the coordinates of the vertex and explain its
meaning in the context of the problem.
342 In attempting to solve the system of equations
y = 3x − 2 and 6x − 2y = 4, John graphed the two
equations on his graphing calculator. Because he
saw only one line, John wrote that the answer to
the system is the empty set. Is he correct? Explain
your answer.
343 Find the zeros of f(x) = (x − 3) 2 − 49, algebraically.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 71
NAME:__________________________
www.jmap.org
344 Franco and Caryl went to a bakery to buy desserts.
Franco bought 3 packages of cupcakes and 2
packages of brownies for $19. Caryl bought 2
packages of cupcakes and 4 packages of brownies
for $24. Let x equal the price of one package of
cupcakes and y equal the price of one package of
brownies. Write a system of equations that
describes the given situation. On the set of axes
below, graph the system of equations.
346 The graph below models the cost of renting video
games with a membership in Plan A and Plan B.
Explain why Plan B is the better choice for Dylan if
he only has $50 to spend on video games, including
a membership fee. Bobby wants to spend $65 on
video games, including a membership fee. Which
plan should he choose? Explain your answer.
Determine the exact cost of one package of
cupcakes and the exact cost of one package of
brownies in dollars and cents. Justify your
solution.
5
(f − 32) to
9
convert degrees Fahrenheit, f, to degrees Celsius,
C(f). If Faith calculated C(68), what would her
result be?
1) 20° Celsius
2) 20° Fahrenheit
3) 154° Celsius
4) 154° Fahrenheit
347 Faith wants to use the formula C(f) =
345 Two friends went to a restaurant and ordered one
plain pizza and two sodas. Their bill totaled
$15.95. Later that day, five friends went to the
same restaurant. They ordered three plain pizzas
and each person had one soda. Their bill totaled
$45.90. Write and solve a system of equations to
determine the price of one plain pizza. [Only an
algebraic solution can receive full credit.]
Algebra I CCSS Regents Exam Questions at Random Worksheet # 72
NAME:__________________________
www.jmap.org
348 The tables below show the values of four different functions for given values of x.
x
1
2
3
4
f(x)
12
19
26
33
Which table represents a linear function?·
1) f(x)
2) g(x)
x
1
2
3
4
g(x)
−1
1
5
13
3)
4)
x
1
2
3
4
h(x)
9
12
17
24
x
1
2
3
4
k(x)
−2
4
14
28
h(x)
k(x)
349 Tanya is making homemade greeting cards. The data table below represents the amount she spends in dollars,
f(x) , in terms of the number of cards she makes, x.
x
4
6
9
10
f(x)
7.50
9
11.25
12
Write a linear function, f(x) , that represents the data. Explain what the slope and y-intercept of f(x) mean in the
given context.
350 Lynn, Jude, and Anne were given the function
f(x) = −2x 2 + 32 , and they were asked to find f(3) .
Lynn's answer was 14, Jude's answer was 4, and
Anne's answer was ±4. Who is correct?
1) Lynn, only
2) Jude, only
3) Anne, only
4) Both Lynn and Jude
351 Given that a > b , solve for x in terms of a and b:
b(x − 3) ≥ ax + 7b
352 Bella recorded data and used her graphing
calculator to find the equation for the line of best
fit. She then used the correlation coefficient to
determine the strength of the linear fit. Which
correlation coefficient represents the strongest
linear relationship?
1) 0.9
2) 0.5
3) -0.3
4) -0.8
Algebra I CCSS Regents Exam Questions at Random Worksheet # 73
NAME:__________________________
www.jmap.org
353 The zeros of the function f(x) = 2x 3 + 12x − 10x 2
are
1) {2,3}
2) {−1,6}
3) {0,2,3}
4) {0,−1,6}
357 The acidity in a swimming pool is considered
normal if the average of three pH readings, p, is
defined such that 7.0 < p < 7.8. If the first two
readings are 7.2 and 7.6, which value for the third
reading will result in an overall rating of normal?
1) 6.2
2) 7.3
3) 8.6
4) 8.8
354 Which recursively defined function represents the
sequence 3,7,15,31,. . .?
1)
2)
3)
4)
f(1) = 3, f(n + 1) = 2
f(n)
+3
358 The graph of a quadratic function is shown below.
f(n)
f(1) = 3, f(n + 1) = 2 − 1
f(1) = 3, f(n + 1) = 2f(n) + 1
f(1) = 3, f(n + 1) = 3f(n) − 2
355 The results of a linear regression are shown below.
y = ax + b
a = −1.15785
b = 139.3171772
r = −0.896557832
r 2 = 0.8038159461
Which phrase best describes the relationship
between x and y?
1) strong negative correlation
2) strong positive correlation
3) weak negative correlation
4) weak positive correlation
356 Which value would be a solution for x in the
inequality 47 − 4x < 7?
1) -13
2) -10
3) 10
4) 11
An equation that represents the function could be
1
1) q(x) = (x + 15) 2 − 25
2
1
2) q(x) = − (x + 15) 2 − 25
2
1
3) q(x) = (x − 15) 2 + 25
2
1
4) q(x) = − (x − 15) 2 + 25
2
Algebra I CCSS Regents Exam Questions at Random Worksheet # 74
NAME:__________________________
www.jmap.org
359 Which function has a constant rate of change equal
to −3?
1)
2)
362 Patricia is trying to compare the average rainfall of
New York to that of Arizona. A comparison
between these two states for the months of July
through September would be best measured in
1) feet per hour
2) inches per hour
3) inches per month
4) feet per month
{(1,5),(2,2),(3,−5),(4,4)}
363 Richard is asked to transform the graph of b(x)
below.
3)
4)
2y = −6x + 10
360 What is the solution to the inequality
4
2 + x ≥ 4 + x?
9
18
1) x ≤ −
5
18
2) x ≥ −
5
54
3) x ≤
5
54
4) x ≥
5
361 In a sequence, the first term is 4 and the common
difference is 3. The fifth term of this sequence is
1) −11
2) −8
3) 16
4) 19
The graph of b(x) is transformed using the equation
h(x) = b(x − 2) − 3. Describe how the graph of b(x)
changed to form the graph of h(x).
364 The highest possible grade for a book report is 100.
The teacher deducts 10 points for each day the
report is late. Which kind of function describes
this situation?
1) linear
2) quadratic
3) exponential growth
4) exponential decay
Algebra I CCSS Regents Exam Questions at Random Worksheet # 75
NAME:__________________________
www.jmap.org
365 The graph of y = f(x) is shown below.
366 The graph below models Craig's trip to visit his
friend in another state. In the course of his travels,
he encountered both highway and city driving.
What is the graph of y = f(x + 1) − 2 ?
1)
2)
3)
4)
Based on the graph, during which interval did
Craig most likely drive in the city? Explain your
reasoning. Explain what might have happened in
the interval between B and C. Determine Craig's
average speed, to the nearest tenth of a mile per
hour, for his entire trip.
367 When 3x + 2 ≤ 5(x − 4) is solved for x, the solution
is
1) x ≤ 3
2) x ≥ 3
3) x ≤ −11
4) x ≥ 11
Algebra I CCSS Regents Exam Questions at Random Worksheet # 76
NAME:__________________________
www.jmap.org
368 The height of a rocket, at selected times, is shown in the table below.
Time (sec)
Height (ft)
0
1
2
3
4
5
180 260 308 324 308 260
6
180
7
68
Based on these data, which statement is not a valid conclusion?
1) The rocket was launched from a height of 3) The rocket was in the air approximately 6
180 feet.
seconds before hitting the ground.
2) The maximum height of the rocket
4) The rocket was above 300 feet for
occurred 3 seconds after launch.
approximately 2 seconds.
369 Erica, the manager at Stellarbeans, collected data on the daily high temperature and revenue from coffee sales.
Data from nine days this past fall are shown in the table below.
High
Temperature, t
Coffee Sales,
f(t)
Day
1
Day
2
Day
3
Day
4
Day
5
Day
6
Day
7
Day
8
Day
9
54
50
62
67
70
58
52
46
48
$2900
$3080
$2500
$2380
$2200
$2700
$3000
$3620
$3720
State the linear regression function, f(t) , that estimates the day's coffee sales with a high temperature of t. Round
all values to the nearest integer. State the correlation coefficient, r, of the data to the nearest hundredth. Does r
indicate a strong linear relationship between the variables? Explain your reasoning.
370 The table below shows 6 students' overall averages and their averages in their math class.
Overall Student
Average
Math Class
Average
92
98
84
80
75
82
91
95
85
85
75
78
If a linear model is applied to these data, which statement best describes the correlation coefficient?
1) It is close to −1.
3) It is close to 0.
2) It is close to 1.
4) It is close to 0.5.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 77
NAME:__________________________
www.jmap.org
371 After performing analyses on a set of data, Jackie
examined the scatter plot of the residual values for
each analysis. Which scatter plot indicates the best
linear fit for the data?
1)
2)
373 For a recently released movie, the function
y = 119.67(0.61) x models the revenue earned, y, in
millions of dollars each week, x, for several weeks
after its release. Based on the equation, how much
more money, in millions of dollars, was earned in
revenue for week 3 than for week 5?
1) 37.27
2) 27.16
3) 17.06
4) 10.11
374 On the set of axes below, draw the graph of
y = x 2 − 4x − 1 .
3)
4)
372 Milton has his money invested in a stock portfolio.
The value, v(x), of his portfolio can be modeled
with the function v(x) = 30,000(0.78) x , where x is
the number of years since he made his investment.
Which statement describes the rate of change of the
value of his portfolio?
1) It decreases 78% per year.
2) It decreases 22% per year.
3) It increases 78% per year.
4) It increases 22% per year.
State the equation of the axis of symmetry.
375 Given: g(x) = 2x 2 + 3x + 10
k(x) = 2x + 16
Solve the equation g(x) = 2k(x) algebraically for x,
to the nearest tenth. Explain why you chose the
method you used to solve this quadratic equation.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 78
NAME:__________________________
www.jmap.org
376 Which function has zeros of -4 and 2?
1) f(x) = x 2 + 7x − 8
379 Which graph represents y =
x−2?
1)
2)
3)
g(x) = x 2 − 7x − 8
2)
4)
377 Which value of x satisfies the equation

5  3
− x  = 16?


6 8

1)
2)
3)
4)
3)
−19.575
−18.825
−16.3125
−15.6875
378 If f(n) = (n − 1) 2 + 3n , which statement is true?
1) f(3) = −2
2) f(−2) = 3
3) f(−2) = −15
4) f(−15) = −2
4)
380 Determine and state whether the sequence
1,3,9,27,. . . displays exponential behavior.
Explain how you arrived at your decision.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 79
NAME:__________________________
www.jmap.org
381 The heights, in inches, of 12 students are listed
below.
61,67,72,62,65,59,60,79,60,61,64,63
Which statement best describes the spread of these
data?
1) The set of data is evenly spread.
2) The median of the data is 59.5.
3) The set of data is skewed because 59 is the
only value below 60.
4) 79 is an outlier, which would affect the
standard deviation of these data.
382 Consider the pattern of squares shown below:
Which type of model, linear or exponential, should
be used to determine how many squares are in the
nth pattern? Explain your answer.
383 Express in simplest form:
(3x 2 + 4x − 8) − (−2x 2 + 4x + 2)
384 Anne invested $1000 in an account with a 1.3%
annual interest rate. She made no deposits or
withdrawals on the account for 2 years. If interest
was compounded annually, which equation
represents the balance in the account after the 2
years?
1) A = 1000(1 − 0.013) 2
2)
3)
4)
A = 1000(1 + 0.013) 2
A = 1000(1 − 1.3) 2
A = 1000(1 + 1.3) 2
385 Which equation is equivalent to y − 34 = x(x − 12) ?
1) y = (x − 17)(x + 2)
2) y = (x − 17)(x − 2)
3)
4)
y = (x − 6) 2 + 2
y = (x − 6) 2 − 2
386 Dan took 12.5 seconds to run the 100-meter dash.
He calculated the time to be approximately
1) 0.2083 minute
2) 750 minutes
3) 0.2083 hour
4) 0.52083 hour
387 Which value of x is a solution to the equation
13 − 36x 2 = −12?
36
1)
25
25
2)
36
6
3) −
5
5
4) −
6
388 Grisham is considering the three situations below.
I. For the first 28 days, a sunflower grows at a
rate of 3.5 cm per day.
II. The value of a car depreciates at a rate of 15%
per year after it is purchased.
III. The amount of bacteria in a culture triples
every two days during an experiment.
Which of the statements describes a situation with
an equal difference over an equal interval?
1) I, only
2) II, only
3) I and III
4) II and III
Algebra I CCSS Regents Exam Questions at Random Worksheet # 80
NAME:__________________________
www.jmap.org
389 Nancy works for a company that offers two types
of savings plans. Plan A is represented on the
graph below.
Plan B is represented by the function
f(x) = 0.01 + 0.05x 2 , where x is the number of
weeks. Nancy wants to have the highest savings
possible after a year. Nancy picks Plan B. Her
decision is
1) correct, because Plan B is an exponential
function and will increase at a faster rate
2) correct, because Plan B is a quadratic function
and will increase at a faster rate
3) incorrect, because Plan A will have a higher
value after 1 year
4) incorrect, because Plan B is a quadratic
function and will increase at a slower rate
390 For a class picnic, two teachers went to the same
store to purchase drinks. One teacher purchased 18
juice boxes and 32 bottles of water, and spent
$19.92. The other teacher purchased 14 juice
boxes and 26 bottles of water, and spent $15.76.
Write a system of equations to represent the costs
of a juice box, j, and a bottle of water, w. Kara said
that the juice boxes might have cost 52 cents each
and that the bottles of water might have cost 33
cents each. Use your system of equations to justify
that Kara's prices are not possible. Solve your
system of equations to determine the actual cost, in
dollars, of each juice box and each bottle of water.
391 Nora says that the graph of a circle is a function
because she can trace the whole graph without
picking up her pencil. Mia says that a circle graph
is not a function because multiple values of x map
to the same y-value. Determine if either one is
correct, and justify your answer completely.
392 Which function defines the sequence
−6,−10,−14,−18,. . ., where f(6) = −26?
1) f(x) = −4x − 2
2) f(x) = 4x − 2
3) f(x) = −x + 32
4) f(x) = x − 26
393 Which function has the greatest y-intercept?
1) f(x) = 3x
2) 2x + 3y = 12
3) the line that has a slope of 2 and passes through
(1,−4)
4)
394 What is the solution to 2h + 8 > 3h − 6
1) h < 14
14
2) h <
5
3) h > 14
14
4) h >
5
Algebra I CCSS Regents Exam Questions at Random Worksheet # 81
NAME:__________________________
www.jmap.org
395 The graph below models the height of a
remote-control helicopter over 20 seconds during
flight.
398 Graph the function y = −
below.
x + 3 on the set of axes
Over which interval does the helicopter have the
slowest average rate of change?
1) 0 to 5 seconds
2) 5 to 10 seconds
3) 10 to 15 seconds
4) 15 to 20 seconds
396 The method of completing the square was used to
solve the equation 2x 2 − 12x + 6 = 0. Which
equation is a correct step when using this method?
1) (x − 3) 2 = 6
2)
3)
4)
399 Graph the function f(x) = −x 2 − 6x on the set of
axes below.
(x − 3) 2 = −6
(x − 3) 2 = 3
(x − 3) 2 = −3
397 An equation is given below.
4(x − 7) = 0.3(x + 2) + 2.11
The solution to the equation is
1) 8.3
2) 8.7
3) 3
4) -3
State the coordinates of the vertex of the graph.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 82
NAME:__________________________
www.jmap.org
400 The table below shows the year and the number of households in a building that had high-speed broadband
internet access.
Number of
Households
Year
11
16
23
33
42
47
2002 2003 2004 2005 2006 2007
For which interval of time was the average rate of change the smallest?
1) 2002 - 2004
3) 2004 - 2006
2) 2003 - 2005
4) 2005 - 2007
401 Which chart could represent the function
f(x) = −2x + 6 ?
1)
402 Morgan throws a ball up into the air. The height of
the ball above the ground, in feet, is modeled by the
function h(t) = −16t 2 + 24t , where t represents the
time, in seconds, since the ball was thrown. What
is the appropriate domain for this situation?
1) 0 ≤ t ≤ 1.5
2) 0 ≤ t ≤ 9
3) 0 ≤ h(t) ≤ 1.5
4) 0 ≤ h(t) ≤ 9
403 Solve the inequality below:
1.8 − 0.4y ≥ 2.2 − 2y
2)
404 If f x  =
3)
4)
f(8) ?
1) 11
2) 17
3) 27
4) 33

