COMPASS Placement Test Review Packet

COMPASS Placement Test Review Packet
COMPASS Placement Test
Review Packet
For preparing to take
the COMPASS Placement Test
East Georgia College
Table of Contentœ
The COMPASS Test
Test-taking Strategies
Additional Resources for the Compass Placement Test
3
5
6
Reading Review
I. Finding the Main Idea
II. Vocabulary: Word Meaning and Context
III. Supporting Details
IV. Inferences
V. Implied Main Ideas and Central Points
Online Reading Resources
7
8
9
11
12
14
18
Writing Review
I. Punctuation
II. Basic Grammar and Usage
III. Sentence Structure
IV. Rhetorical Skills
Online Grammar & Writing Resources
19
20
25
38
38
47
Math Review
I. General Overview
Topics Covered in EGC Math Classes
Are You Prepared?
II. Refreshing your Math
Additional Math Review Resources
48
50
50
57
88
107
EGC COMPASS Placement Test Review Packet
2
The COMPASS Test
The COMPASS placement test is offered in Reading, Writing, and Math. The test helps
to determine whether you have the knowledge to succeed in the classes you are
planning to take or whether taking some preparatory classes will ensure your success.
Taking the three tests separately is usually helpful to ensure best results in all three
tests.
The COMPASS test is a self-adjusting, multiple choice test that is taken at the computer.
The answer to your current question will determine the next question; it will stop once
it has determined your level. Consequently the test is untimed and has a different
number of questions for each student. It also means that you will see questions that you
don’t know, because the test will ask you more and more difficult questions until it has
found something that you don’t know. Just do your best you can for each question the
test presents to you.
You will receive paper, pencil, and a calculator. Since you will work on the computer
you will not be allowed to bring food or drink. Once you have completed a test you will
receive a printout with your scores and a recommendation of classes to take. You
should then make an appointment with an advisor to discuss your course work.
EGC COMPASS Placement Test Review Packet
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The COMPASS Entrance exam can taken at the main campus in
Swainsboro. Students are not required to schedule an appointment for the
COMPASS Exam and is offered at the main campus in Swainsboro
Monday - Thursday 8:00am-4:00pm and on Fridays 8:00am-10:00am
except holidays and during Orientations.
Students who are unable to test at the Swainsboro office are able to take
the exam at a COMPASS Internet Remote Testing Site of their choosing.
Please be aware that each institution charges a fee for this service which
the student will be responsible for.
To find one in your area, please visit:
http://www.act.org/COMPASS/sites/index.html. Once you have located a
testing site convenient for you, please contact the Office of Admissions to
set up the registration.
After you have taken the COMPASS Entrance exam in the any or all of the
three subjects of Reading, Writing, and Algebra, you will receive a
printout of your scores explaining whether or not you are exempt or
placed in Learning Support Courses. Here are the locations and hours for
each campus:
Swainsboro Campus
131 College Circle
Swainsboro, GA 30401
(478) 289-2017
Office hours:
o Monday-Thursday: 8:00am - 6:00pm
o Friday: 8:00am - 12:00pm
EGC @ Statesboro
10449 US Highway 301 South
Statesboro, GA 30458
(912) 623-2400
Office hours:
o Monday to Thursday: 8:00am - 6:00pm
o Friday: 8:00am - 12:00pm
Testing Center website: http://www.ega.edu/admissions
EGC COMPASS Placement Test Review Packet
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Test-aking Strategies
1. Take the Placement Test Seriously
Giving your best during the test can save you several terms of math, reading,
and writing classes, and therefore a lot of time and money. What you don’t
know, you don’t know. That’s fine. But if you know something, make sure you
show it on the test so that you are placed into the appropriate class for your skill
level.
2. Prepare For the Test
It is important that you review your knowledge before you take the test,
particularly if you have not been in school for many years. Go over the following
parts in this review packet to refresh your memory about the things you once
knew. This packet is not designed to help you learn material that you never
knew. For that you should take a class.
It is equally important, however, that you are physically prepared for the test. Be
sure to get enough sleep the night before, and eat something nutritious before
arriving for the test. Don’t consume anything with caffeine or a lot of sugar right
before the test. Caffeine might make you feel more jittery and less patient,
causing you to skip important steps. Too much sugar will give you a short
energy boost followed by a sense of fatigue. Drink water or tea instead.
3. Take ˜ž›ȱTime
The Compass Test is not timed which means that you can take as much time as
you need. Make use of that! Read the questions carefully, think about them, do
your work on paper, and then choose an answer. Your score does not depend on
how long you take for each question. Your score only depends on whether you
choose the right answer.
4. Read the Questions Carefully
Don’t assume anything. Follow the instructions of the question exactly. Read all
the details very carefully. A simple 'not' can change everything around. It helps
to copy the question onto paper and underline the important information or
rewrite it in your own words.
EGC COMPASS Placement Test Review Packet
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5. Work Math Problems out on Paper
Since the COMPASS Test is a test that you take on the computer make sure to
copy math problems onto paper and work them step by step. It’s worth it!
Working a problem out carefully and minding all the details gets you the points
to place you in the right class.
6. Take a Break
You can take a break whenever you like! Just go to the testing supervisor, and
s/he will save your work. You can continue when you come back. You can even
come back the next day.
This is very important because in order to do well on the test you need to
concentrate. So if you need to use the restroom, go. If you are thirsty or hungry,
go drink and eat. If you are tired, get up and take a walk or go home and come
back the next day.
Additional Resources
for the COMPASS placement test
The testing centers website: http://www.ega.edu/admissions
The testing centers website for the COMPASS placement test:
http://www.ega.edu/compass
The COMPASS website: http://www.act.org/compass/student/index.html
Sample test questions on the COMPASS website:
http://www.act.org/compass/sample/index.html
EGC COMPASS Placement Test Review Packet
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Math Review – Part I
On the previous page you found a flow chart of the math sequence. The placement test
will determine where you enter the sequence. Your educational goal will determine
where you will exit the sequence. Please see an advisor for that.
In the following pages the topics are listed that are covered in each class.
