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:__________________________ www.jmap.org 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:__________________________ www.jmap.org 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:__________________________ www.jmap.org 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:__________________________ www.jmap.org 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:__________________________ www.jmap.org 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:__________________________ www.jmap.org 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:__________________________ www.jmap.org 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:__________________________ www.jmap.org 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:__________________________ www.jmap.org 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:__________________________ www.jmap.org 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:__________________________ www.jmap.org 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:__________________________ www.jmap.org 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:__________________________ www.jmap.org 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:__________________________ www.jmap.org 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:__________________________ www.jmap.org 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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