1 2  1
x −  x + 3  , what is the value of
2
4

Algebra I CCSS Regents Exam Questions at Random Worksheet # 83
NAME:__________________________
www.jmap.org
405 A two-inch-long grasshopper can jump a horizontal
distance of 40 inches. An athlete, who is five feet
nine, wants to cover a distance of one mile by
jumping. If this person could jump at the same
ratio of body-length to jump-length as the
grasshopper, determine, to the nearest jump, how
many jumps it would take this athlete to jump one
mile.
407 The expression 49x 2 − 36 is equivalent to
1) (7x − 6) 2
2)
3)
4)
(24.5x − 18) 2
(7x − 6)(7x + 6)
(24.5x − 18)(24.5x + 18)
408 Solve the equation x 2 − 6x = 15 by completing the
square.
406 Noah conducted a survey on sports participation.
He created the following two dot plots to represent
the number of students participating, by age, in
soccer and basketball.
Which statement about the given data sets is
correct?
1) The data for soccer players are skewed right.
2) The data for soccer players have less spread
than the data for basketball players.
3) The data for basketball players have the same
median as the data for soccer players.
4) The data for basketball players have a greater
mean than the data for soccer players.
409 Let h(t) = −16t 2 + 64t + 80 represent the height of
an object above the ground after t seconds.
Determine the number of seconds it takes to
achieve its maximum height. Justify your answer.
State the time interval, in seconds, during which
the height of the object decreases. Explain your
reasoning.
410 Which value of x results in equal outputs for
j(x) = 3x − 2 and b(x) = |x + 2| ?
1) −2
2) 2
2
3)
3
4) 4
411 The daily cost of production in a factory is
calculated using c(x) = 200 + 16x, where x is the
number of complete products manufactured.
Which set of numbers best defines the domain of
c(x)?
1) integers
2) positive real numbers
3) positive rational numbers
4) whole numbers
Algebra I CCSS Regents Exam Questions at Random Worksheet # 84
NAME:__________________________
www.jmap.org
412 An airplane leaves New York City and heads
toward Los Angeles. As it climbs, the plane
gradually increases its speed until it reaches
cruising altitude, at which time it maintains a
constant speed for several hours as long as it stays
at cruising altitude. After flying for 32 minutes, the
plane reaches cruising altitude and has flown 192
miles. After flying for a total of 92 minutes, the
plane has flown a total of 762 miles. Determine the
speed of the plane, at cruising altitude, in miles per
minute. Write an equation to represent the number
of miles the plane has flown, y, during x minutes at
cruising altitude, only. Assuming that the plane
maintains its speed at cruising altitude, determine
the total number of miles the plane has flown 2
hours into the flight.
413 When solving the equation x 2 − 8x − 7 = 0 by
completing the square, which equation is a step in
the process?
1) (x − 4) 2 = 9
2)
3)
4)
(x − 4) 2 = 23
(x − 8) 2 = 9
(x − 8) 2 = 23
414 What are the solutions to the equation
3x 2 + 10x = 8?
2
and −4
1)
3
2
2) − and 4
3
4
3)
and −2
3
4
4) − and 2
3
415 A student plotted the data from a sleep study as
shown in the graph below.
The student used the equation of the line
y = −0.09x + 9.24 to model the data. What does the
rate of change represent in terms of these data?
1) The average number of hours of sleep per day
increases 0.09 hour per year of age.
2) The average number of hours of sleep per day
decreases 0.09 hour per year of age.
3) The average number of hours of sleep per day
increases 9.24 hours per year of age.
4) The average number of hours of sleep per day
decreases 9.24 hours per year of age.
416 The equation A = 1300(1.02) 7 is being used to
calculate the amount of money in a savings
account. What does 1.02 represent in this
equation?
1) 0.02% decay
2) 0.02% growth
3) 2% decay
4) 2% growth
Algebra I CCSS Regents Exam Questions at Random Worksheet # 85
NAME:__________________________
www.jmap.org
417 Jordan works for a landscape company during his
summer vacation. He is paid $12 per hour for
mowing lawns and $14 per hour for planting
gardens. He can work a maximum of 40 hours per
week, and would like to earn at least $250 this
week. If m represents the number of hours mowing
lawns and g represents the number of hours
planting gardens, which system of inequalities
could be used to represent the given conditions?
1) m + g ≤ 40
2)
12m + 14g ≥ 250
m + g ≥ 40
3)
12m + 14g ≤ 250
m + g ≤ 40
4)
12m + 14g ≤ 250
m + g ≥ 40
419 The function h(x), which is graphed below, and the
function g(x) = 2 |x + 4| − 3 are given.
12m + 14g ≥ 250
418 What type of relationship exists between the
number of pages printed on a printer and the
amount of ink used by that printer?
1) positive correlation, but not causal
2) positive correlation, and causal
3) negative correlation, but not causal
4) negative correlation, and causal
Which statements about these functions are true?
I. g(x) has a lower minimum value than h(x).
II. For all values of x, h(x) < g(x).
III. For any value of x, g(x) ≠ h(x) .
1) I and II, only
2) I and III, only
3) II and III, only
4) I, II, and III
420 A survey of 100 students was taken. It was found that 60 students watched sports, and 34 of these students did not
like pop music. Of the students who did not watch sports, 70% liked pop music. Complete the two-way
frequency table.
Watch Sports
Like Pop
Don’t Like Pop
Total
Don’t Watch Sports
Total
Algebra I CCSS Regents Exam Questions at Random Worksheet # 86
NAME:__________________________
www.jmap.org
421 The heights, in feet, of former New York Knicks basketball players are listed below.
6.4 6.9 6.3 6.2 6.3 6.0 6.1 6.3 6.8 6.2
6.5 7.1 6.4 6.3 6.5 6.5 6.4 7.0 6.4 6.3
6.2 6.3 7.0 6.4 6.5 6.5 6.5 6.0 6.2
Using the heights given, complete the frequency table below.
Interval
6.0-6.1
6.2-6.3
6.4-6.5
6.6-6.7
6.8-6.9
7.0-7.1
Frequency
Based on the frequency table created, draw and label a frequency histogram on the grid below.
Determine and state which interval contains the upper quartile. Justify your response.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 87
NAME:__________________________
www.jmap.org
422 A public opinion poll was taken to explore the relationship between age and support for a candidate in an election.
The results of the poll are summarized in the table below.
Age
For
21-40
30
41-60
20
Over 60 25
Against
12
40
35
No Opinion
8
15
15
What percent of the 21-40 age group was for the candidate?
1) 15
3) 40
2) 25
4) 60
423 When (2x − 3) 2 is subtracted from 5x 2 , the result is
1)
2)
3)
4)
x 2 − 12x − 9
x 2 − 12x + 9
x 2 + 12x − 9
x 2 + 12x + 9
424 What is the minimum value of the function
y = |x + 3 | − 2 ?
1) −2
2) 2
3) 3
4) −3
425 A construction company uses the function f(p) ,
where p is the number of people working on a
project, to model the amount of money it spends to
complete a project. A reasonable domain for this
function would be
1) positive integers
2) positive real numbers
3) both positive and negative integers
4) both positive and negative real numbers
426 Michael borrows money from his uncle, who is
charging him simple interest using the formula
I = Pr t . To figure out what the interest rate, r, is,
Michael rearranges the formula to find r. His new
formula is r equals
I−P
1)
t
P−I
2)
t
I
3)
Pt
Pt
4)
I
427 Loretta and her family are going on vacation.
Their destination is 610 miles from their home.
Loretta is going to share some of the driving with
her dad. Her average speed while driving is 55
mph and her dad's average speed while driving is
65 mph. The plan is for Loretta to drive for the
first 4 hours of the trip and her dad to drive for the
remainder of the trip. Determine the number of
hours it will take her family to reach their
destination. After Loretta has been driving for 2
hours, she gets tired and asks her dad to take over.
Determine, to the nearest tenth of an hour, how
much time the family will save by having Loretta's
dad drive for the remainder of the trip.
Algebra I CCSS Regents Exam Questions at Random Worksheet # 88
www.jmap.org
428 Vinny collects population data, P(h) , about a
specific strain of bacteria over time in hours, h, as
shown in the graph below.
Which equation represents the graph of P(h) ?
1)
2)
3)
4)
P(h) = 4(2) h
46
6
P(h) =
h+
5
5
P(h) = 3h 2 + 0.2h + 4.2
2
P(h) = h 3 − h 2 + 3h + 4
3
429 Jakob is working on his math homework. He
1 6 5
+
3
7
must be rational because it is a fraction. Is Jakob
correct? Explain your reasoning.
decides that the sum of the expression
430 Which expression is equivalent to 16x 4 − 64?
1) (4x 2 − 8) 2
2)
3)
4)
(8x 2 − 32) 2
(4x 2 + 8)(4x 2 − 8)
(8x 2 + 32)(8x 2 − 32)
NAME:__________________________
ID: A
Algebra I Common Core State Standards Regents at Random Worksheets
Answer Section
1 ANS:
y = 0.25(2) x . I inputted the four integral values from the graph into my graphing calculator and determined the
exponential regression equation.
PTS: 2
REF: 011532ai
2 ANS: 4
PTS: 2
TOP: Solving Quadratics
3 ANS:
8x + 11y ≥ 200 8x + 11(15) ≥ 200
NAT: F.LE.A.2
REF: 011503ai
TOP: Modeling Exponential Functions
NAT: A.SSE.B.3
NAT: A.CED.A.3
REF: 081514ai
TOP: Modeling Linear Inequalities
NAT: F.LE.A.2
8x + 165 ≥ 200
8x ≥ 35
x ≥ 4.375
5 hours
PTS:
4 ANS:
TOP:
5 ANS:
15 > 5
4
1
Sequences
3
REF: fall1309ai
PTS: 2
PTS: 2
REF: 081502ai
NAT: A.REI.C.6
6 ANS: 4
PTS: 2
REF: spr1304ai
TOP: Geometric Applications of Quadratics
7 ANS: 2
PTS: 2
REF: 011502ai
TOP: Conversions KEY: dimensional analysis
8 ANS:
185 + 0.03x = 275 + 0.025x
TOP: Graphing Linear Systems
NAT: A.CED.A.1
NAT: N.Q.A.1
0.005x = 90
x = 18000
PTS: 2
KEY: substitution
REF: 081427ai
NAT: A.REI.C.6
TOP: Solving Linear Systems
ID: A
9 ANS:
(2x + 8)(2x + 6) = 100 The frame has two parts added to each side, so 2x must be added to the length and width.
4x 2 + 28x + 48 = 100
x 2 + 7x − 13 = 0
Multiply length and width to find area and set equal to 100. x =
PTS: 6
10 ANS:
REF: 081537ai
NAT: A.CED.A.1
−7 ±
7 2 − 4(1)(−13) −7 + 101
=
≈ 1.5
2(1)
2
TOP: Geometric Applications of Quadratics
120x = 70x + 1600
y = 120x and y = 70x + 1600
50x = 1600
x = 32
y = 120(35) = 4200
Green Thumb is less expensive.
y = 70(35) + 1600 = 4050
PTS: 6
REF: fall1315ai
NAT: A.REI.C.6
TOP: Graphing Linear Systems
11 ANS: 3
PTS: 2
REF: 011522ai
NAT: A.SSE.A.2
TOP: Factoring the Difference of Perfect Squares
KEY: higher power AI
12 ANS: 3
PTS: 2
REF: 061415ai
NAT: F.LE.A.2
TOP: Families of Functions
13 ANS: 3
A correlation coefficient close to –1 or 1 indicates a good fit. For a residual plot, there should be no observable
pattern and a similar distribution of residuals above and below the x-axis.
PTS: 2
REF: fall1303ai
NAT: S.ID.B.6
TOP: Residuals
ID: A
14 ANS: 1
f(−1) < g(−1)
3 −1 < 2(−1) + 5
1
<3
3
PTS: 2
REF: 061515ai
NAT: F.LE.A.3
TOP: Families of Functions
15 ANS:
w(52) − w(38)
15(x − 40) + 400 = 445 Since w(x) > 400, x > 40. I substituted 445 for w(x) and solved
15(52 − 40) + 400 − 10(38)
180 + 400 − 380
15(x − 40) = 45
x − 40 = 3
x = 43
200
for x.
PTS:
16 ANS:
TOP:
17 ANS:
4
REF: 061534ai
3
PTS: 2
Modeling Exponential Functions
3
1
2
3
4
median salary
mean salary
salary range
mean age
NAT: F.IF.A.2
REF: 011515ai
Company 1
33,500
33,750
8,000
28.25
PTS: 2
REF: 081404ai
NAT: S.ID.A.2
18 ANS:
2(60)
1
A = h(b 1 + b 2 ) b 1 =
− 12 = 20 − 12 = 8
2
6
TOP: Functional Notation
NAT: F.LE.B.5
Company 2
36,250
44,125
36,000
28.25
TOP: Central Tendency and Dispersion
2A
= b1 + b2
h
2A
− b2 = b1
h
PTS:
19 ANS:
TOP:
20 ANS:
TOP:
4
REF: 081434ai
3
PTS: 2
Families of Functions
2
PTS: 2
Graphing Linear Functions
NAT: A.CED.A.4
REF: 081412ai
TOP: Transforming Formulas
NAT: F.LE.A.1
REF: 081413ai
NAT: A.CED.A.2
KEY: bimodalgraph
ID: A
21 ANS:
TOP:
22 ANS:
TOP:
23 ANS:
2
PTS: 2
Operations with Polynomials
3
PTS: 2
Modeling Linear Inequalities
REF: 011510ai
NAT: A.APR.A.1
KEY: multiplication
REF: 011513ai
NAT: A.CED.A.1
2
3
2 225
1
2
x= 
= − ⋅−
= 75 y = −
(75) 2 + (75) = −25 + 50 = 25