TOPICS
covered in EGC Math Classes
To be successful studying the topics covered in these courses, students should be
appropriately prepared by:
1. Taking the prerequisite math course within the last three years with a passing
grade of A or B, or within the last one year with a passing grade of C, or
2. Placing into the course by taking the COMPASS placement test.
MTH 20 – Basic Math
Fractions, Decimals, Integers  addition, subtraction, multiplication, division,
Order of operations
Ratio and Proportion
Percent  percents  decimals  fractions
Measurements  Metric system  American system
Geometry
Statistics
Place value, rounding, inequalities, exponents, power of ten
Prime numbers, multiples, prime factorization, least common multiples
EGC COMPASS Placement Test Review Packet
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MTH 60 – Introductory Algebra I
I. Integer arithmetic
a.The four basic operations of addition, subtraction, multiplication, and
division
b. Absolute value, exponents, order of operations
II. One variable linear equations and inequalities
III. Application (i.e. word/story) problems with formulas
IV. Graphing lines
a. Finding and interpreting slope
b. Finding and interpreting intercepts
c. Interpret relationships between variables
d. Modeling with linear equations
MTH 65 – Introductory Algebra II
1. Systems of linear equations in two variables
a. Graphing method
b. Substitution method
c. Addition method
d. Applications
2. Working with algebraic expressions
a. Add, subtract, multiply, and divide by a monomial
b. Factoring polynomials
3. Solving quadratic equations
a. Square Root Property (includes – simplify and approximate
numeric square roots)
b. Factoring Property
c. Quadratic Formula
d. Graphing (includes – interpret vertex, axis of symmetry and
vertical/horizontal intercepts)
e. Applications
4. Relations and functions
a. Function notation
b. Evaluate
EGC COMPASS Placement Test Review Packet
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MTH 70 – Review of Introductory Algebra
1.
2.
3.
4.
Solving equations
A.
Linear equations
B.
Quadratic equations
C.
Rational equations
D.
Radical equations
Graphing
A.
Linear functions
B.
Quadratic functions
Simplifying expressions
A.
Polynomial expressions
B.
Rational expressions
Function concepts
A.
Domain
B.
Range
C.
Function notation
D.
Graph reading
MTH 95 – Intermediate Algebra
1.
2.
3.
4.
Applications and Modeling
A. Linear functions
B. Quadratic functions
C. Exponential functions
Graphing
A. Linear functions
B. Quadratic functions
C. Exponential functions
Solve equations and inequalities
A. Symbolically
B. Numerically
C. Graphically
Function concepts
A. Domain
B. Range
C. Inverses
D. Compositions
E. Transformations
EGC COMPASS Placement Test Review Packet
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MTH 111 – College Algebra (MTH 111B or MTH 111C)
1.
Graphing and solving equations and applications involving:
A. Polynomial functions
B. Rational functions
C. Exponential functions
D. Logarithmic functions
2.
Functions Operations
A. Inverses of functions
B. Compositions of functions
C. Transformations of functions
MTH 112 – Elementary Functions (Trigonometry)
1.
2.
3.
4.
Right triangle trigonometry
Law of Sines and Law of Cosines and their applications
Solutions to trigonometric equations
Applications
A. Vectors
B. Parametric equations
C. Polar coordinates and graphs
D. Complex numbers
MTH 211 – Foundations of Elementary Math I
1.
Topics for Math 211:
A. Problem solving
B. Set Theory – union, intersection, complement, Venn Diagrams
C. Historic Numeration Systems
D. Whole Number Operations – properties, algorithms, models, non-decimal
bases.
E. Number Theory – divisibility, primes, GCD, LCM, modular arithmetic.
EGC COMPASS Placement Test Review Packet
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ARE YOU PREPARED?
 The mini quizzes on the following pages are meant to serve only as an indicator of a
few of the math skills that you are expected to know at the beginning of each
course. Do not use these problems as a study guide thinking that they will
adequately prepare you for the course.
 These example problems are merely representative of some of the most important
concepts that are taught in the prerequisite courses.
 The courses will offer little or no time for any type of review; they assume that you
are prepared to do the work the first day of class.
Below is a sample of some skills you should have BEFORE entering
MTH 20 – Basic Math
You MAY NOT use a calculator.
1. Without using a calculator, can you complete these problems in 45 seconds?
6x4
9x6
7x8
9x9
0x6
6x9
8 x 10
9x4
6x7
7x2
9x0
6x2
4x7
8x9
9x7
EGC COMPASS Placement Test Review Packet
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6x5
8x9
8x4
3x6
8x8
12 4
56 8
72 9
40 5
36 6
NOTE: If you miss more than 5 problems, then you should consider taking the
previous math course – ABE 0750 or ALC 60, 61, 62, 63.
2. Without using a calculator, can you get at least 8 correct answers on the following
problems?
a) 20 x 30
d) 4984
8
g) 305 x 27
b) 25 + 4 + 125
c) 872 - 431
e) 68 x 34
f) 17575
h) 5843 - 2338
i) 4590
25
15
j) 45 + 2,341 + 8 + 124
3.
Without using a calculator, can you get at least 4 correct answers on the following
problems?
a) Find the change from a $20 bill after purchasing 2 records at $6 each, and 1 pair
of earrings that cost $3.
b) A computer screen consists of small rectangular dots called pixels. How many
pixels are there on a screen that has 600 rows with 800 pixels in each row?
c) Before going back to college, David buys 4 shirts at $59 each and
6 pairs of pants at $78 each. What is the total cost of the purchase?
d) Portland community college is constructing new dorms. Each dorm room has a
small kitchen. If someone buys 85 microwave ovens at $90 each, what is the total
cost of the purchase?
e) Hershey Chocolate USA makes small, fun-size chocolate bars. How many 20-bar
packages can be filled with 8,110 bars? How many bars will be left over?
EGC COMPASS Placement Test Review Packet
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Answers
QUESTION 2:
a) 600
b) 154
c) 441
d) 623
e) 2,312
f) 703
g) 8,235
h) 3,505
i) 306
j) 2,518
QUESTION 3:
a) $5
b) 480,000 PIXELS
c) $704
d) $7,650
e) 405 Packages with 10 bars left over
How many of these problems can you miss and still succeed in MTH 20?
Ideally, NONE.
These problems are just a sample of the larger number of skills that you should be
familiar with BEFORE taking this course.
If some of these ideas are not familiar to you, you should consider enrolling in one of
the previous math courses (ABE 0750 or ALC 60, 61, 62, or 63).
Below is a sample of some skills you should have BEFORE entering
MTH 60 – Introductory Algebra I
You MAY NOT use a calculator.
1.Without using a calculator, can you get at least 16 correct answers on the following
problems?
a) Round 6.8449 to the nearest
hundredth.
EGC COMPASS Placement Test Review Packet
b) Round 7.995 to the nearest tenth.
5
c) Round 37,328 to the nearest
hundred.
d) Change 0.625 to a fraction
e) Write 70% as a fraction and
reduce to the lowest terms.
g) Multiply:
f) Change
9
2
x2
16
3
2
to a decimal.
5
h) Divide: 1
i) Find the average of
1
1
7 , 12.5, 8, 10
4
4
2
10
3
j) Perform the indicated operations.