3
2
225
3
 1 

2  −

225


−
(75,25) represents the horizontal distance (75) where the football is at its greatest height (25). No, because the
1
2
(135) 2 + (135) = −81 + 90 = 9
ball is less than 10 feet high y = −
225
3
PTS: 6
REF: 061537ai
NAT: F.IF.B.4
TOP: Graphing Quadratic Functions
KEY: context
24 ANS: 4
3(x 2 − 4x + 4) − 2x + 2 = 3x 2 − 12x + 12 − 2x + 2 = 3x 2 − 14x + 14
PTS: 2
REF: 081524ai
KEY: multiplication
25 ANS: 1
f(2) = 0
NAT: A.APR.A.1
TOP: Operations with Polynomials
f(6) = 8
PTS:
KEY:
26 ANS:
P(x) =
2
REF: 081411ai
NAT: F.IF.A.2
TOP: Domain and Range
limited domain
2
−0.5x 2 + 800x − 100 − (300x + 250) = −0.5x 2 + 500x − 350
PTS: 2
REF: 081406ai
27 ANS:
T(d) = 2d + 28 T(6) = 2(6) + 28 = 40
PTS: 2
REF: 081532ai
NAT: F.BF.A.1
TOP: Operations with Functions
NAT: F.BF.A.1
TOP: Modeling Linear Functions
ID: A
28 ANS: 1
x 2 − 12x + 7
x 2 − 12x + 36 − 29
(x − 6) 2 − 29
PTS: 2
29 ANS: 3
16 +
REF: 081520ai
9=
NAT: F.IF.C.8
TOP: Vertex Form of a Quadratic
7
may be expressed as the ratio of two integers.
1
PTS: 2
REF: 061413ai
NAT: N.RN.B.3
TOP: Operations with Radicals
KEY: classify
30 ANS: 2
PTS: 2
REF: 061424ai
NAT: F.LE.A.2
TOP: Sequences
31 ANS:
(−4,1), because then every element of the domain is not assigned one unique element in the range.
PTS: 2
REF: 011527ai
KEY: ordered pairs
32 ANS:
At 6 hours, 3
PTS: 4
33 ANS:
REF: spr1307ai
NAT: F.IF.A.1
TOP: Defining Functions
1
inches of snow have fallen.
2
NAT: F.IF.B.4
TOP: Relating Graphs to Events
No, because (3,2) is not on the graph.
PTS: 2
REF: 061429ai
NAT: A.REI.D.10
TOP: Identifying Solutions
ID: A
34 ANS:
The cost for each additional hour increases after the first 2 hours.
PTS: 4
35 ANS: 4
3x 2 − 3x − 6 = 0
REF: fall1311ai
NAT: F.IF.C.7
TOP: Graphing Step Functions
PTS: 2
REF: 081513ai
36 ANS: 2
PTS: 2
TOP: Graphing Linear Functions
37 ANS:
h(n) = 1.5(n − 1) + 3
NAT: A.SSE.B.3
REF: 081501ai
TOP: Solving Quadratics
NAT: F.BF.B.3
PTS: 2
REF: 081525ai
38 ANS: 3
f(0 + 1) = −2f(0) + 3 = −2(2) + 3 = −1
NAT: F.LE.A.2
TOP: Modeling Linear Functions
REF: 011520ai
NAT: F.IF.A.3
TOP: Sequences
REF: 011507ai
NAT: A.REI.B.3
TOP: Solving Linear Inequalities
3(x 2 − x − 2) = 0
3(x − 2)(x + 1) = 0
x = 2,−1
f(1 + 1) = −2f(1) + 3 = −2(−1) + 3 = 5
PTS: 2
KEY: term
39 ANS: 1
2
7− x < x −8
3
15 <
5
x
3
9<x
PTS: 2
ID: A
40 ANS:
B = 3000(1.042) t
PTS: 2
KEY: AI
41 ANS:
6. 3x + 9 ≤ 5x − 3
REF: 081426ai
NAT: F.BF.A.1
TOP: Modeling Exponential Functions
REF: 081430ai
NAT: A.REI.B.3
TOP: Interpreting Solutions
12 ≤ 2x
6≤x
PTS: 2
42 ANS:
Range: y ≥ 0 . The function is increasing for x > −1.
PTS: 4
43 ANS: 1
x 2 − 6x = 19
REF: fall1310ai
NAT: F.IF.C.7
TOP: Graphing Absolute Value Functions
NAT: A.REI.B.4
TOP: Solving Quadratics
NAT: A.REI.B.4
TOP: Solving Quadratics
REF: 011505ai
NAT: F.LE.A.1
x 2 − 6x + 9 = 19 + 9
(x − 3) 2 = 28
x −3 = ± 4⋅7
x = 3±2 7
PTS: 2
REF: fall1302ai
KEY: quadratic formula
44 ANS: 2
x 2 − 6x = 12
x 2 − 6x + 9 = 12 + 9
(x − 3) 2 = 21
PTS:
KEY:
45 ANS:
TOP:
2
REF: 061408ai
completing the square
3
PTS: 2
Families of Functions
ID: A
46 ANS: 1
PTS: 2
REF:
TOP: Graphing Linear Inequalities
47 ANS: 3
PTS: 2
REF:
TOP: Modeling Quadratics
48 ANS: 2
PTS: 2
REF:
TOP: Domain and Range
49 ANS: 2
PTS: 2
REF:
TOP: Graphing Polynomial Functions
50 ANS: 3
PTS: 2
REF:
TOP: Modeling Linear Functions
51 ANS: 1
PTS: 2
REF:
TOP: Identifying Properties
52 ANS: 3
PTS: 2
REF:
TOP: Graphing Systems of Linear Inequalities
53 ANS:
f(x) = 6.50x + 4(12)
PTS:
54 ANS:
TOP:
55 ANS:
061505ai
NAT: A.REI.D.12
081409ai
NAT: A.CED.A.1
011506ai
NAT: F.IF.B.5
011512ai
NAT: F.BF.B.3
061501ai
NAT: F.LE.B.5
061401ai
NAT: A.REI.A.1
081506ai
NAT: A.REI.D.12
KEY: bimodalgraph | graph
2
REF: 061526ai
NAT: F.BF.A.1
2
PTS: 2
REF: 061404ai
Graphing Systems of Linear Inequalities
4
(x + 2) 2 − 25 = 0
TOP: Modeling Linear Functions
NAT: A.REI.D.12
KEY: bimodalgraph | graph
((x + 2) + 5))((x + 2) − 5)) = 0
x = −7,3
PTS: 2
REF: 081418ai
KEY: AI
56 ANS: 1
110 − 40 350 − 230
>
8−6
2−1
NAT: A.APR.B.3
TOP: Zeros of Polynomials
NAT: F.IF.B.6
TOP: Rate of Change
70 > 60
PTS: 2
KEY: AI
57 ANS: 2
2(3x − y = 4)
REF: 061418ai
6x − 2y = 8
PTS: 2
REF: 061414ai
NAT: A.REI.C.5
58 ANS:
b 2 − 4ac = (−2) 2 − 4(1)(5) = 4 − 20 = −16 None
PTS: 2
KEY: AI
REF: 081529ai
NAT: A.REI.B.4
TOP: Solving Linear Systems
TOP: Using the Discriminant
ID: A
59 ANS:
x 2 + 46 = 60 + 5x John and Sarah will have the same amount of money saved at 7 weeks. I set the
x 2 − 5x − 14 = 0
(x − 7)(x + 2) = 0
x=7
expressions representing their savings equal to each other and solved for the positive value of x by factoring.
PTS: 2
REF: 061527ai
NAT: A.REI.D.11 TOP: Quadratic-Linear Systems
KEY: AI
60 ANS:
A(n) = 175 − 2.75n 0 = 175 − 2.75n After 63 weeks, Caitlin will not have enough money to rent another movie.
2.75n = 175
n = 63.6
PTS: 4
REF: 061435ai
61 ANS: 1
PTS: 2
TOP: Solving Quadratics
62 ANS: 2
(x + 4)(x + 6) = 0
NAT: F.BF.A.1
TOP: Modeling Linear Functions
REF: 061521ai
NAT: A.REI.B.4
KEY: taking square roots
x 2 + 10x + 24 = 0
PTS: 2
REF: spr1303ai
NAT: A.APR.B.3 TOP: Zeros of Polynomials
KEY: AI
63 ANS: 2
PTS: 2
REF: 061416ai
NAT: A.CED.A.1
TOP: Modeling Linear Equations
64 ANS:
Exponential, because the function does not grow at a constant rate.
PTS: 2
REF: 081527ai
NAT: F.LE.A.1
TOP: Families of Functions
ID: A
65 ANS:
Since according to the graph, 8 pencils cost $14 and 10 pencils cost $12.50, the
cashier is correct.
PTS: 4
66 ANS: 4
x 2 + 6x = 7
REF: fall1312ai
NAT: F.IF.C.7
TOP: Graphing Piecewise-Defined Functions
x 2 + 6x + 9 = 7 + 9
(x + 3) 2 = 16
PTS: 2
REF: 011517ai
NAT: A.REI.B.4
TOP: Solving Quadratics
KEY: completing the square
67 ANS:
(x − 3)(2x) = 1.25x 2 Because the original garden is a square, x 2 represents the original area, x − 3 represents the
side decreased by 3 meters, 2x represents the doubled side, and 1.25x 2 represents the new garden with an area
25% larger. (x − 3)(2x) = 1.25x 2 1.25(8) 2 = 80
2x 2 − 6x = 1.25x 2
.75x 2 − 6x = 0
x 2 − 8x = 0
x(x − 8) = 0
x=8
PTS: 6
REF: 011537ai
NAT: A.CED.A.1 TOP: Geometric Applications of Quadratics
68 ANS: 4
PTS: 2
REF: 061502ai
NAT: F.IF.B.4
TOP: Relating Graphs to Events
69 ANS:
y = 836.47(2.05) x The data appear to grow at an exponential rate. y = 836.47(2.05) 2 ≈ 3515.
PTS: 4
REF: fall1313ai
KEY: choose model
NAT: S.ID.B.6
TOP: Regression
ID: A
70 ANS:
a) p + d ≤ 800 b) 6(440) + 9d ≥ 5000 Since 440 + 263 ≤ 800, it is possible.
6p + 9d ≥ 5000
2640 + 9d ≥ 5000
9d ≥ 2360
d ≥ 262. 2
PTS: 2
71 ANS:
15x + 36 = 10x + 48
REF: spr1306ai
NAT: A.CED.A.3
TOP: Modeling Systems of Linear Inequalities
PTS: 2
REF: 011531ai
72 ANS: 1
PTS: 2
TOP: Functional Notation
73 ANS: 4
4.7 − 2.3 2.4
=
= −0.04.
−60
20 − 80
NAT: A.CED.A.1
REF: 061420ai
TOP: Modeling Linear Equations
NAT: F.IF.A.2
5x = 12
x = 2.4
PTS: 2
REF: 081414ai
NAT: F.IF.B.6
TOP: Rate of Change
KEY: AI
74 ANS: 3
PTS: 2
REF: 011518ai
NAT: A.REI.D.11
TOP: Other Systems
KEY: AI
75 ANS:
7x − 3(4x − 8) ≤ 6x + 12 − 9x 6, 7, 8 are the numbers greater than or equal to 6 in the interval.
7x − 12x + 24 ≤ −3x + 12
−5x + 24 ≤ −3x + 12
12 ≤ 2x
6≤x
PTS: 4
REF: 081534ai
NAT: A.REI.B.3
TOP: Interpreting Solutions
ID: A
76 ANS: 2
x 2 − 2x − 8 =
1
x−1
4
4x 2 − 8x − 32 = x − 4
4x 2 − 9x − 28 = 0
(4x + 7)(x − 4) = 0
7
x = − ,4
4
PTS: 2
KEY: AI
77 ANS: 3
REF: 081517ai
Semester 1
Semester 2
Mean
86.8
87
NAT: A.REI.D.11
Q1
80.5
80
Median
88
88
PTS: 2
REF: 061419ai
NAT: S.ID.A.2
78 ANS:
−3x + 7 − 5x < 15 0 is the smallest integer.
TOP: Quadratic-Linear Systems
Q3
92.5
92
IQR
12
12
TOP: Central Tendency and Dispersion
−8x < 8
x > −1
PTS: 2
79 ANS:
REF: 061530ai
NAT: A.REI.B.3
TOP: Interpreting Solutions
2 down. 4 right.
PTS: 4
REF: 081433ai
NAT: F.BF.B.3
TOP: Graphing Absolute Value Functions
80 ANS:
0.5 represents the rate of decay and 300 represents the initial amount of the compound.
PTS: 2
REF: 061426ai
NAT: F.LE.B.5
TOP: Modeling Exponential Functions
ID: A
81 ANS:
g(x) has a greater value: 2 20 > 20 2
PTS: 4
82 ANS: 3
 1 
2   + 3
 2
REF: 081533ai
PTS: 2
83 ANS:
24x + 27y = 144
REF: 081512ai
NAT: F.LE.A.3
TOP: Families of Functions
NAT: F.IF.A.2
TOP: Functional Notation
4
2
=
=
= −1
 1 
−2
−2




6   − 5
 2
24x + 10y = 42
−8.5y = −51 Agree, as both systems have the same solution.
y=6
17y = 102 8x + 9(6) = 48
8x = −6
y=6
8x + 9(6) = 48
8x = −6
x= −
PTS:
84 ANS:
TOP:
85 ANS:
TOP:
x= −
3
4
3
4
4
REF: 061533ai
4
PTS: 2
Graphing Quadratic Functions
2
PTS: 2
Modeling Linear Functions
NAT:
REF:
KEY:
REF:
A.REI.C.5
081405ai
no context
081402ai
TOP: Solving Linear Systems
NAT: F.IF.B.4
NAT: F.LE.B.5
ID: A
86 ANS:
4x 2 − 12x − 7 = 0
(4x 2 − 14x) + (2x − 7) = 0
2x(2x − 7) + (2x − 7) = 0
(2x + 1)(2x − 7) = 0
1 7
x= − ,
2 2
PTS:
KEY:
87 ANS:
TOP:
88 ANS:
2
REF: 011529ai
factoring
1
PTS: 2
Graphing Step Functions
4
NAT: A.REI.B.4
REF: 061507ai
NAT: F.IF.C.7
KEY: bimodalgraph
Over the interval 0 ≤ x ≤ 3, the average rate of change for h(x) =
g(x) =
3−0 3
= = 1.
3−0 3
PTS: 2
KEY: AI
89 ANS: 4
TOP: Sequences
90 ANS:
(2w)(w) = 34
TOP: Solving Quadratics
9−2 7
7−1 6
= , f(x) =
= = 2, and
3−0 3
3−0 3
REF: spr1301ai
NAT: F.IF.B.6
TOP: Rate of Change
PTS: 2
REF: 061421ai
NAT: F.LE.A.2
NAT: A.CED.A.1
TOP: Geometric Applications of Quadratics
NAT: A.APR.A.1
TOP: Operations with Polynomials
REF: 081421ai
NAT: S.ID.B.6
REF: 081507ai
KEY: AI
NAT: F.LE.A.2
w 2 = 17
w ≈ 4.1
PTS: 2
REF: 061532ai
91 ANS:
(2x 2 + 7x − 10)(x + 5)
2x 3 + 7x 2 − 10x + 10x 2 + 35x − 50
2x 3 + 17x 2 + 25x − 50
PTS:
KEY:
92 ANS:
TOP:
93 ANS:
TOP:
2
REF: 081428ai
multiplication
4
PTS: 2
Regression
KEY: linear
3
PTS: 2
Modeling Exponential Functions
ID: A
94 ANS: 2
x 2 + 4x = 16
x 2 + 4x + 4 = 16 + 4
(x + 2) 2 = 20
x +2 = ± 4⋅5
= −2 ± 2 5
PTS: 2
REF: 061410ai
NAT: A.REI.B.4
TOP: Solving Quadratics
KEY: completing the square
95 ANS:
Yes, because every element of the domain is assigned one unique element in the range.
PTS: 2
REF: 061430ai
KEY: ordered pairs
96 ANS:
w(w + 40) = 6000
NAT: F.IF.A.1
TOP: Defining Functions
w 2 + 40w − 6000 = 0
(w + 100)(w − 60) = 0
w = 60, l = 100
PTS: 4
REF: 081436ai
NAT: A.CED.A.1 TOP: Geometric Applications of Quadratics
97 ANS: 4
PTS: 2
REF: 061509ai
NAT: F.IF.A.2
TOP: Domain and Range
KEY: graph
98 ANS: 3
PTS: 2
REF: 081523ai
NAT: A.REI.B.4
TOP: Solving Quadratics
KEY: taking square roots
99 ANS:
a) A(x) = 1.50x + 6 b) 1.50x + 6 = 2x + 2.50 c) A(x) = 1.50(5) + 6 = 13.50 Carnival B has a lower cost.
B(x) = 2x + 2.50
.50x = 3.50
B(x) = 2(5) + 2.50 = 12.50
x=7
PTS:
100 ANS:
TOP:
101 ANS:
6
REF: spr1308ai
NAT: A.REI.C.6
2
PTS: 2
REF: 061516ai
Analysis of Data
3
1.75(165 − p) + 2.5p = 337.5
a + p = 165
TOP: Graphing Linear Systems
NAT: S.ID.C.9
1.75a + 2.5p = 337.5 288.75 − 1.75p + 2.5p = 337.5
0.75p = 48.75
p = 65
PTS: 2
REF: 061506ai
NAT: A.CED.A.3
TOP: Modeling Linear Systems
ID: A
102 ANS:
PTS: 2
REF: 061425ai
103 ANS: 1
PTS: 2
TOP: Zeros of Polynomials
104 ANS: 3
PTS: 2
TOP: Zeros of Polynomials
105 ANS: 4
750 + 2.25p
750 + 2.25p
> 2.75
< 3.25
p
p
NAT:
REF:
KEY:
REF:
KEY:
F.IF.C.7
011524ai
AI
spr1302ai
AI
TOP: Graphing Root Functions
NAT: A.APR.B.3
NAT: A.APR.B.3
750 + 2.25p > 2.75p 750 + 2.25p < 3.25p
750 >.50p
750 < p
1500 > p
PTS:
106 ANS:
TOP:
107 ANS:
x4
2
REF: 061524ai
NAT: A.CED.A.1
1
PTS: 2
REF: 081407ai
Graphing Systems of Linear Inequalities
TOP: Modeling Linear Inequalities
NAT: A.REI.D.12
KEY: solution set
+ 6x 2 − 7
(x 2 + 7)(x 2 − 1)
(x 2 + 7)(x + 1)(x − 1)
PTS: 2
REF: 061431ai
NAT: A.SSE.A.2
TOP: Factoring the Difference of Perfect Squares
108 ANS:
2(−1) + a(−1) − 7 > −12 a = 2
KEY: higher power AI
−a − 9 > −12
−a > −3
a<3
PTS:
109 ANS:
TOP:
110 ANS:
TOP:
2
REF: 061427ai
1
PTS: 2
Transforming Formulas
1
PTS: 2
Graphing Polynomial Functions
NAT: A.REI.B.3
REF: 011516ai
TOP: Interpreting Solutions
NAT: A.CED.A.4
REF: 081417ai
NAT: F.BF.B.3
ID: A
111 ANS:
m(x) = (3x − 1)(3 − x) + 4x 2 + 19
m(x) = 9x − 3x 2 − 3 + x + 4x 2 + 19
x 2 + 10x + 16 = 0
(x + 8)(x + 2) = 0
x = −8,−2
m(x) = x 2 + 10x + 16
PTS: 4
KEY: factoring
112 ANS:
PTS:
KEY:
113 ANS:
TOP:
114 ANS:
TOP:
115 ANS:
REF: 061433ai
2
REF: 061432ai
represent
1
PTS: 2
Modeling Exponential Functions
3
PTS: 2
Factoring Polynomials
NAT: A.REI.B.4
TOP: Solving Quadratics
NAT: S.ID.A.1
TOP: Box Plots
REF:
KEY:
REF:
KEY:
NAT: F.BF.A.1
011504ai
AI
081509ai
quadratic
NAT: A.SSE.A.2
(4,−1). f(x − 2) is a horizontal shift two units to the right.
PTS: 2
116 ANS:
V
πr 2 h
=
d=2
πh
πh
REF: 061428ai
NAT: F.BF.B.3
TOP: Graphing Polynomial Functions
66
≈5
3.3π
V
= r2
πh
V
=r
πh
PTS: 4
REF: 081535ai
NAT: A.CED.A.4 TOP: Transforming Formulas
117 ANS:
1 − 0.95 = 0.05 = 5% To find the rate of change of an equation in the form y = ab x , subtract b from 1.
PTS: 2
REF: 081530ai
NAT: F.LE.B.5
TOP: Modeling Exponential Functions
ID: A
118 ANS:
(2x + 16)(2x + 12) = 396. The length, 2x + 16, and the width, 2x + 12, are multiplied and set equal to the area.
(2x + 16)(2x + 12) = 396
4x 2 + 24x + 32x + 192 = 396
4x 2 + 56x − 204 = 0
x 2 + 14x − 51 = 0
(x + 17)(x − 3) = 0
x = 3 = width
PTS: 4
REF: 061434ai
NAT: A.CED.A.1
119 ANS: 1
PTS: 2
REF: 081401ai
TOP: Operations with Radicals
KEY: classify
120 ANS:
x 2 + 10x + 24 = (x + 4)(x + 6) = (x + 6)(x + 4). 6 and 4
TOP: Geometric Applications of Quadratics
NAT: N.RN.B.3
PTS: 2
121 ANS:
TOP: Solving Quadratics
REF: 081425ai
NAT: A.SSE.B.3
The graph has shifted three units to the right.
PTS: 2
REF: 061525ai
NAT: F.BF.B.3
122 ANS: 2
PTS: 2
REF: 081516ai
TOP: Graphing Piecewise-Defined Functions
123 ANS:
8m2 + 20m − 12 = 0
TOP: Graphing Absolute Value Functions
NAT: F.IF.C.7
KEY: bimodalgraph
4(2m2 + 5m − 3) = 0
(2m − 1)(m + 3) = 0
m=
1
,−3
2
PTS: 2
REF: fall1305ai
NAT: A.SSE.B.3
TOP: Solving Quadratics
124 ANS:
Graph A is a good fit because it does not have a clear pattern, whereas Graph B does.
PTS: 2
REF: 061531ai
NAT: S.ID.B.6
TOP: Residuals
ID: A
125 ANS: 2
d=
1 2
at
2
2d = at 2
2d
= t2
a
2d
=t
a
PTS: 2
REF: 061519ai
NAT: A.CED.A.4
126 ANS: 2
PTS: 2
REF: 081422ai
TOP: Graphing Piecewise-Defined Functions
127 ANS:
2p + 3d = 18.25 4p + 6d = 36.50 4p + 2(2.25) = 27.50
4p + 2d = 27.50 4p + 2d = 27.50
4d = 9
TOP: Transforming Formulas
NAT: F.IF.C.7
4p = 23
p = 5.75
d = 2.25
PTS: 2
128 ANS: 4
y + 3 = 6(0)
REF: 011533ai
NAT: A.CED.A.3
TOP: Modeling Linear Systems
REF: 011509ai
NAT: F.IF.B.4
TOP: Graphing Linear Functions
y = −3
PTS: 2
129 ANS:
PTS: 2
REF: fall1304ai
NAT: F.IF.C.7
TOP: Graphing Root Functions
130 ANS:
r ≈ 0.94. The correlation coefficient suggests that as calories increase, so does sodium.
PTS:
131 ANS:
TOP:
132 ANS:
TOP:
4
REF: 011535ai
4
PTS: 2
Families of Functions
2
PTS: 2
Modeling Linear Functions
NAT: S.ID.C.8
REF: 061406ai
TOP: Correlation Coefficient
NAT: F.LE.A.1
REF: 011501ai
NAT: F.LE.B.5
ID: A
133 ANS:
Based on the residual plot, the equation is a good fit for the data
y = 6.32x + 22.43
because the residual values are scattered without a pattern and are fairly evenly distributed above and below the
x-axis.
PTS: 4
REF: fall1314ai
134 ANS: 2
PTS: 2
TOP: Families of Functions
135 ANS:
NAT: S.ID.B.6
REF: 061513ai
C (x) =
TOP: Residuals
NAT: F.LE.A.2
10
10
x 180 =
x
3
3
540 = 10x
54 = x
PTS: 4
REF: fall1308ai
NAT: A.CED.A.2
136 ANS: 4
f(1) = 3; f(2) = −5; f(3) = 11; f(4) = −21; f(5) = 43
TOP: Graphing Linear Functions
PTS:
KEY:
137 ANS:
TOP:
NAT: F.IF.A.3
TOP: Sequences
REF: 081515ai
KEY: AI
NAT: F.IF.B.6
2
REF: 081424ai
term
1
PTS: 2
Rate of Change
ID: A
138 ANS:
PTS: 2
139 ANS: 3
REF: 011530ai
NAT: F.IF.C.7
x
A = 5000(x − 1) + 10000
6
7
8
9
35,000
40,000
45,000
50,000
PTS: 2
REF: 081518ai
140 ANS: 2
PTS: 2
TOP: Modeling Exponential Functions
141 ANS:
1 2
x −4 = 0
2
TOP: Graphing Piecewise-Defined Functions
B = 500(2) x − 1
16,000
32,000
64,000
128,000
NAT: F.LE.A.3
REF: 061517ai
TOP: Families of Functions
NAT: F.LE.B.5
NAT: A.REI.B.4
TOP: Solving Quadratics
x2 − 8 = 0
x2 = 8
x = ±2 2
PTS: 2
REF: fall1306ai
KEY: taking square roots
ID: A
142 ANS:
 1 
12x + 9(2x) + 5(3x) = 15 6   = 2 pounds
 3 
45x = 15
x=
1
3
PTS: 2
143 ANS: 3
h(x) = −x 2 + x + 6
x=
REF: spr1305ai
TOP: Modeling Linear Equations
Maximum of f(x) = 9 k(x) = −5x 2 − 12x + 4
1
−1
=
2(−1) 2
x=
Maximum of g(x) < 5
12
6
= −
2(−5)
5
 6  2
 6 
y = −5  −  − 12  −  + 4
 5
 5
 1  2 1
y = −   + + 6
2
2
1 2
= − + +6
4 4
=6
NAT: A.CED.A.1
= −
1
4
=
36 72 20
+
+
5
5
5
56
5
= 11
1
5
PTS: 2
REF: 061514ai
NAT: F.IF.C.9
KEY: AI
144 ANS: 1
25,000(0.86) 2 − 25,000(0.86) 3 = 18490 − 15901.40 = 2588.60
TOP: Comparing Functions
PTS: 2
REF: 011508ai
NAT: F.IF.A.2
145 ANS: 2
PTS: 2
REF: 061503ai
TOP: Factoring the Difference of Perfect Squares
146 ANS: 3
PTS: 2
REF: 061411ai
TOP: Correlation Coefficient
147 ANS: 4
PTS: 2
REF: 081505ai
TOP: Modeling Linear Inequalities
148 ANS: 1
A: x = 6; σ x = 3.16 B: x = 6.875; σ x = 3.06
TOP:
NAT:
KEY:
NAT:
PTS: 2
149 ANS: 1
4x − 5(0) = 40
Functional Notation
A.SSE.A.2
multivariable AI
S.ID.C.8
NAT: A.CED.A.1
REF: 081519ai
NAT: S.ID.A.2
TOP: Central Tendency and Dispersion
REF: 081408ai
NAT: F.IF.B.4
TOP: Graphing Linear Functions
4x = 40
x = 10
PTS: 2
ID: A
150 ANS: 4
PTS: 2
TOP: Modeling Expressions
151 ANS:
REF: 081503ai
NAT: A.SSE.A.1
PTS: 2
152 ANS:
33 + 12
= 25%
180
REF: 081528ai
NAT: F.IF.B.4
TOP: Relating Graphs to Events
PTS: 2
REF: 011526ai
KEY: two-way
153 ANS: 1
f(x) = (x + 2)(x + 4)(x − 1)
NAT: S.ID.B.5
TOP: Frequency Tables
PTS:
KEY:
154 ANS:
TOP:
155 ANS:
TOP:
156 ANS:
NAT: A.APR.B.3
TOP: Zeros of Polynomials
REF: 081511ai
KEY: mixed
REF: 011523ai
NAT: F.IF.A.1
2
REF: 081504ai
AI
2
PTS: 2
Defining Functions
4
PTS: 2
Modeling Linear Functions
NAT: F.BF.A.1
The graphs of the production costs intersect at x = 3. The company should
use Site A, because the cost of Site A is lower at x = 2 .
PTS: 6
KEY: AI
REF: 061437ai
NAT: A.REI.D.11
TOP: Quadratic-Linear Systems
ID: A
157 ANS: 4
11 − 1
10
m=
=
= 2 y = mx + b y = 2x + 5
3 − (−2)
5
11 = 2(3) + b 9 = 2(2) + 5
5=b
PTS: 2
REF: 011511ai
158 ANS: 1
0.8(10 2 ) − 0.8(5 2 ) 80 − 20
=
= 12
5
10 − 5
NAT: A.REI.D.10
TOP: Identifying Solutions
PTS: 2
KEY: AI
159 ANS: 4
x 2 − 5x = −3
NAT: F.IF.B.6
TOP: Rate of Change
x 2 − 5x +
REF: 011521ai
25 −12 25
=
+
4
4
4