7 3 2 10 5
l) Perform the indicated operations.
18 2(3) 2 2 5
k) Subtract: 8.3 .973
m) List these numbers from
smallest to largest:
n) Solve the proportion:
5 7
, , 0.555, 0.583
9 12
2.5
4
1.1
x
o) How many inches equal 2 yd?
p) Change 72 mg to grams.
q) If 1 km is approximately 0.6 miles,
how many miles in 18 km?
r) Find the area of a circle whose
diameter is 6 cm.
s) Find the perimeter of this figure:
16 m
10 m
10m
8m
EGC COMPASS Placement Test Review Packet
t) Find the volume of this figure:
18 in
25 m
5 in
5
2. Without using a calculator, can you get at least 4 correct answers on the following
problems?
a) A family’s monthly income is $1,200. It is spent as follows: 20% on food, 35% on
rent, 17% on utilities, 8% on automobile, and the rest on miscellaneous expense.
What dollar amount is spent on miscellaneous expenses?
b) A TV is priced to sell at $585. What is the sale price if the sale sign says ‚
c) A machinist needs a bar that is
is the bar?
1
off‛?
3
3
3
in. thick. If she cuts off
in. thick, how thick
8
32
d) A teacher assigns problems 96 to 128 that are multiples of 8. Which problems
should the students do?
e) Find the unit price if the total cost of a 5-lb. steak is $21.
Answers
Question 1:
a) 6.84 b) 8.0
g)
3
2
m) 0.555,
h)
c) 37,300
1
6
I) 9
1
2
5
7
, 0.583,
9
12
p) 0.072 g
q) 10.8 mi
d)
5
8
e)
j) 3
7
10
f) 0.4
k) 7.327
n) 1.76
l) 26
o) 72 inches
r) 28. 26 cm2
s) 44 m
t) 2,250 in 3
Question 2:
a) $240
b) $390
d) 96, 104, 112, 120, 128
15
in. thick
32
e) $4.20 per lb
c)
How many of these problems can you miss and still succeed in MTH 60?
Ideally, NONE.
EGC COMPASS Placement Test Review Packet
These problems are just a sample of the larger number of skills that you should be
familiar with BEFORE taking this course.
If some of these ideas are not familiar to you, you should enroll in the previous course
(MTH 20 or ALC 60, 61, 62, or 63)
Below is a sample of some skills you should have BEFORE entering
MTH 65 – Introductory Algebra II
You MAY NOT use a calculator.
a) Perform the indicated operations:
18 2( 3) ( 2) 3 5
c) Simplify:
(12 x 2 4 x 1) 3( 2 x 2 5 x 3)
e) Solve for x:
x 1
x
2 10 5
1
2
f) Solve for W:
P 2L 2 W
i) Given two points on a line, find the
slope and indicate whether the line rises,
falls, (is 3horizontal,
,4)
( or
5, is2)vertical.
and
2,
k) Given the slope,
( 1,4), and a point
passing through
write an
equation in the point-slope form and
slope-intercept form.
EGC COMPASS Placement Test Review Packet
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b) Evaluate 7 x x , when x
d) Solve for x:
5( x 2 )
2
3 6( x 7 )
f) Solve for x and graph on a number line.
2 6 x 2 (5 x )
h) Find the slope and the y-intercept of the
2x y 6
line when
j) Write an equation
for the following
graph.
l) Graph the inequality on a rectangular
coordinate system.
4
y
< x 1
3
This is a graph of Frank’s body temperature from 8 a.m. to 3 p.m.
Let x represent the number of hours after 8 a.m. and y equal Frank’s temperature (in F)
at time x.
m) What is the y-intercept? What does this mean about
Frank’s temperature at 8 a.m.?
n) During which period of time is Frank’s temperature
decreasing?
o) Estimate Frank’s minimum temperature during the
time period shown. How many hours after 8 a.m.
does this occur? At what time does this occur?
p) How many grams of an alloy that is 80% gold should be
melted with 40 grams of an alloy that is 50% gold to produce
an alloy that is 70% gold?

q) Vikki has $200 to spend on clothing. She buys a skirt for $68. She would like to buy
some sweaters that sell for $15.50 each. How many sweaters can she buy and stay
within her budget?
r) The pressure of water on an object below the surface is proportional to its distance
below the surface. If a submarine experiences a pressure of 25 pounds per square inch
60 feet below the surface, how much pressure will it experience 330 feet below the
surface?
Answers
a)
g)
j)
b)
24
P 2L
2
W
x
l) y
18
3
c)
6x2 11x 8
d)
x
5
h) Slope =2, y-intercept = ( 0, 6 )
e)
x
2
f)
x
2
i) Slope = 3, rises
k) Point-slope form: y – 4 = - 2(x + 1) and slope-intercept form: y = - 2x + 2
4
x 1
3
m) The y-intercept is (0,101). At 8:00 a.m. Frank’s body temperature is at 101 F.

EGC COMPASS Placement Test Review Packet
n) Frank’s temperature is decreasing during the time from 8:00 a.m. to 11:00 a.m.
o) Frank’s minimum temperature is 98.6 F. This occurs about 3 hours afterwards
and the time would be 11:00 a.m.

p) Eighty grams of an alloy that is 80% gold should be melted with 40 grams of an alloy
that is 50% gold to produce an alloy that is 70% gold.
q) Vikki can buy at most eight sweaters.
r) A submarine will experience a pressure of 137.5 pounds per square inch 330 feet
below the surface.
How many of these problems can you miss and still succeed in MTH 65?
Ideally, NONE.
These problems are just a sample of the larger number of skills which you should be
familiar with BEFORE taking this course
If some of these ideas are not familiar to you, you should consider enrolling in the
previous course (MTH 60 or ALC 60, 61, 62, or 63)
Below is a sample of some skills you should have BEFORE entering
MTH 70 – Review of Introductory Algebra
Part I
Work with positive and negative real numbers, fractions, and the order of
operations.
a)
100 4 5
b)
( 3)( 4) 3 2
4 6
c)
2
3
1
3
3
8
EGC COMPASS Placement Test Review Packet
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Part II
1. Simplify expressions:
3(2 x 2 3xy y ) ( y
a)
b) 12 2( x 2)
c)
27 x 2 y 5
9x 6 y 2
x2
2 xy )
3
2. Factor:
a)
x 2 5 x 14
b) 6a 2 b 3 3a 2 b
3. Solve for x:
3x x 4 5 5( x 4) 4
a)
b) 3x 5 y 6 0
c)
x2
5x 14
0
4. Evaluate expressions:
If x
3 , evaluate x 2
2x 1
5. Graph by HAND and on your GRAPHING CALCULATOR*
a)
4x 3 y
12
2
y 6 x 90 x 600
b)
6. Find the equation of the line passing through 2 given points:
(2, 1) ( 1, 7)
7. Solve a first-degree inequality in one variable:
Given: 8 5x 3x 9, solve for x
8. Given f ( x)
3x 2
a) Evaluate f ( 2)
b) Solve for x if f ( x)
2
Answers
Part I
a) 125
b)
3
2
EGC COMPASS Placement Test Review Packet
c)
16
17
6
Part II
1. a) 7 x
11 xy 2 y b) 16 2 x
2
2. a) ( x 7)(x 2)
3. a) x
4.