2
 x − 5  = 13

2 
4

PTS: 2
REF: 061518ai
NAT: A.REI.B.4
TOP: Solving Quadratics
KEY: completing the square
160 ANS:
The vertex represents a maximum since a < 0. f(x) = −x 2 + 8x + 9
= −(x 2 − 8x − 9)
= −(x 2 − 8x + 16) + 9 + 16
= −(x − 4) 2 + 25
PTS: 4
161 ANS:
−16t 2 + 64t = 0
REF: 011536ai
NAT: F.IF.C.8
TOP: Vertex Form of a Quadratic
0 ≤ t ≤ 4 The rocket launches at t = 0 and lands at t = 4
−16t(t − 4) = 0
t = 0,4
PTS: 2
REF: 081531ai
NAT: F.IF.B.4
TOP: Graphing Quadratic Functions
KEY: context
162 ANS:
y = 80(1.5) x 80(1.5) 26 ≈ 3,030,140. No, because the prediction at x = 52 is already too large.
PTS: 4
REF: 061536ai
KEY: exponential AI
NAT: S.ID.B.6
TOP: Regression
ID: A
163 ANS:
PTS: 2
164 ANS: 1
9 
7 
= 20
x+


28 
3
REF: 081526ai
NAT: A.REI.D.12
TOP: Graphing Linear Inequalities
3 80
7
x+ =
4
4
3
7
77
x=
3
4
x=
33
= 8.25
4
PTS: 2
REF: 061405ai
NAT: A.REI.B.3
KEY: fractional expressions
165 ANS:
Correct. The sum of a rational and irrational is irrational.
TOP: Solving Linear Equations
PTS: 2
KEY: classify
166 ANS:
TOP: Operations with Radicals
y ≥ 2x − 3 .
PTS: 4
KEY: graph
REF: 011525ai
NAT: N.RN.B.3
Oscar is wrong. (2) + 2(1) < 4 is not true.
REF: 011534ai
NAT: A.REI.D.12
TOP: Graphing Systems of Linear Inequalities
ID: A
167 ANS:
x + y ≤ 15
One hour at school and eleven hours at the library.
4x + 8y ≥ 80
PTS: 6
168 ANS: 4
x 2 − 13x − 30 = 0
REF: 081437ai
NAT: A.CED.A.3
TOP: Modeling Systems of Linear Inequalities
(x − 15)(x + 2) = 0
x = 15,−2
PTS: 2
REF: 061510ai
NAT: A.APR.B.3 TOP: Zeros of Polynomials
KEY: AI
169 ANS: 3
PTS: 2
REF: 081410ai
NAT: F.LE.A.1
TOP: Families of Functions
KEY: bimodalgraph
170 ANS:
(3x 2 − 2x + 5) − (x 2 + 3x − 2) = 2x 2 − 5x + 7
5
7
1 2 2
x (2x − 5x + 7) = x 4 − x 3 + x 2
2
2
2
PTS: 2
REF: 061528ai
KEY: multiplication
171 ANS: 2
y = (x − 3)(x + 2)(x − 1)
NAT: A.APR.A.1
TOP: Operations with Polynomials
PTS: 2
REF: 061512ai
KEY: AI
172 ANS: 4
There are no negative or fractional cars.
NAT: A.APR.B.3
TOP: Zeros of Polynomials
NAT: F.IF.B.5
TOP: Domain and Range
PTS: 2
REF: 061402ai
ID: A
173 ANS:
A combination of 2 printers and 10 computers meets all the constraints
because (2,10) is in the solution set of the graph.
PTS: 4
REF: 061535ai
174 ANS: 3
PTS: 2
TOP: Defining Functions
175 ANS:
y = 0.05x − 0.92
NAT: A.CED.A.3 TOP: Modeling Systems of Linear Inequalities
REF: 061504ai
NAT: F.IF.A.1
KEY: ordered pairs
PTS: 2
REF: fall1307ai
NAT: S.ID.B.6
KEY: linear
176 ANS:
y = 0.16x + 8.27 r = 0.97, which suggests a strong association.
TOP: Regression
PTS: 4
REF: 081536ai
KEY: linear with correlation coefficient
177 ANS: 4
PTS: 2
TOP: Modeling Linear Equations
178 ANS: 4
16 2t = n 4t
NAT: S.ID.B.6
TOP: Regression
REF: 061422ai
NAT: A.CED.A.3
NAT: A.SSE.B.3
TOP: Modeling Exponential Functions
(16 2 ) t = (n 4 ) t
((4 2 ) 2 ) t = ((n 2 ) 2 ) t
PTS: 2
KEY: AI
179 ANS:
REF: 011519ai
g. The maximum of f is 6. For g, the maximum is 11. x =
−b
−4
−4
=   =
=4
2a
 1  −1
2  − 
 2
1
y = − (4) 2 + 4(4) + 3 = −8 + 16 + 3 = 11
2
PTS: 2
KEY: AI
REF: 081429ai
NAT: F.IF.C.9
TOP: Comparing Functions
ID: A
180 ANS:
TOP:
181 ANS:
TOP:
182 ANS:
TOP:
183 ANS:
4
PTS: 2
REF: 081419ai
NAT: A.CED.A.3
Modeling Linear Systems
4
PTS: 2
REF: 011514ai
NAT: S.ID.A.2
Central Tendency and Dispersion
1
PTS: 2
REF: 081415ai
NAT: A.SSE.A.2
Factoring Polynomials
KEY: higher power AI
2
L + S = 20
27.98L + 10.98(20 − L) = 355.60
27.98L + 10.98S = 355.60 27.98L + 219.60 − 10.98L = 355.60
17L = 136
L=8
PTS: 2
REF: 081510ai
184 ANS: 3
Median remains at 1.4.
NAT: A.CED.A.3
TOP: Modeling Linear Systems
PTS: 2
185 ANS:
NAT: S.ID.A.3
TOP: Central Tendency and Dispersion
REF: 061520ai
The line is a poor fit because the residuals form a pattern.
PTS: 2
REF: 081431ai
186 ANS: 3
PTS: 2
TOP: Sequences
187 ANS: 3
PTS: 2
TOP: Modeling Linear Functions
188 ANS: 1
x 2 − 8x + 16 = 24 + 16
NAT: S.ID.B.6
REF: 061522ai
TOP: Residuals
NAT: F.LE.A.2
REF: 061407ai
NAT: F.LE.B.5
NAT: A.REI.B.4
TOP: Solving Quadratics
(x − 4) 2 = 40
x − 4 = ± 40
x = 4 ± 2 10
PTS: 2
REF: 061523ai
KEY: completing the square
ID: A
189 ANS: 2
0 = −16t 2 + 144
16t 2 = 144
t2 = 9
t=3
PTS: 2
190 ANS:
REF: 081423ai
NAT: F.IF.B.5
TOP: Domain and Range
2
 6 
Since (x + p) 2 = x 2 + 2px + p 2 , p is half the coefficient of x, and the constant term is equal to p 2 .   = 9
2
191
192
193
194
195
196
197
PTS: 2
REF: 081432ai
KEY: completing the square
ANS: 4
PTS: 2
TOP: Modeling Linear Equations
ANS: 3
PTS: 2
TOP: Solving Quadratics
ANS: 2
PTS: 2
TOP: Operations with Radicals
ANS: 2
PTS: 2
TOP: Sequences
ANS: 3
PTS: 2
TOP: Graphing Quadratic Functions
ANS: 4
PTS: 2
TOP: Domain and Range
ANS:
A = 600(1.016) 2 ≈ 619.35
PTS: 2
REF: 061529ai
198 ANS: 3
36.6 − 15 21.6
=
= 5.4
4−0
4
PTS: 2
KEY: AI
REF: 061511ai
NAT: A.REI.B.4
TOP: Solving Quadratics
REF: 081508ai
NAT: A.CED.A.3
REF:
KEY:
REF:
KEY:
REF:
081403ai
NAT: A.REI.B.4
taking square roots
061508ai
NAT: N.RN.B.3
classify
081416ai
NAT: F.LE.A.2
REF:
KEY:
REF:
KEY:
061409ai
NAT: F.IF.B.4
context
061417ai
NAT: F.IF.A.2
real domain, linear
NAT: A.CED.A.1
TOP: Modeling Exponential Functions
NAT: F.IF.B.6
TOP: Rate of Change
ID: A
199 ANS:
x = −2,1
PTS: 4
KEY: AI
200 ANS:
−2x 2 + 6x + 4
REF: 081435ai
NAT: A.REI.D.11
TOP: Quadratic-Linear Systems
PTS: 2
REF: 011528ai
NAT: A.APR.A.1 TOP: Operations with Polynomials
KEY: subtraction
201 ANS:
c + d = 22
2.35c + 5.50d = 89.50 Pat’s numbers are not possible: 2.35(8) + 5.50(14) ≠ 89.50
18.80 + 77.00 ≠ 89.50 2.35c + 5.50(22 − c) = 89.50
95.80 ≠ 89.50 2.35c + 121 − 5.50c = 89.50
−3.15c = −31.50
c = 10
PTS: 4
REF: 061436ai
202 ANS: 2
1
1 1 5
1
+
= + =
9 2 3 6
4
PTS: 2
KEY: classify
REF: 081522ai
NAT: A.CED.A.3
TOP: Modeling Linear Systems
NAT: N.RN.B.3
TOP: Operations with Radicals
ID: A
203 ANS: 4
2
−(−1)
g(1) − g(−1) 4 − 6 −2
 1 
1  1 
1
1
= − ; g  −  =−  −  + + 6 = 6
=
=
= −1 2) g(0) = 6 3) x =
1)
2
2
2(−1)
2  2
2
4
1 − −1
2
 
n(0) = 8
n(1) − n(−1) 9 − 5 4
x = 1; n(1) = 9
=
= =2
1 − −1
2
2
−(−1)
= −1
4) g:S =
−1
n: S = −2 + 4 = 2
PTS: 2
KEY: AI
204 ANS: 2
REF: 081521ai
NAT: F.IF.C.9
TOP: Comparing Functions
1
(4,3) is on the boundary of y > − x + 5, so (4,3) is not a solution of the system.
2
PTS:
KEY:
205 ANS:
TOP:
206 ANS:
TOP:
207 ANS:
2
REF: fall1301ai
solution set
3
PTS: 2
Solving Quadratics
2
PTS: 2
Operations with Polynomials
1
1
V = πr 2 h
3
NAT: A.REI.D.12
TOP: Graphing Systems of Linear Inequalities
REF: 061412ai
NAT: A.SSE.B.3
REF: 061403ai
KEY: subtraction
NAT: A.APR.A.1
NAT: A.CED.A.4
TOP: Transforming Formulas
NAT: A.REI.B.3
TOP: Solving Linear Equations
3V = π r 2 h
3V
= r2
πh
3V
=r
πh
PTS: 2
208 ANS: 1
x−2 4
=
6
3
REF: 061423ai
6x − 12 = 12
6x = 24
x=4
PTS: 2
REF: 081420ai
KEY: fractional expressions
ID: A
Algebra I Common Core State Standards Regents at Random Worksheets
Answer Section
209 ANS: 2
PTS: 2
REF: 081620ai
TOP: Domain and Range
210 ANS: 3
C(t) = 10(1.029) 24t = 10(1.029 24 ) t ≈ 10(1.986) t
NAT: F.IF.B.5
PTS: 2
REF: 061614ai
NAT: A.SSE.B.3
TOP: Modeling Exponential Functions
KEY: AI
211 ANS: 3
median = 3, IQR = 4 − 2 = 2, x = 2.75. An outlier is outside the interval [Q 1 − 1.5(IQR),Q 3 + 1.5(IQR)].
[2 − 1.5(2),4 + 1.5(2)]
[-1,7]
PTS:
212 ANS:
TOP:
213 ANS:
2
REF: 061620ai
1
PTS: 2
Operations with Radicals
3
PTS: 2
214 ANS: 2
REF: 061621ai
NAT: S.ID.A.1
REF: 011604ai
KEY: classify
TOP: Dot Plots
NAT: N.RN.B.3
NAT: F.LE.A.3
TOP: Families of Functions
f(x) = x 2 + 2x − 8 = x 2 + 2x + 1 − 9 = (x + 1) 2 − 9
PTS: 2
REF: 061611ai
NAT: F.IF.A.2
TOP: Domain and Range
KEY: real domain, quadratic
215 ANS:
1 − 0.85 = 0.15 = 15% To find the rate of change of an equation in the form y = ab x , subtract b from 1.
PTS: 2
REF: 061728ai
NAT: F.LE.B.5
TOP: Modeling Exponential Functions
ID: A
216 ANS:
m
70
=
351 70 + 35
105m = 24570
m = 234
PTS: 2
KEY: two-way
217 ANS: 3
x=3
REF: 011630ai
NAT: S.ID.B.5
TOP: Frequency Tables
PTS: 2
REF: 061717ai
NAT: F.IF.C.9
KEY: AI
218 ANS:
Linear, because the function has a constant rate of change.
TOP: Comparing Functions
PTS: 2
REF: 011625ai
219 ANS: 3
1, 3, 6, 10, 15, 21, 28, ...
TOP: Families of Functions
NAT: F.LE.A.1
PTS: 2
REF: 081715ai
NAT: F.IF.A.3
KEY: term
220 ANS: 2
V = 15,000(0.81) t = 15,000((0.9) 2 ) t = 15,000(0.9) 2t
TOP: Sequences
PTS: 2
REF: 081716ai
NAT: A.SSE.B.3
221 ANS:
 0.62 m 
 = 7.44 m 26.2 m ≈ 3.5 hours
12 km

1
km
7.44 mph


TOP: Modeling Exponential Functions
PTS: 2
REF: 011726ai
KEY: dimensional analysis
222 ANS:
TOP: Conversions
1.25x + 2.5y = 25
NAT: N.Q.A.1
There are 11 combinations, as each dot represents a possible combination.
x + 2y = 20
PTS: 6
REF: 081737ai
NAT: A.REI.C.6
TOP: Graphing Linear Systems
ID: A
223 ANS:
Two of the following: quadratic formula, complete the square, factor by grouping or graphically.
x=
−16 ±
16 2 − 4(4)(9) −16 ± 112
=
≈ −0.7,−3.3
2(4)
8
PTS: 4
REF: 011634ai
KEY: quadratic formula
224 ANS: 2
PTS: 2
TOP: Modeling Exponential Functions
225 ANS: 3
PTS: 2
TOP: Zeros of Polynomials
226 ANS: 3
j(x) = x 2 − 12x + 36 + 7 − 36
NAT: A.REI.B.4
TOP: Solving Quadratics
REF: 061617ai
NAT: F.BF.A.1
REF: 061710ai
NAT: A.APR.B.3
= (x − 6) 2 − 29
PTS:
227 ANS:
TOP:
228 ANS:
TOP:
229 ANS:
TOP:
230 ANS:
TOP:
231 ANS:
2
REF: 061616ai
NAT: F.IF.C.8
TOP:
2
PTS: 2
REF: 061624ai
NAT:
Families of Functions
2
PTS: 2
REF: 061604ai
NAT:
Correlation Coefficient
2
PTS: 2
REF: 011717ai
NAT:
Graphing Polynomial Functions
3
PTS: 2
REF: 081614ai
NAT:
Modeling Linear Equations
4
5
8
6−1
14 − 6
24 − 14
=
≈.07 (2)
=
≈.57 (3)
(1)
1971 − 1898 73
1985 − 1971 14
2006 − 1985
PTS: 2
REF: 011613ai
KEY: AI
232 ANS: 3
3(x 2 + 4x + 4) − 12 + 11
NAT: F.IF.B.6
Vertex Form of a Quadratic
F.LE.A.1
S.ID.C.8
F.BF.B.3
A.CED.A.1
=
10
11
35 − 24
≈.48 (4)
=
≈ 1.83
21
6
2012 − 2006
TOP: Rate of Change
3(x + 2) 2 − 1
PTS: 2
REF: 081621ai
NAT: F.IF.C.8
TOP: Vertex Form of a Quadratic
233 ANS:
7 2 is irrational because it can not be written as the ratio of two integers.
PTS: 2
KEY: classify
REF: 081629ai
NAT: N.RN.B.3
TOP: Operations with Radicals
ID: A
234 ANS:
4ax + 12 − 3ax = 25 + 3a
ax = 13 + 3a
x=
13 + 3a
a
PTS: 2
REF: 081632ai
235 ANS: 4
PTS: 2
TOP: Modeling Linear Functions
236 ANS:
x2 = x
NAT: A.CED.A.4
REF: 081709ai
TOP: Transforming Formulas
NAT: F.LE.B.5
x2 − x = 0
x(x − 1) = 0
x = 0,1
PTS: 2
REF: 061731ai
NAT: A.REI.D.11
KEY: AI
237 ANS:
g(x) = x 3 + 2x 2 − 4 , because g(x) is a translation down 4 units.
238
239
240
241
242
TOP: Quadratic-Linear Systems
PTS: 2
REF: 061632ai
NAT: F.BF.B.3
TOP: Graphing Polynomial Functions
ANS: 4
PTS: 2
REF: 061623ai
NAT: F.IF.B.5
TOP: Domain and Range
ANS: 3
PTS: 2
REF: 061601ai
NAT: A.SSE.A.2
TOP: Factoring the Difference of Perfect Squares
KEY: higher power AI
ANS: 1
PTS: 2
REF: 011708ai
NAT: F.LE.A.2
TOP: Sequences
ANS: 2
PTS: 2
REF: 011605ai
NAT: A.REI.D.12
TOP: Graphing Linear Inequalities
ANS:
The slope represents the amount paid each month and the y-intercept represents the initial cost of membership.
PTS: 2
REF: 011629ai
243 ANS: 3
PTS: 2
TOP: Comparing Functions
244 ANS: 1
f(x) = x 2 − 5x − 6 = (x + 1)(x − 6) = 0
NAT: F.LE.B.5
REF: 011622ai
KEY: AI
TOP: Modeling Linear Functions
NAT: F.IF.C.9
NAT: A.APR.B.3
TOP: Zeros of Polynomials
x = −1,6
PTS: 2
KEY: AI
REF: 061612ai
ID: A
245 ANS: 2
x 2 − 8x + 16 = 10 + 16
(x − 4) 2 = 26
x − 4 = ± 26
x = 4±
246
247
248
249
26
PTS: 2
REF: 061722ai
KEY: completing the square
ANS: 2
PTS: 2
TOP: Modeling Linear Functions
ANS: 3
PTS: 2
TOP: Modeling Exponential Functions
ANS: 1
PTS: 2
TOP: Modeling Exponential Functions
ANS:
480 − 140
= 68 mph
7−2
PTS: 2
REF: 011731ai
250 ANS: 2
16x 2 − 36 = 4(2x + 3)(2x − 3)
NAT: A.REI.B.4
TOP: Solving Quadratics
REF: 011709ai
NAT: F.LE.B.5
REF: 011724ai
NAT: F.LE.B.5
REF: 081617ai
KEY: AI
NAT: F.LE.A.2
NAT: F.IF.B.6
TOP: Rate of Change
PTS: 2
REF: 011701ai
NAT: A.SSE.A.2
TOP: Factoring the Difference of Perfect Squares
251 ANS: 2
PTS: 2
REF: 081708ai
TOP: Analysis of Data
252 ANS:
12x + 8.50(50) ≥ 1000
x + y ≤ 200
12x + 8.50y ≥ 1000
KEY: quadratic
NAT: S.ID.C.9
12x + 425 ≥ 1000
12x ≥ 575
x≥
575
12
48
PTS: 4
REF: 081635ai
253 ANS: 1
PTS: 2
TOP: Families of Functions
NAT: A.CED.A.3
REF: 081618ai
TOP: Modeling Systems of Linear Inequalities
NAT: F.LE.A.3
ID: A
254 ANS:
x + y ≤ 200 Marta is incorrect because 12.5(30) + 6.25(80) < 1500
12.5x + 6.25y ≥ 1500
375 + 500 < 1500
875 < 1500
PTS: 6
REF: 011637ai
NAT: A.REI.D.12 TOP: Graphing Systems of Linear Inequalities
KEY: graph
255 ANS:
5x + 4x 2 (2x + 7) − 6x 2 − 9x = −4x + 8x 3 + 28x 2 − 6x 2 = 8x 3 + 22x 2 − 4x
PTS: 2
REF: 081731ai
NAT: A.APR.A.1 TOP: Operations with Polynomials
KEY: multiplication
256 ANS:
2x 2 + 5x − 42 = 0
Agree, as shown by solving the equation by factoring.
(x + 6)(2x − 7) = 0
x = −6,
7
2
PTS: 2
KEY: factoring
257 ANS: 4
36x + 30y = 96
REF: 061628ai
NAT: A.REI.B.4
TOP: Solving Quadratics
PTS: 2
258 ANS:
REF: 081724ai
NAT: A.REI.C.5
TOP: Solving Linear Systems
NAT: A.REI.D.12
TOP: Graphing Linear Inequalities
y < −2x + 4
PTS: 2
REF: 061730ai
ID: A
259 ANS:
S
= n −2
180
S
+2= n
180
PTS: 2
260 ANS:
261
262
263
264
265
266
PTS:
ANS:
TOP:
ANS:
TOP:
ANS:
TOP:
ANS:
TOP:
ANS:
TOP:
ANS:
REF: 061631ai
NAT: A.CED.A.4
4
REF: 081634ai
NAT:
4
PTS: 2
REF:
Modeling Expressions
3
PTS: 2
REF:
Defining Functions
KEY:
3
PTS: 2
REF:
Modeling Linear Equations
1
PTS: 2
REF:
Modeling Linear Systems
4
PTS: 2
REF:
Conversions KEY: dimensional analysis
A.REI.D.12
061602ia
TOP: Transforming Formulas
TOP: Graphing Linear Inequalities
NAT: A.SSE.A.1
061709ai
NAT: F.IF.A.1
ordered pairs
081616ai
NAT: A.CED.A.1
061605ai
NAT: A.CED.A.3
061720ai
NAT: N.Q.A.1
No, (3,7) is on the boundary line, and not included in the solution set, because this is a
strict inequality.
PTS:
KEY:
267 ANS:
TOP:
4
REF: 081735ai
graph
4
PTS: 2
Identifying Properties
NAT: A.REI.D.12
TOP: Graphing Systems of Linear Inequalities
REF: 081701ai
NAT: A.REI.A.1
ID: A
268 ANS:
(6,2) is not a solution as its falls on the edge of each inequality.
PTS: 4
REF: 061634ai
NAT: A.REI.D.12
KEY: graph
269 ANS: 2
PTS: 2
REF: 011714ai
TOP: Modeling Exponential Functions
270 ANS:
The data is continuous, i.e. a fraction of a cookie may be eaten.
271
272
273
274
275
PTS: 2
REF: 081729ai
ANS: 4
PTS: 2
TOP: Box Plots
KEY: interpret
ANS: 2
PTS: 2
TOP: Vertex Form of a Quadratic
ANS: 2
PTS: 2
TOP: Graphing Linear Functions
ANS: 2
PTS: 2
TOP: Modeling Expressions
ANS: 2
14
= 28%
16 + 20 + 14
PTS: 2
REF: 011705ai
KEY: two-way
276 ANS: 1
PTS: 2
TOP: Zeros of Polynomials
277 ANS:
y 2 − 6y + 9 = 4y − 12
TOP: Graphing Systems of Linear Inequalities
NAT: A.SSE.B.3
NAT: F.IF.B.4
REF: 081603ai
TOP: Graphing Linear Functions
NAT: S.ID.A.1
REF: 011601ai
NAT: F.IF.C.8
REF: 011602ai
NAT: A.CED.A.2
REF: 081712ai
NAT: A.SSE.A.1
NAT: S.ID.B.5
TOP: Frequency Tables
REF: 081707ai
KEY: AI
NAT: A.APR.B.3
NAT: A.REI.B.4
TOP: Solving Quadratics
y 2 − 10y + 21 = 0
(y − 7)(y − 3) = 0
y = 7,3
PTS: 2
KEY: factoring
REF: 011627ai
ID: A
278 ANS:
H(1) − H(2) = −16(1) 2 + 144 − (−16(2) 2 + 144) = 128 − 80 = 48
−16t 2 = −144
t2 = 9
t=3
PTS:
KEY:
279 ANS:
TOP:
280 ANS:
TOP:
281 ANS:
−3,1
4
REF: 061633ai
taking square roots
4
PTS: 2
Solving Linear Systems
4
PTS: 2
Families of Functions
PTS: 2
REF: 081630ai
KEY: AI
282 ANS: 1
PTS: 2
TOP: Domain and Range
283 ANS: 4
2(2) < −12(−3) + 4 4 < −6(−3) + 4
4 < 40
NAT: A.REI.B.4
TOP: Solving Quadratics
REF: 081622ai
NAT: A.REI.C.5
REF: 011616ai
NAT: F.LE.A.2
NAT: A.REI.D.11
TOP: Other Systems
REF: 081710ai
NAT: F.IF.A.2
KEY: limited domain
4 < 22
PTS: 2
REF: 011716ai
NAT: A.REI.D.12 TOP: Graphing Systems of Linear Inequalities
KEY: solution set
284 ANS:
0 = (B + 3)(B − 1) Janice substituted B for 8x, resulting in a simpler quadratic. Once factored, Janice substituted
0 = (8x + 3)(8x − 1)
3 1
x= − ,
8 8
8x for B.
PTS: 4
REF: 081636ai
NAT: A.SSE.B.3
TOP: Solving Quadratics
285 ANS:
3 2 ⋅ 8 18 = 24 36 = 144 is rational, as it can be written as the ratio of two integers.
PTS:
KEY:
286 ANS:
TOP:
287 ANS:
TOP:
288 ANS:
TOP:
2
REF: 061626ai
NAT:
classify
2
PTS: 2
REF:
Families of Functions
KEY:
3
PTS: 2
REF:
Factoring Polynomials
KEY:
2
PTS: 2
REF:
Geometric Applications of Quadratics
N.RN.B.3
TOP: Operations with Radicals
081714ai
NAT: F.LE.A.2
AI
011612ai
NAT: A.SSE.A.2
higher power AI
011611ai
NAT: A.CED.A.1
ID: A
289 ANS: 3
2(x + 2) 2 = 32
(x + 2) 2 = 16
x + 2 = ±4
x = −6,2
PTS: 2
REF: 061619ai
NAT: A.REI.B.4
KEY: taking square roots
290 ANS:
No, because the relation does not pass the vertical line test.
TOP: Solving Quadratics
PTS: 2
KEY: graphs
291 ANS:
TOP: Defining Functions
REF: 011626ai
NAT: F.IF.A.1
PTS: 2
REF: 011729ai
NAT: A.REI.D.12
292 ANS: 3
PTS: 2
REF: 081602ai
TOP: Identifying Solutions
293 ANS: 1
The graph is steepest between hour 0 and hour 1.
TOP: Graphing Linear Inequalities
NAT: A.REI.D.10
PTS: 2
REF: 081601ai
NAT: F.IF.B.6
TOP: Rate of Change
KEY: AI
294 ANS: 2
PTS: 2
REF: 011619ai
NAT: F.IF.A.2
TOP: Domain and Range
KEY: real domain, exponential
295 ANS: 2
f(1) = 2 ; f(2) = −5(2) + 2 = −8; f(3) = −5(−8) + 2 = 42; f(4) = −5(42) + 2 = −208
PTS: 2
REF: 061718ai
KEY: term
296 ANS: 1
PTS: 2
TOP: Zeros of Polynomials
297 ANS:
There is 2 inches of snow every 4 hours.
NAT: F.IF.A.3
TOP: Sequences
REF: 081623ai
KEY: AI
NAT: A.APR.B.3
PTS: 2
REF: 061630ai
298 ANS: 1
PTS: 2
TOP: Rate of Change
NAT: S.ID.C.7
REF: 011721ai
TOP: Modeling Linear Functions
NAT: F.IF.B.6
ID: A
299 ANS:
108 = x(24 − x) 18 × 6
108 = 24x − x 2
x 2 − 24x + 108 = 0
(x − 18)(x − 6) = 0
x = 18,6
PTS: 4
REF: 011636ai
NAT: A.CED.A.1 TOP: Geometric Applications of Quadratics
300 ANS:
−128
x=
= 4 h(4) = −16(4) 2 + 128(4) + 9000 = −256 + 512 + 9000 = 9256 (4,9256). The y coordinate represents
2(−16)
the pilot’s height above the ground after ejection. 9256 − 9000 = 256
PTS: 4
REF: 081736ai
NAT: F.IF.B.4
KEY: context
301 ANS: 3
PTS: 2
REF: 011704ai
TOP: Transforming Formulas
302 ANS:
g(x) is f(x) shifted right by a, h(x) is f(x) shifted down by a.
TOP: Graphing Quadratic Functions
PTS: 2
303 ANS:
x 2 + 3x − 18 = 0
TOP: Graphing Absolute Value Functions
REF: 061732ai
NAT: F.BF.B.3
NAT: A.CED.A.4
The zeros are the x-intercepts of r(x).
(x + 6)(x − 3) = 0
x = −6,3
PTS: 4
304 ANS:
REF: 061733ai
NAT: A.SSE.B.3
TOP: Solving Quadratics
1, because the graphs only intersect once.
PTS: 4
KEY: AI
REF: 061636ai
NAT: A.REI.D.11
TOP: Other Systems
ID: A
305 ANS: 2