5y 6
3
c) x
7, x
2
4
a)
5.
6. y
b) 3a 2 b(2b 2 1)
b) x
5
27 y 9
c)
x 24
2x 5
8. a) f ( 2)
8
b)
7. x
1
or
8
b) x
4
3
1
8
x
*Students with no graphing calculator experience should
enroll concurrently in MATH 93.
MATH 70 IS AN OPTIONAL COURSE
CONSULT A MATH ADVISOR
How many of these problems can you miss and still succeed in MTH 70?
a) If you missed any of the problems in Part I you should consider
enrolling in MTH 60.
b) If you missed several of the problems in Part II, MTH 70 is the
course for you. These topics will be reviewed in MTH 70.
c) If you missed none of the problems, enroll in MTH 95.
EGC COMPASS Placement Test Review Packet
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Below is a sample of some skills you should have BEFORE entering
MTH 95 – Intermediate Algebra
You MAY NOT use a calculator, except where indicated.
1. Work with positive and negative real numbers, and the order of operations.
5 ( 4)( 3) 3 2
Simplify
2. Simplify expressions:
3(2 x 2 3xy y ) ( y
a)
b)
5
x2
2 xy )
2
12 a b
8a 3b7
3. Expand and collect like terms:
a)
(3x 5)(6 x 7)
b) (2 x 3) 2
4. Factor:
x 2 5 x 14
a)
b) 6a 2 b 3 3a 2 b
5. Solve for x:
a) 3x ( x 4) 5 5( x 4) 4
b) 3x 5 y 6 0
c)
x2
5x 14
0
6. Evaluate expressions:
If x
3 , evaluate x 2 2 x 1
7. Graph by HAND and on your GRAPHING CALCULATOR*
4x 3 y
12
a)
2
y x 5 x 14
b)
8. Find the equation of the line passing through 2 given points:
(2, 1) ( 1, 7)
EGC COMPASS Placement Test Review Packet
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9. Solve a system of equations by all of the following methods: substitution,
elimination by addition (linear combinations), and graphically.
2x y
3
Given:
3x 4 y
2
10: Solve a first degree inequality in one variable:
Given:
8 5x
3x 9 , solve for x
Answers
-2
1.
3.
2. a) 7 x 2 11 xy 2 y
a)
18x 2
4. a)
6.
14
7.
a)
b) x
5
b)
3a 2 b(2b 2 1)
5y 6
3
c) x
y
15
1
-4
-3
-2
-1
10
x
1
5
2
-1
-4 -3 -2 -1
-5
-2
-1 5
-4
-2 0
-5
8. y
10. x
4x
-6
3y
x
1 2 3 4 5 6 7 8 9 10
-1 0
-3
Figure 1:
2
20
2
-5
7, x
b)
y
-6
3a 8
2b 9
b) 4 x 2 12 x 9
9 x 35
( x 7)(x 2)
5. a) x
b)
-2 5
-3 0
12
Figure 2: y
9. x
2x 5
1 / 8 or
1/ 8
x2
5x
14
2, y 1
x
* Students with no graphing calculator experience
should enroll concurrently in MTH 93.
EGC COMPASS Placement Test Review Packet
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How many of these problems can you miss and still succeed in MTH 95?
Ideally, NONE.
These problems are just a sample of the larger number of skills that you should be
familiar with BEFORE taking this course.
If some of these ideas are not familiar to you, you should consider enrolling in one of
the prerequisite courses (MTH 65 or MTH 70 or ALC 60, 61, 62, or 63).
Below is a sample of some skills you should have BEFORE entering
MTH 111 – College Algebra (MTH 111B or MTH 111C)
1. What is the equation of a line with slope m
( 6, 4) ?
1
which passes through the point
2
2. Write each of these inequalities using interval notation:
a) 2 x 7
b) x 1
c) 5 x
3
3. Find the x-intercepts, the y-intercepts and the vertex of y
the equation.
x2
8 x 7 then graph
4. Simplify these exponential expressions:
2x 3 y 2 z 5
a)
8x 5 y 3 z 7 y
2
b)
2
3
1
4
5
3
5
x y
x6z
1
2
5. Given the points (0,2) and (2,18), find the equation for an exponential function of the
form f (t ) a b t which passes through both points.
6. Find the inverse of the function f ( x)
EGC COMPASS Placement Test Review Packet
2x 5 .
6
7. Given the function y f (x) in Figure 1, find the domain and range of the function.
What is the value of f (1) ? Estimate the horizontal and vertical intercepts.
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
Figure 1: y
8. Given
f ( x)
x
3
x and g ( x)
y
x
1 2 3 4 5
f x
2
3x 2
, evaluate the composition ( f  g )
5
x
9. Find the value of f (g (2)) from the table below. For the function h , which
function type best describes its graph: linear; quadratic, or exponential?
x
f (x)
g (x)
h(x)
1
3
-1
0.5
2
0
3
2
3
-5
7
4.5
4
-14
11
8
EGC COMPASS Placement Test Review Packet
6
Answers
1
x 1
2
1. y
2) (a) (2,7]
3. x -intercepts: (1,0), (7,0)
(b) (1, )
(c)
3,5)
y -intercept: (0,7)
Vertex: (4, 9)
y
10
8
6
4
2
x
-2 -1
-2
1
2
3
4
5
6
7
8
9 10
-4
-6
-8
-1 0
Figure 2: y
4. (a)
7.
8.
16 z
x 16
4
(b)
1
8
y z
3
10
1
12
5. f (t )
( f  g)
2
5
6
8x
6. f 1 ( x)
2 3t
x
Domain: ( ,3]
Range: (
Horizontal intercept is (1,0)
x2
7
x 5
2
, 4]
f (1) 2
Vertical intercept is
9. f ( g (2))
5,
(0,1.8)
h is quadratic
How many of these problems can you miss and still succeed in MTH 111B or
MTH 111C?
Ideally, NONE.
These problems are just a sample of the larger number of skills that you should be
familiar with BEFORE taking this course.
If some of these ideas are not familiar to you, you should enroll in the prerequisite
course (MATH 95).
EGC COMPASS Placement Test Review Packet
7
Below is a sample of some skills you should have BEFORE entering
MTH 112 – Elementary Functions (Trigonometry)
You MAY use a calculator.
1. Find the inverse function for f ( x)
23 x .
2. If an initial sample of 50 mg of a radioactive substance decays to 40 mg in 235 years,
find the half-life of the substance.
3. Solve ln x + ln (x 2)
3.
4. On January 1, 1995, a park ranger estimates that there are 65 wolves in a wilderness
area and that the wolf population is growing at an annual rate of 2.3%. When will
there be 100 wolves in the area?
5. Draw a graph of a 5th degree polynomial with a negative leading coefficient, three
single zeroes and a double zero.
6. Graph g ( x)
4 x2
and label all asymptotes and intercepts.
x2 9
7. Given h( x) 2 x 3 5 x 2 14 x 8 , a) find intervals where h is increasing and intervals
where h is decreasing.
Solve for x if h(x) 10.
17 cm
8 cm
8. Solve for x given the similar
triangles shown in Figure 1.
12 cm
x
Figure 1: Triangles for #8
y
9. Given the function y f (x) in
Figure 2, graph the following
transformations:
y f (x) 2
a)
y f (x 3)
b)
y
2 f ( x)
c)
5
4
3
2
1
-1
-1
x
1
2
3
4
5
6
7
8
9
-2
-3
-4
-5
Figure 2: y
EGC COMPASS Placement Test Review Packet
f x
10. From a common location, Car A heads north at 55 mph at the same time as Car B
heads east at 45 mph. Assuming the roads are straight, how far apart are the two
cars after 20 minutes?
Answers
1.
f 1 ( x)
3 log 2 x
2. The half life is almost 730 years ( 729.977)
3. x
5.592
4. There will be 100 wolves in December of 2013.
5.
y
5
y
3
4
2
3
1
2
1
-3
-2
-1
-1
x
1
2
-5 -4 -3 -2 -1
-1
7. a)
b)
8. x
3
4
5
y
1
-4
-5
-3
Figure 3: A Solution to #5
2
-3
-2
-5
x
1
-2
3
-4
2, 0
4
y-int.: 0,
9
x-int.:
4
5
x
3
Figure 4: y
x
3
4 x2
x2 9
h is increasing on ( , 0.907) (2.573, )
h is decreasing on ( 0.907, 2.573)
h(x) 10 when x
1.565, 0.152, or 4.216
25.5cm
EGC COMPASS Placement Test Review Packet
9.
y
y
5
5
5
4
4
4
3
3
2
2
1
y
1
-1
-1
3
2
x
1
2
3
4
5
6
7
8
9
-1
-1
-2
-3
-4
1
x
1
2
3
4
5
6
7
8
-1
-1
9
-2
-2
-3
-3
-4
-4
Figure 5: y
f x
Figure 6: y
2
2
3
4
5
6
7
8
9
-5
-5
-5
x
1
f x
3
Figure 7: y
2f x
10. The cars are approximately 23.688 miles apart in 20 minutes.
How many of these problems can you miss and still succeed in MTH 112?
Ideally, NONE.
These problems are just a sample of the larger number of skills that you should be
familiar with BEFORE taking this course.
If some of these ideas are not familiar to you, you should consider enrolling in one of
the prerequisite courses (MTH 111B or MTH 111C)
Below is a sample of some skills you should have BEFORE entering
MTH 211 – Foundations of Elementary Math I
You MAY use a calculator.
1. The temperature at 10:00 pm in West Yellowstone was 5 degrees below zero. By
3:00am the temperature had dropped 8 degrees. What was the temperature at
3:00am?
a) 3
b) 3 
c) 12
d) 13
e) 13
2.
What is the equation of a line with slope
(6, 4) ?
a) 6 x 4 y
1
b) y
2
1
x 1 c) 2 x 4 y
2
EGC COMPASS Placement Test Review Packet
1
which passes through the point
2
2 c) y
6x
1
2
7
3.
A roast is to be cooked 20 minutes per pound. If the roast weighs 6 pounds and the
cook wants it to finish cooking by 5:30pm, what is the latest time he can begin
cooking the roast?
a) 11:30am b) 2:30pm c) 3:30pm
4.
If x 2 y
a) 6
5.
b) 8
e) 12
c) 12%
d) 20%
e) 32%
The acceleration A that results when force F is applied to a body of mass M can be
calculated from the formula F = MA. What is the value of A if M = 1200 and F =
90,000?
If
a)
8.
d) 10
?
c) 9
b) 8%
a) 75
7.
e) 4:10pm
Les saved $8 on the purchase of a tire whose regular price was $40. What percent
of the regular price did he save?
a) 5%
6.
6, then 2 x 4 y
d) 4:00pm
4
x
b) 750
c) 7500
d) 1,080,000
e) 108,000,000
8, then x 1 ?
1
1
2
2
3
b)
c)
1
2
d)
1
2
e) 1
Consider the problem: ‚Fr ank’s average speed riding a bicycle is 4 miles per hour
less than twice Liz’s. If Frank’s average speed is 12 miles per hour, what is Liz’s
average speed?‛
If s represents Liz’s average speed riding a bicycle, which of the following
equations can be used to solve the problem.
a) 4 2s 12
d) s
b) 2s 4 12
2(12) 4
e) s
EGC COMPASS Placement Test Review Packet
c) 2s 4 12
2(12) 4
7
9.
If a
a)
2, then the value of 4a 2
65
10. If y
a)
1
64
b)
17
c) 15
2a 3 is
d) 23
e) 71
1
, then what is the value of y?
4
1
1
1
3
b)
c)
d)
e)
16
12
4
4
x 3 and x
11. Given the function y f (x) in Figure 1, find the domain and range of the function.
What is the value of f (1) ? Estimate the horizontal and vertical
intercepts.
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
Figure 1: y
y
x
1 2 3 4 5
f x
Answers
1. d
6. a
2 b
7. c
3. c
8. c
4. e
9. d
5. d
10. a
,3 , Range:
,4 , f (1) 2 .
11. Domain:
Horizontal intercept is 1, vertical intercept is 1.8.
How many of these problems can you miss and still succeed in MTH 211?
Ideally, NONE.
These problems are just a sample of the larger number of skills that you should be
familiar with BEFORE taking this course.
If some of these ideas are not familiar to you, you should enroll in the prerequisite
course (MTH 95).