|x − 3 | + 1 = 2x + 1 x − 3 = 2x
|x − 3 | =2x
−3 = x
extraneous
PTS: 2
KEY: AI
306 ANS:
I = 1000 − 60x
REF: 061622ai
NAT: A.REI.D.11
x − 3 = −2x
3x = 3
x=1
TOP: Other Systems
. x = 10 . 1000 − 60(10) = 400. Ian is incorrect because I = 1000 − 6(16) = 40 ≠ 0
K = 600 − 20x
1000 − 60x = 600 − 20x
PTS: 6
REF: 011737ai
NAT: A.CED.A.3 TOP: Modeling Linear Systems
307 ANS:
7 − 2 is irrational because it can not be written as the ratio of two integers.
PTS: 2
REF: 061727ai
KEY: classify
308 ANS: 1
1
1
x + 3 = |x | − x − 3 = x
2
2
1
x+3 = x
2
x + 6 = 2x
6=x
NAT: N.RN.B.3
TOP: Operations with Radicals
−x − 6 = 2x
−6 = 3x
−2 = x
PTS: 2
REF: 011617ai
NAT: A.REI.D.11 TOP: Other Systems
KEY: AI
309 ANS:
f(x) = 10 + 100x , g(x) = 10(2) x ; both, since f(7) = 10 + 100(7) = 710 and g(7) = 10(2) 7 = 1280
PTS: 4
REF: 061736ai
NAT: F.LE.A.3
310 ANS:
y = 17.159x − 2.476. y = 17.159(.65) − 2.476 ≈ 8.7
PTS: 4
KEY: linear
REF: 081633ai
NAT: S.ID.B.6
TOP: Families of Functions
TOP: Regression
ID: A
311 ANS:
During 1960-1965 the graph has the steepest slope.
PTS: 2
REF: 011628ai
NAT: F.IF.B.6
KEY: AI
312 ANS:
C = 1.29 +.99(s − 1) No, because C = 1.29 +.99(52 − 1) = 51.78
TOP: Rate of Change
PTS: 2
REF: 011730ai
NAT: A.CED.A.2
313 ANS:
No, −2 is the coefficient of the term with the highest power.
TOP: Modeling Linear Equations
PTS: 2
314 ANS:
V=
REF: 081628ai
NAT: A.SSE.A.1
TOP: Modeling Expressions
REF: 081727ai
NAT: A.CED.A.4
TOP: Transforming Formulas
1 2
πr h
3
3V = π r 2 h
3V
= r2
πh
3V
=r
πh
PTS: 2
315 ANS: 4
5 − 4.6 .4
=
= 0.2 4(0.2x + 4.2) + 2x = 33.6 y = 0.2(6) + 4.2 = 5.4
4−2
2
0.8x + 16.8 + 2x = 33.6
5 =.2(4) + b
2.8x = 16.8
4.2 = b
x=6
y = 0.2x + 4.2
m=
PTS:
KEY:
316 ANS:
TOP:
317 ANS:
TOP:
2
REF: 061618ai
substitution
3
PTS: 2
Families of Functions
4
PTS: 2
Solving Linear Systems
NAT: A.REI.C.6
TOP: Solving Linear Systems
REF: 011711ai
NAT: F.LE.A.1
REF: 011621ai
NAT: A.REI.C.5
ID: A
318 ANS:
a + b is irrational because it cannot be written as the ratio of two integers. b + c is rational because it can be
35
written as the ratio of two integers, .
2
PTS: 2
REF: 081725ai
NAT: N.RN.B.3
KEY: classify
319 ANS: 2
PTS: 2
REF: 061702ai
TOP: Dependent and Independent Variables
320 ANS: 4
2(3g − 4) − (8g + 3) = 6g − 8 − 8g − 3 = −2g − 11
TOP: Operations with Radicals
NAT: A.SSE.A.1
PTS: 2
REF: 011707ai
NAT: A.APR.A.1 TOP: Operations with Polynomials
KEY: subtraction
321 ANS: 3
PTS: 2
REF: 061701ai
NAT: F.IF.B.4
TOP: Relating Graphs to Events
322 ANS:
g(x) = 2(2x + 1) 2 − 1 = 2(4x 2 + 4x + 1) − 1 = 8x 2 + 8x + 2 − 1 = 8x 2 + 8x + 1
PTS: 2
323 ANS: 1
2x 2 − 4x − 6 = 0
REF: 061625ai
NAT: F.IF.A.2
TOP: Functional Notation
NAT: A.SSE.B.3
REF: 081723ai
TOP: Solving Quadratics
NAT: A.CED.A.1
REF: 061721ai
NAT: F.LE.A.1
NAT: A.SSE.B.3
TOP: Modeling Exponential Functions
2(x 2 − 2x − 3) = 0
2(x − 3)(x + 1) = 0
x = 3,−1
PTS: 2
REF: 011609ai
324 ANS: 4
PTS: 2
TOP: Modeling Quadratics
325 ANS: 3
PTS: 2
TOP: Families of Functions
326 ANS:
f(5) = (8) ⋅ 2 5 = 256
f(t) = g(t)
g(5) = 2 5 + 3 = 256
(8) ⋅ 2 t = 2 t + 3
23 ⋅ 2t = 2t + 3
2t + 3 = 2t + 3
PTS: 2
KEY: AI
REF: 011632ai
ID: A
327 ANS:
y = 10x + 5
In 2016, the swim team and chorus will each have 65 members.
y = 5x + 35
PTS: 6
REF: 061737ai
NAT: A.REI.C.6
328 ANS:
4−1
3
1
m=
=
= − y − y 1 = m(x − x 1 )
−3 − 6 −9
3
1
1
y − 4 = − (x + 3)
4 = − (−3) + b
3
3
TOP: Graphing Linear Systems
4 = 1+b
3=b
1
y = − x+3
3
PTS: 2
REF: 061629ai
NAT: A.REI.D.10
KEY: other forms
329 ANS: 2
36x 2 − 100 = 4(9x 2 − 25) = 4(3x + 5)(3x − 5)
PTS: 2
REF: 081608ai
NAT: A.SSE.A.2
TOP: Factoring the Difference of Perfect Squares
330 ANS: 1
3(−2x + 2x + 8) = 12
TOP: Writing Linear Equations
KEY: quadratic
24 ≠ 12
PTS: 2
REF: 061708ai
NAT: A.REI.C.6
TOP: Solving Linear Systems
KEY: substitution
331 ANS: 3
(2x + 3)(4x 2 − 5x + 6) = 8x 3 − 10x 2 + 12x + 12x 2 − 15x + 18 = 8x 3 + 2x 2 − 3x + 18
PTS: 2
REF: 081612ai
KEY: multiplication
NAT: A.APR.A.1
TOP: Operations with Polynomials
ID: A
332 ANS: 2
3(x 2 − 1) − (x 2 − 7x + 10)
3x 2 − 3 − x 2 + 7x − 10
2x 2 + 7x − 13
PTS: 2
REF: 061610ai
NAT: A.APR.A.1 TOP: Operations with Polynomials
KEY: subtraction
333 ANS: 3
PTS: 2
REF: 061723ai
NAT: A.CED.A.4
TOP: Transforming Formulas
334 ANS: 3
3 − −7
m=
= −5 3 = (−5)(2) + b y = −5x + 13 represents the line passing through the points (2,3) and (4,−7). The
2−4
b = 13
fourth equation may be rewritten as y = 5x − 13, so is a different line.
PTS:
KEY:
335 ANS:
TOP:
336 ANS:
TOP:
337 ANS:
2
REF: 081720ai
other forms
4
PTS: 2
Correlation Coefficient
3
PTS: 2
Solving Quadratics
NAT: A.REI.D.10
TOP: Writing Linear Equations
REF: 011703ai
NAT: S.ID.C.8
REF: 011702ai
NAT: A.SSE.B.3
Yes, because the graph of f(x) intersects the graph of g(x) at x = −2.
PTS: 4
REF: 011733ai
NAT: A.REI.D.11
KEY: AI
338 ANS: 3
E(10) = 1(1.11) 10 ≈ 3 S(10) = 30(1.04) 10 ≈ 44
TOP: Other Systems
E(53) = 1(1.11) 53 ≈ 252 S(53) = 30(1.04) 53 ≈ 239
PTS:
339 ANS:
TOP:
340 ANS:
TOP:
2
REF: 081721ai
1
PTS: 2
Graphing Polynomial Functions
4
PTS: 2
Modeling Expressions
NAT: F.LE.A.2
REF: 081706ai
TOP: Modeling Exponential Functions
NAT: F.BF.B.3
REF: 011718ai
NAT: A.SSE.A.1
ID: A
341 ANS:
The ball reaches a maximum height of 55 units at 2.5 seconds.
PTS: 4
REF: 011736ai
KEY: context
342 ANS:
No. There are infinite solutions.
NAT: F.IF.B.4
TOP: Graphing Quadratic Functions
PTS: 2
KEY: substitution
343 ANS:
(x − 3) 2 − 49 = 0
REF: 011725ai
NAT: A.REI.C.6
TOP: Solving Linear Systems
PTS: 2
REF: 081631ai
KEY: taking square roots
344 ANS:
NAT: A.REI.B.4
TOP: Solving Quadratics
(x − 3) 2 = 49
x − 3 = ±7
x = −4,10
3x + 2y = 19
6x + 4y = 38
2(3.50) + 4y = 24
2x + 4y = 24
2x + 4y = 24
7 + 4y = 24
4x = 14
4y = 17
x = 3.50
PTS: 6
REF: 061637ai
NAT: A.REI.C.6
y = 4.25
TOP: Graphing Linear Systems
ID: A
345 ANS:
p + 2s = 15.95 5p + 10s = 79.75
3p + 5s = 45.90 6p + 10s = 91.80
p = 12.05
PTS: 4
REF: 011734ai
NAT: A.CED.A.3 TOP: Modeling Linear Systems
346 ANS:
Plan A: C = 2G + 25, Plan B: C = 2.5G + 15. 50 = 2.5G + 15 50 = 2G + 25 With Plan B, Dylan can rent 14
35 = 2.5G
25 = 2G
G = 14
G = 12.5
games, but with Plan A, Dylan can buy only 12. 65 = 2(20) + 25 = 2.5(20) + 15 Bobby can choose either plan, as
he could rent 20 games for $65 with both plans.
PTS: 2
347 ANS: 1
C(68) =
REF: 081728ai
NAT: A.CED.A.3
TOP: Modeling Linear Systems
5
(68 − 32) = 20
9
PTS: 2
REF: 011710ai
NAT: N.Q.A.1
TOP: Conversions
KEY: formula
348 ANS: 1
PTS: 2
REF: 061606ai
NAT: F.LE.A.1
TOP: Families of Functions
349 ANS:
f(x) = 0.75x + 4.50. Each card costs 75¢ and start-up costs were $4.50.
PTS: 4
REF: 011735ai
350 ANS: 1
f(3) = −2(3) 2 + 32 = −18 + 32 = 14
NAT: F.LE.A.2
TOP: Modeling Linear Functions
PTS: 2
351 ANS:
b(x − 3) ≥ ax + 7b
NAT: F.IF.A.2
TOP: Functional Notation
NAT: A.REI.B.3
REF: 061714ai
TOP: Solving Linear Inequalities
NAT: S.ID.C.8
REF: 061705ai
bx − 3b ≥ ax + 7b
bx − ax ≥ 10b
x(b − a) ≥ 10b
x≤
10b
b−a
PTS: 2
REF: 011631ai
352 ANS: 1
PTS: 2
TOP: Correlation Coefficient
ID: A
353 ANS: 3
2x 3 + 12x − 10x 2 = 0
2x(x 2 − 5x + 6) = 0
2x(x − 3)(x − 2) = 0
x = 0,2,3
PTS: 2
REF: 081719ai
354 ANS: 3
PTS: 2
TOP: Sequences
355 ANS: 1
PTS: 2
TOP: Correlation Coefficient
356 ANS: 4
47 − 4x < 7
NAT: A.APR.B.3
REF: 011618ai
TOP: Zeros of Polynomials
NAT: F.LE.A.2
REF: 081722ai
NAT: S.ID.C.8
−4x < −40
x > 10
PTS: 2
REF: 061713ai
NAT: A.REI.B.3
357 ANS: 2
7.2 + 7.6 + p H
7.2 + 7.6 + p L
7<
< 7.8
and
3
3
6.2 < p L
TOP: Interpreting Solutions
p H < 8.6
PTS: 2
REF: 061607ai
NAT: A.CED.A.1
358 ANS: 4
Vertex (15,25), point (10,12.5) 12.5 = a(10 − 15) 2 + 25
TOP: Modeling Linear Inequalities
−12.5 = 25a
1
− =a
2
PTS: 2
REF: 061716ai
NAT: F.IF.B.4
KEY: no context
359 ANS: 4
−5 − 2
= −7; 3) y = −2x + 3 ; 4) y = −3x + 5
1) y = 3x + 2 ; 2)
3−2
PTS: 2
REF: 081615ai
NAT: F.IF.B.6
TOP: Graphing Quadratic Functions
TOP: Rate of Change
ID: A
360 ANS: 1
4
2+ x ≥ 4+x
9
−2 ≥
5
x
9
x≤−
18
5
PTS: 2
361 ANS: 3
a n = 3n + 1
REF: 081711ai
NAT: A.REI.B.3
TOP: Solving Linear Inequalities
PTS: 2
REF: 061613ai
KEY: term
362 ANS: 3
PTS: 2
TOP: Using Rate
363 ANS:
2 units right and 3 units down.
NAT: F.IF.A.3
TOP: Sequences
REF: 081609ai
NAT: N.Q.A.2
PTS:
364 ANS:
TOP:
365 ANS:
TOP:
366 ANS:
NAT: F.BF.B.3
REF: 081717ai
TOP: Transformations with Functions
NAT: F.LE.A.1
a 5 = 3(5) + 1 = 16
2
REF: 081626ai
1
PTS: 2
Families of Functions
1
PTS: 2
Transformations with Functions
REF: 011620ai
NAT: F.BF.B.3
KEY: bimodalgraph
D-E, because his speed was slower. Craig may have stayed at a rest stop during B-C.
PTS: 4
367 ANS: 4
3x + 2 ≤ 5x − 20
REF: 061734ai
NAT: F.IF.B.4
230 − 0
≈ 32.9
7−0
TOP: Relating Graphs to Events
22 ≤ 2x
11 ≤ x
PTS: 2
REF: 061609ai
NAT: A.REI.B.3
TOP: Solving Linear Inequalities
368 ANS: 3
The rocket was in the air more than 7 seconds before hitting the ground.
PTS: 2
KEY: context
REF: 081613ai
NAT: F.IF.B.4
TOP: Graphing Quadratic Functions
ID: A
369 ANS:
f(t) = −58t + 6182 r = −.94 This indicates a strong linear relationship because r is close to -1.
PTS: 4
REF: 011635ai
KEY: linear with correlation coefficient
370 ANS: 2
r = 0.92
NAT: S.ID.B.6
TOP: Regression
PTS: 2
REF: 081606ai
NAT: S.ID.C.8
TOP: Correlation Coefficient
371 ANS: 3
For a residual plot, there should be no observable pattern and a similar distribution of residuals above and below
the x-axis.
PTS: 2
REF: 011624ai
372 ANS: 2
PTS: 2
TOP: Modeling Exponential Functions
373 ANS: 3
119.67(0.61) 5 − 119.67(0.61) 3 ≈ 17.06
NAT: S.ID.B.6
REF: 081624ai
TOP: Residuals
NAT: F.LE.B.5
PTS: 2
374 ANS:
NAT: F.IF.A.2
TOP: Evaluating Functions
REF: 011603ai
x=
PTS: 2
KEY: no context
375 ANS:
REF: 061627ai
2x + 3x + 10 = 4x + 32 x =
2
−b −(−4) 4
=
= =2
2a
2(1)
2
1±
NAT: F.IF.B.4
TOP: Graphing Quadratic Functions
(−1) 2 − 4(2)(−22)
≈ −3.1,3.6 . Quadratic formula, because the answer must be
2(2)
2x 2 − x − 22 = 0
to the nearest tenth.
PTS:
KEY:
376 ANS:
TOP:
4
REF: 061735ai
AI
4
PTS: 2
Zeros of Polynomials
NAT: A.REI.D.11
TOP: Quadratic-Linear Systems
REF: 011706ai
NAT: A.APR.B.3
ID: A
377 ANS: 2
 5  3