EGC COMPASS Placement Test Review Packet
7
Math Review – Part II
Refreshing your Math
Please note that the following information is meant for review only. If the material or
part of it is unfamiliar to you, it is recommended that you take the corresponding math
class. Under each topic you will find the math class in which that particular material is
taught.
Multiplication can be symbolized in different ways. For example: 5 • 2, 5 x 2, or (5)(2).
The use of ‚x‛ is not useful for algebra and will therefore not be used here. The other
two variations will be used interchangeably. If variables are used multiplication is
assumed if no sign appears. For example: 3a or ab.
Integers
(Math 20)
Definitions
Integers are counting numbers, their negative counterparts, and zero:
The distance of a number from zero is called the absolute value. The absolute value is
always positive: |5| = 5 and |-5| = 5
EGC COMPASS Placement Test Review Packet
7
Multiplying, Dividing, Adding, and Subtracting Integers
Examples:
12 4 = 3
-2 • (-3) = 6
8 (-2) = -4
-5 • 6 = 30
Practice Problems:
1. 10 • (-7)
2. -8 • (-5)
3. -3 • (-15)
4. (-1)(15)
4 + 9 = 13
-6 + (-11) = -17
9 + (-7) = 2
-14 + 6 = -8
5.
6.
7.
8.
(0)(-8)
80 (-10)
-63 7
-81 (-9)
Answers to Practice Problems:
1. -70
5. 0
2. 40
6. -8
3. 45
7. -9
4. -15
8. 9
9. 0 (-5)
10. -7 0
11. -3 + (-8)
12. 10 + (-4)
9. 0
10. undefined
11. -11
12. 6
EGC COMPASS Placement Test Review Packet
9 – 12 = 9 + (-12) = -3
-14 – 7 = -14 + (-7) = -21
15 – (-3) = 15 + 3 = 18
-4 – (-5) = -4 + 5 = 1
13. 5 + (-9)
14. -7 + 2
15. -6 + 8
16. 8 – 13
13. -4
14. -5
15. 2
16. -5
17. -7 – 10
18. 12 – (-4)
19. -5 – (-1)
20. -9 – (-9)
17. -17
18. 16
19. -4
20. 0
7
Fractions
(Math 20)
Definitions
Fraction =
Numerator
Denominator
When the numerator is smaller than the denominator we call the fraction proper. If the
numerator is greater than the denominator we call the fraction improper. Improper
fractions can be written as mixed numbers, which is as an addition of a whole number
and a proper fraction. For example:
2
is a proper fraction;
3
4
1
is an improper fraction and can be written as a mixed number: 1
3
3
5
Whole Numbers such as 5 can be written as
1
The reciprocal of a fraction has the numerator and denominator switched. For example:
3
2
is the reciprocal of
2
3
Mixed Numbers
Mixed numbers can be converted to improper fractions like this:
3
4
5
3 5 4
5
19
5
Improper fractions can be converted to mixed numbers by dividing with remainder:
4
19 5 3 R 4 which translates into 3
5
Simplifying Fractions
When simplifying fractions we divide the numerator and the denominator by a
common factor. Like this:
28 28 4 7
48 48 4 12
EGC COMPASS Placement Test Review Packet
7
28
48
This can also be done in several steps:
28 2
48 2
14
24
14 2
24 2
7
12
At the end of a calculation fractions should always be simplified.
Multiplying, Dividing, Adding, and Subtracting Fractions
Examples:
5 9 45
3 20 60
3
4
5 15
3 7
or
1
5
13
93
204
2 3
5 7
35
45
7
9
2
3
1
7
2 7
3 7
or
1 3
1 4
Practice Problems:
3 5
1.
4 11
2.
5 7
3 15
3
4
5 15
3 7
1 3
7 3
14 3 17
21 21 21
and
1
5 7
3 153
1 7
3 3
7
9
5 1
6 8
5 4 1 3
6 4 8 3
20
24
3
24
3.
7
9
3
5
5. 9
5
6
7.
2
5
3
4
9.
8 2
15 5
4.
5
21
14
25
6.
1
5
3
4
8.
7
10
5
9
10.
4
4
5
EGC COMPASS Placement Test Review Packet
17
24
7
11.
2
3
1
4
12.
1
3
5 10
1
6
14.
8
15
72
32
8.
1
50
50
4
1
9.
1
3
3
1
5
11
11.
12
1
12.
2
13.
Answers to Practice Problems:
15
2
1.
4.
44
15
6
15
1
2.
5.
7
35
2
2
21
4
3.
6.
45
15
7
9
7.
10.
5
1
8 12
15.
5
12
3
10
11
18
17
14.
24
43
15.
60
13.
Order of Operations
(Math 20)
When evaluating numerical expressions we follow the Order of Operations:
1. Evaluate the inside of the parentheses or other grouping symbols first.
Grouping symbols include also brackets, absolute value, square roots, and
complex numerators and denominators.
2. Evaluate exponents.
3. Multiply or divide, whichever comes first as you read left to right.
4. Add or subtract, whichever comes first as you read left to right.
Example 1:
25 (2 4) 2 4 2 1 Evaluate inside of parantheses first.
25 62 4 2 1
25 36 4 2 1
25 9 2 1
25 18 1
7 1
8
Evaluate exponents next.
Divide first since the division is further left than the multiplication
Multiply.
Subtract first since the subtraction is further left than the addition.
Add.
EGC COMPASS Placement Test Review Packet
Example 2:
5 1
)
Evaluate inside of parantheses first.
3 2
5 1
25 ( 6) 2 ( 8) • ( )
Evaluate exponents next.
3 2
5 1
25 36 ( 8) • ( )
Divide first since the division is further left than the multiplication.
3 2
3
9
5
1
25
•(
)
Multiplication next by first simplifying the fractions.
2
31 2
25 (2 8) 2 ( 8) • (
25
25
25
1
50
2
35
2
36
2
18
3
•(
2
15
2
15
2
15
2
1
2
5 1
)
1 2
1
2
1
2
1
2
Multiply.
Subtract first since the subtraction is further left than the addition.
The common denominator is 2.
Add.
Simplify.
Practice Problems:
1. 10 (9 2 2) 2 5 3
2.
2
3
3. 7 2
1
3
4. 25 36 32 22 24 2 3 (5 ( 6))
2
3
5
2
4 3 23
5 8
4 5 4(4 1)
Answers to Practice Problems:
1. 8
23
1
2.
11
2
2
5. (36 42 2 2) 2 ( 5 30 2 3 40) 2
6.
25
1
12
2
2
4. 75
3.
EGC COMPASS Placement Test Review Packet
10 15
3 27
36 48 30
45 36 24
5. 300
27
6.
4
6
3
4
8
Solving Linear Equations
(Math 60)
Definitions
A variable is a place holder for a number. It is represented by a letter.
Example: x, y, a, b
A term is a number, variable, or a combination of both if multiplied together. Different
terms are separated by addition and subtraction.
Example: In the expression 5 + 7x – 7(x+2) the terms are 5 and 7x, and -7(x+2).
Like terms are terms that have the same variables with the same exponents. In an
equation like terms can be combined.
Example: 7x and 2x are like terms, 8x and 4x2 are not like terms.
Distributive property: a(x+y) = ax + ay
Example: 2(3x-4) = 6x – 8
The Golden Rule of Algebra
What you do to one side of an equation or inequality you have to do to the other side
of the equation or inequality as well.
The objective for solving equations or inequalities is to isolate the variable on one side
of the equation or inequality. To achieve that we can do a combination of the following
operations (‚s omething‛ c an be a number, variable, or a combination of both):
Add something to both sides.
Subtract something from both sides.
Multiply something to both sides.
Divide both sides by something.
Square both sides.
Take the square root of both sides.
In case of an inequality, if multiplied or divided by a negative number the sign will turn
around (for instance from < to >).
EGC COMPASS Placement Test Review Packet
Example 1:
2x 8 7 x 2
2x 8 7 x 7 x 2 7 x
5x 8 2
5x 8 8 2 8
5 x 10
5x
5
x
10
5
2
subtracting 7 x from both sides to bring variables to the same side
combining like terms
adding 8 to both sides to isolate variable
combining like terms
dividing both sides by
5 to isolate variable
simplify fractions
Example 2:
7 a (a 1) 8(a 4) 3(7 a 12) 3
7 a a 1 8a 32 21a 36 3
distributing
14a 31 21a 39
simplifying like terms
14a 31 21a 21a 39 21a subtracting 21a from both sides to bring variables to the same side
7 a 31 39
7 a 31 31 39 31
7 a 70
7 a 70
7
7
a
10
combining like terms
adding 31 to both sides to isolate variable
combining like terms
dividing both sides by
7, turning around the inequality sign
simplify fractions
Practice Problems:
Solve each equation or inequality.
1. 5x – 3 + 2x = 15 + 3x + 2
2. 9b – 8 + 8b > 17 + 2b + 5
3. 41y – 53 + 38y = 46 + 73y + 81
4. 4 + 7a – 11 = 24a – 6 – 13a
5. 2 + 8z – 5 < 8z – 9 – 4z
Answers to Practice Problems:
1. x = 5
2. b > 2
3. y = 30
1
4. x
4
3
5. x
2
EGC COMPASS Placement Test Review Packet
6. 54 + 79k – 91 = 34k – 37 + 45k
7. 15 – 3(b+7) = 2(b+2)
8. 23(x+1) + 7(2x–1) = 43x – 6(x–2)
9. 4n – 7(n–5) +10 < 8 – 15(n+2) – 6x
10. 54x + 6(7x–4) ≥ 7(8x+7) – 9(4x–8x)
6. all real numbers
7. x = -2
8. no solutions
67
9. x
18
73
10. x
4
8
Graphing Lines
(Math 60)
Definitions
A line is the graphic representation of a linear equation in two variables.
Example: The linear equation y = 2x + 1 can be graphically represented as:
y = 2x+1
y
x
The slope is a measure of how steep the line is.
The x-intercept is the intersection of the line and the x-axis.
The y-intercept is the intersection of the line and the y-axis.
If the line is in the form y = mx + b we call it the slope-intercept form. With m
representing the slope and b representing the y-intercept (0,b).
If the line is in the form ax + bx = c we call it the standard form.
We get the slope-intercept form from the standard form by solving for y.
We get the standard form from the slope-intercept form by subtracting mx from both
sides (add if m is negative) and multiply by the common denominator (if there are
fractions).
Graphing a Line
To graph a line in slope-intercept form we make a table of values by choosing several
values for x and solving the equation for y respectively.
EGC COMPASS Placement Test Review Packet
8
1
x 1 we choose 0, 2, and -2 for our x values (2 was
2
chosen so the fraction simplifies easily). We then substitute these values for x and solve
for y. In the case of x=2 this is how:
Example: For the equation y
y
1
x 1
2
1
(2) 1
2
2
1
2
1 1
y
2
y
y
y
Finding the other points the same way we get the following table:
x
0
2
-2
y
-1
-2
0
Graphing each of those points and connecting the dots, we get the following graph:
y = -1/2*x-1
y
x
To graph a line in standard form we make a table of values by choosing 0 for x and
solving the equation for y, and then choosing 0 for y and solving the equation for x.
Example: For the equation x 2 y
2 we choose 0 for x and y and then solve for the
other variable respectively. For x=0 this is how:
x 2y
0 2y
2y
y
y
2
2
2
2
2
1
Finding the other points the same way we get the following table:
EGC COMPASS Placement Test Review Packet
x
0
-2
y
-1
0
8
Graphing each of those points and connecting the dots, we get the following graph:
y
x
Finding the Slope and Intercepts
If the equation appears in slope-intercept form y = mx + b then m represents the slope
and b is the y-intercept (0,b).
Another way of finding the slope is by using two points from the line and the slope
y2 y1
formula: m
x2 x1
The y-intercept can also be found by choosing 0 (zero) for x and solving for y.
The x-intercept can be found by choosing 0 (zero) for y and solving for x.
1
1
and the y-intercept is
x 1 we know the slope is
2
2
(0,-1). We find the x-intercept by choosing 0 for y and solving for x:
Example: In the example of y
0
2(0)
0
0
0 x
x
1
x 1
2
1
2(
x 1)
2
1
2(
x) 2(1)
2
x 2
So the x-intercept it (-2,0).
x 2 x
2
EGC COMPASS Placement Test Review Packet
8
Practice Problems:
Graph each line and find its slope and intercepts.
1. y = x – 1
4. 2x + 3y = 5
2. y = -3x – 4
5. x – y = -2
1
6. 3x – y = 4
x 2
3. y
3
Answers to Practice Problems:
1. m=1
x-intercept: (1,0)
y-intercept: (0,1)
1
3
x-intercept: (-6,0)
y-intercept: (0,2)
3. m=
y
y
x
x
2. m=-3
4. m=
4
,0)
3
y-intercept: (0,-4)
x-intercept: (
2
3
5
,0)
2
5
y-intercept: (0, )
3
x-intercept: (
y
y
x
x
EGC COMPASS Placement Test Review Packet
8
5. m= 1
x-intercept: (-2,0)
y-intercept: (0,2)
6. m= 3
2
,0)
3
y-intercept: (0,-2)
x-intercept: (
y
y
x
x
Laws of Exponents
(Math 65)
When simplifying expressions with exponents we follow these laws:
aman
am
an
(a m ) n
8
n
am
n
a mn
a0
1
am
1 (a
(ab) m
a mb m
a
Examples:
1. x5x3 = x5+3 = x8
h6
2. 14 h6 14 h
h
am
m
0)
1
h8
EGC COMPASS Placement Test Review Packet
8
3.