6   − x  = 16 
6 8




  3




8  5  − x  = 96 

  8



15 − 40x = 768
−40x = 753
x = −18.825
PTS: 2
REF: 081713ai
KEY: fractional expressions
378 ANS: 2
f(−2) = (−2 − 1) 2 + 3(−2) = 9 − 6 = 3
NAT: A.REI.B.3
TOP: Solving Linear Equations
PTS: 2
REF: 081605ai
NAT: F.IF.A.2
TOP: Functional Notation
379 ANS: 4
PTS: 2
REF: 061703ai
NAT: F.IF.C.7
TOP: Graphing Root Functions
KEY: bimodalgraph
380 ANS:
Yes, because the sequence has a common ratio, 3.
PTS: 2
REF: 081726ai
NAT: F.LE.A.1
TOP: Families of Functions
381 ANS: 4
(1) The box plot indicates the data is not evenly spread. (2) The median is 62.5. (3) The data is skewed because
the mean does not equal the median. (4) an outlier is greater than Q3 + 1.5 ⋅ IRQ = 66 + 1.5(66 − 60.5) = 74.25.
PTS: 2
REF: 061715ai
NAT: S.ID.A.3
TOP: Central Tendency and Dispersion
382 ANS:
Exponential, because the function does not have a constant rate of change.
PTS: 2
383 ANS:
5x 2 − 10
PTS: 2
KEY: subtraction
REF: 081627ai
NAT: F.LE.A.1
TOP: Families of Functions
REF: 061725ai
NAT: A.APR.A.1
TOP: Operations with Polynomials
ID: A
384 ANS: 2
PTS: 2
TOP: Modeling Exponential Functions
385 ANS: 4
y − 34 = x 2 − 12x
REF: 061712ai
KEY: AI
NAT: F.BF.A.1
PTS: 2
REF: 011607ai
KEY: completing the square
386 ANS: 1
1 min
12.5 sec ×
= 0.2083 min
60 sec
NAT: A.REI.B.4
TOP: Solving Quadratics
PTS: 2
REF: 061608ai
KEY: dimensional analysis
387 ANS: 4
36x 2 = 25
NAT: N.Q.A.1
TOP: Conversions
y = x 2 − 12x + 34
y = x 2 − 12x + 36 − 2
y = (x − 6) 2 − 2
x2 =
25
36
x= ±
5
6
PTS: 2
REF: 011715ai
NAT: A.REI.B.4
TOP: Solving Quadratics
KEY: taking square roots
388 ANS: 1
PTS: 2
REF: 011623ai
NAT: F.LE.A.1
TOP: Families of Functions
389 ANS: 2
PTS: 2
REF: 011723ai
NAT: F.IF.C.9
TOP: Comparing Functions
390 ANS:
18j + 32w = 19.92 14(.52) + 26(.33) = 15.86 ≠ 15.76 7(18j + 32w = 19.92) 18j + 32(.24) = 19.92
14j + 26w = 15.76
9(14j + 26w = 15.76)
18j + 7.68 = 19.92
126j + 224w = 139.44
18j = 12.24
126j + 234w = 141.84
j =.68
10w = 2.4
w =.24
PTS: 6
REF: 081637ai
NAT: A.CED.A.3
TOP: Modeling Linear Systems
ID: A
391 ANS:
Neither is correct. Nora’s reason is wrong since a circle is not a function because it fails the vertical line test. Mia
is wrong since a circle is not a function because multiple values of y map to the same x-value.
PTS: 2
REF: 011732ai
KEY: graphs
392 ANS: 1
PTS: 2
TOP: Sequences
393 ANS: 4
1) b = 0; 2) b = 4; 3) b = −6; 4) b = 5
NAT: F.IF.A.1
TOP: Defining Functions
REF: 081610ai
NAT: F.LE.A.2
PTS: 2
KEY: AI
394 ANS: 1
2h + 8 > 3h − 6
NAT: F.IF.C.9
TOP: Comparing Functions
REF: 081611ai
14 > h
h < 14
PTS: 2
REF: 081607ai
NAT: A.REI.B.3
395 ANS: 2
The slope of a line connecting (5,19) and (10,20) is lowest.
TOP: Solving Linear Inequalities
PTS: 2
KEY: AI
396 ANS: 1
2(x 2 − 6x + 3) = 0
NAT: F.IF.B.6
TOP: Rate of Change
NAT: A.REI.B.4
TOP: Solving Quadratics
NAT: A.REI.B.3
TOP: Solving Linear Equations
REF: 081705ai
x 2 − 6x = −3
x 2 − 6x + 9 = −3 + 9
(x − 3) 2 = 6
PTS: 2
REF: 011722ai
KEY: completing the square
397 ANS: 1
4(x − 7) = 0.3(x + 2) + 2.11
4x − 28 = 0.3x + 0.6 + 2.11
3.7x − 28 = 2.71
3.7x = 30.71
x = 8.3
PTS: 2
KEY: decimals
REF: 061719ai
ID: A
398 ANS:
PTS: 2
399 ANS:
REF: 081625ai
NAT: F.IF.C.7
TOP: Graphing Root Functions
PTS: 2
REF: 061726ai
KEY: no context
400 ANS: 1
PTS: 2
TOP: Rate of Change
401 ANS: 4
PTS: 2
TOP: Modeling Linear Functions
402 ANS: 1
0 = −16t 2 + 24t
NAT: F.IF.B.4
TOP: Graphing Quadratic Functions
REF: 061603ai
KEY: AI
REF: 081604ai
NAT: F.IF.B.6
NAT: F.IF.B.4
TOP: Graphing Quadratic Functions
NAT: A.REI.B.3
TOP: Solving Linear Inequalities
NAT: F.IF.A.2
TOP: Functional Notation
NAT: F.LE.A.2
0 = −8t(2t − 3)
t = 0,
3
2
PTS: 2
REF: 061724ai
KEY: context
403 ANS:
1.8 − 0.4y ≥ 2.2 − 2y
1.6y ≥ 0.4
y ≥ 0.25
PTS: 2
REF: 011727ai
404 ANS: 3
 1

1
f 8 = (8) 2 -  (8) + 3  = 32 − 5 = 27
2
4

PTS: 2
REF: 081704ai
ID: A
405 ANS:
2
5.75 5280
≈ 46
=
115
40
x
x = 115
PTS: 2
REF: 081730ai
NAT: N.Q.A.2
406 ANS: 4
PTS: 2
REF: 011720ai
TOP: Central Tendency and Dispersion
407 ANS: 3
PTS: 2
REF: 081703ai
TOP: Factoring the Difference of Perfect Squares
408 ANS:
x 2 − 6x + 9 = 15 + 9
TOP: Using Rate
NAT: S.ID.A.2
NAT: A.SSE.A.2
KEY: quadratic
(x − 3) 2 = 24
x − 3 = ± 24
x = 3±2 6
PTS: 2
REF: 081732ai
NAT: A.REI.B.4
TOP: Solving Quadratics
KEY: completing the square
409 ANS:
−b
−64
−64
t=
=
=
= 2 seconds. The height decreases after reaching its maximum at t = 2 until it lands at
2a 2(−16) −32
t = 5 −16t 2 + 64t + 80 = 0
t 2 − 4t − 5 = 0
(t − 5)(t + 1) = 0
t=5
PTS:
KEY:
410 ANS:
|x + 2 |
4
context
2
=3x − 2
REF: 011633ai
NAT: F.IF.B.4
TOP: Graphing Quadratic Functions
NAT: A.REI.D.11
TOP: Other Systems
REF: 011719ai
NAT: F.IF.B.5
x + 2 = 3x − 2
4 = 2x
x=2
PTS:
KEY:
411 ANS:
TOP:
2
REF: 081702ai
AI
4
PTS: 2
Domain and Range
ID: A
412 ANS:
762 − 192 570
=
= 9.5 y = 9.5x T = 192 + 9.5(120 − 32) = 1028
60
92 − 32
PTS: 4
413 ANS: 2
x 2 − 8x = 7
REF: 061635ai
NAT: A.CED.A.2
TOP: Speed
NAT: A.REI.B.4
TOP: Solving Quadratics
x 2 − 8x + 16 = 7 + 16
(x − 4) 2 = 23
PTS: 2
REF: 011614ai
KEY: completing the square
414 ANS: 1
3x 2 + 10x − 8 = 0
(3x − 2)(x + 4) = 0
x=
415
416
417
418
419
PTS:
KEY:
ANS:
TOP:
ANS:
TOP:
ANS:
TOP:
ANS:
TOP:
ANS:
2
,−4
3
2
REF: 081619ai
NAT:
factoring
2
PTS: 2
REF:
Modeling Linear Functions
4
PTS: 2
REF:
Modeling Exponential Functions
1
PTS: 2
REF:
Modeling Systems of Linear Inequalities
2
PTS: 2
REF:
Analysis of Data
2
PTS: 2
REF: 081718ai
A.REI.B.4
TOP: Solving Quadratics
061704ai
NAT: S.ID.C.7
011608ai
NAT: F.LE.B.5
061711ai
NAT: A.CED.A.3
011713ai
NAT: S.ID.C.9
NAT: F.IF.C.9
TOP: Comparing Functions
ID: A
420 ANS:
PTS: 2
KEY: two-way
421 ANS:
REF: 061729ai
NAT: S.ID.B.5
TOP: Frequency Tables
6.4-6.5
PTS: 4
REF: 081734ai
KEY: frequency histograms
422 ANS: 4
30
= 0.6
30 + 12 + 8
NAT: S.ID.A.1
TOP: Frequency Histograms
PTS: 2
REF: 061615ai
KEY: two-way
423 ANS: 3
5x 2 − (4x 2 − 12x + 9) = x 2 + 12x − 9
NAT: S.ID.B.5
TOP: Frequency Tables
NAT: A.APR.A.1
TOP: Operations with Polynomials
REF: 011712ai
NAT: F.IF.C.7
REF: 011615ai
NAT: F.IF.B.5
REF: 011606ai
NAT: A.CED.A.4
424
425
426
427
PTS:
KEY:
ANS:
TOP:
ANS:
TOP:
ANS:
TOP:
ANS:
2
REF: 011610ai
multiplication
1
PTS: 2
Graphing Absolute Value Functions
1
PTS: 2
Domain and Range
3
PTS: 2
Transforming Formulas
610 − 55(4) = 390
390
500
= 6 4 + 6 = 10 610 − 55(2) = 500
≈ 7.7 10 − (2 + 7.7) ≈ 0.3
65
65
PTS: 4
REF: 081733ai
428 ANS: 1
PTS: 2
TOP: Families of Functions
NAT: A.CED.A.2
REF: 061707ai
TOP: Speed
NAT: F.LE.A.2
ID: A
429 ANS:
No. The sum of a rational and irrational is irrational.
PTS:
KEY:
430 ANS:
TOP:
2
REF: 011728ai
NAT: N.RN.B.3
classify
3
PTS: 2
REF: 061706ai
Factoring the Difference of Perfect Squares
TOP: Operations with Radicals
NAT: A.SSE.A.2
KEY: higher power AI
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