83
4
83 4
812
4.
54 x 7 y13 z 5 y12
56 x 2 z 5
2
54 6 x 7 2 y13 12 z 5
5 2 x5 y 25 1
52(
2)
2
2
5 2 x5 y 25 z 0
5 2 x5 y 25
5
2
2
x 2(5) y 2(25)
5 4 x10 y 50
x10 y 50
54
Practice Problems:
Simplify:
1. 52•54
x 11
2.
x3
3. (a4)5
4. c–7
5. (yz3)6
73 x 4 7 2 x3
6.
74 x5
Answers to Practice Problems:
1. 56
2. x8
3. a20
1
4. 7
c
5. y6z18
7.
8.
a 2b3
3
a 5b10
47 s 2t
2
43 st 4
32 x 3 y 4 z 4 313 x 6 z
9.
310 xy12 35 y 3 z 4
10.
6. 7x2
a
7.
b
411 s 3
8.
t2
EGC COMPASS Placement Test Review Packet
4 3 a 3b 4c5 2 10 a 6 c
2 8 a 1c 12 4 5 b 3c 4
9.
x8 z
y11
10.
4c14
a 2b
8
Functions
Consider a function f(x). Then x is the input and f(x) the output. All eligible inputs make
up the domain. All outputs make up the range.
Unless otherwise noted the domain is usually all real numbers. The two most common
exceptions are:
1. If the function contains a fraction the domain will be restricted because the
denominator cannot be zero. The function has a vertical asymptote at that point.
2. If the function contains an even root the domain will be restricted because the
radicand has to be greater or equal to zero.
To find the range it is often helpful to graph the function by solving f(x) for as many x
as needed to see what the function looks like.
Example1: For the function f(x) = 2x+1 the domain is all real numbers and so is the
range.
Example 2: For the function f ( x)
cannot be zero. 5x+2=0 when x
3
the domain is restricted by the fact that 5x+2
5x 2
2
. Therefore the domain is all real numbers with the
5
2
. We can write that mathematically in different ways:
5
2
2
2
,
,
1. Domain:
2. Domain: x | x
5
5
5
2
.
We there for have a vertical asymptote x
5
To find the range we graph the function. We will start by choosing 0, 1, -1, 2, -2 for x
and solve f(x). For x=2 this is how:
exception of
3
5x 2
3
f (2)
5(2) 2
3
12
f ( x)
EGC COMPASS Placement Test Review Packet
Finding the other points the same way we get the following table:
x
0
1
-1
2
-2
y
3
1.5
2
3
0.4
7
-1
3
0.25
12
3
0.4
8
If we put everything we have so far in a picture we get:
y
x
It can be helpful to choose a few more points and we will find this graph:
y
x
Knowing that we have a vertical and a horizontal asymptote we can see from here that
the range is
,0
0, .
EGC COMPASS Placement Test Review Packet
Function Transformation
We relate many functions back to a few basic function types by using transformations.
That can be very helpful in graphing the function and finding its range.
Function
f(x) + k
f(x) – k
f(x+k)
f(x-k)
–f(x)
f(–x)
k•f(x)
f(k•x)
Transformation
Shift vertically up k units
Shift vertically down k units
Shift horizontally left k units
Shift horizontally right k units
Reflect vertically about the x-axis
Reflect horizontally about the y-axis
Stretch/Shrink vertically by a factor of k
Stretch/Shrink horizontally by a factor of 1/k
Example:
The function f(x) = (x-2)2 –3 has the function g(x) = x2 as the base. Looking at the above
transformation table we can see that we can find the graph of f(x) by shifting g(x) 3
units down and 2 units to the right. If we know that g(x) has a range of [0,∞) we know
that the range of f(x) is [-3,∞). And we can graph f(x) easily:
y
x
Practice Problems:
For each of the functions:
a) Find the domain.
1.
f ( x)
2.
f ( x)
3.
f ( x)
2x2 4
1
x 2
4 x 4 x3 5 x 2
b) Find the range.
x 1
EGC COMPASS Placement Test Review Packet
c) Graph the function.
4.
f ( x)
5.
f ( x)
6.
f ( x)
2x 6
x 4 2
x
2
x x 2
9
Answers to Practice Problems:
1. a) all real numbers
b) [-4,∞)
c)
4. a) [-3,∞)
b) *0,∞)
c)
y
y
x
2. a)
b)
, 2
,0
x
5. a) (-∞,4+
b) [-2,∞)
c)
2,
0,
c)
y
y
x
x
6. a)
3. a) all real numbers
b) (-∞,4)
c)
, 1
1,
(2, )
b) all real numbers
c)
y
y
x
EGC COMPASS Placement Test Review Packet
x
9
Laws of Logarithms
(Math 111)
The logarithm is defined as the inverse of the exponent. If we want to solve b x
then the logarithm is defined as the solution:
x log b m
m for x
When simplifying expressions with logarithms we follow the laws of logarithms, just
like we did with the laws of exponents. It is important to notice that the laws of
logarithms are different, inverse to be exact. That is because the logarithm is the inverse
function of the exponent.
log b m log b n log b (m n)
log b m logb n logb
m
n
r log b m log b (m r )
log b 1 0
logb b 1
log b m
log a m
log a b
The logarithms to the base 10 and e have special expressions:
log m log10 m
ln x log e x
Practice Problems:
Simplify, using the laws of logarithms.
1. log10 log 3
2. log 28 log 4
3. 4ln 3
Answers to Practice Problems:
1. log 30
2. log 7
3. ln81
EGC COMPASS Placement Test Review Packet
4. log9 2log3
5. log 20 4 log 20 5
6. ln 20 ln3 ln 6
4. 0
5. 1
6. ln10
9
Additional Math Review Resources
Online Websites
http://www.coolmath.com/
http://www.testprepreview.com/modules/algebra1c.htm
http://www.testprepreview.com/modules/algebra2.htm
http://www.testprepreview.com/modules/fractionsandsquareroots.htm
http://www.testprepreview.com/modules/mathematics3.htm
http://www.testprepreview.com/modules/exponents.htm
http://www.testprepreview.com/modules/percentandratios.htm
http://www.khanacademy.org
EGC COMPASS Placement Test Review Packet
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