ACT PREP

1
?
ACT PREP
MATH
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Content
?14 questions dealing with Pre-Algebra ? 10
questions from Elementary Algebra ? 9 questions
based on Intermediate Algebra ? 9 questions from
Coordinate Geometry ? 14 questions from Plane
Geometry ? 4 Trigonometry questions
The questions assume knowledge of basic formulas
and computational skills but do not require
memorization of complex formulas or extensive
computation
3
Pace Yourself

• 60 questions
• ?60 minutes
• ?Dont waste time on any one problem, spend your
  dftime doing as many problems as you can
• ?The questions are arranged in order of
  difficulty
• ?RELAX answering only half of the questions
  right onwill give you a score of 20 on the math
  section

4
Pace Yourself
Go Through The Test Twice

• Take 45 minutes to go through the test
• Answer the questions that you know how to do
• Guess on the questions you know youll never get
• Mark the harder questions that youll come back
  to later

• Spend the last 15 minutes going over the test
  again
• ?Answer the questions you skipped
• Make sure you have answered every question
• Spend any remaining time checking your work

5
Calculators
ALL PROBLEMS ON THE ACT CAN BE SOLVED WITHOUT
USING A CALCULATOR

• You may use a four-function, scientific, or
  graphing calculator on the Math test
• Calculators, such as TI-89 and TI-92 are NOT
  permitted (see page 4 in the ACT prep booklet)
• Bring a calculator that you know how to use
  bringing a more powerful calculator that you do
  not know how to use isnt going to help you

6
Understand the Problem

• Read the problem carefully
• Pay attention to what the question asks you to
  find
• Watch for unnecessary information
• Label the figures with numbers or letters
• Draw a picture

7
Solving the Problem

• Theres more than one way to solve these problems
• Its a timed test find a quick and reliable way
  to solve the problem
• Do your work in your test booklet
• Be careful using your calculator its easy to
  push the wrong button
• Dont get involved in long, complicated, or
  tricky calculations

8
Check Your Answer

• Make sure you answered the question that was
  asked
• Each of the wrong answers represents a common
  mistake that you might have made
• If your answer isnt one of the choices, reread
  the question and check your work

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When You
Get Stuck
10
BACKSOLVE
Take advantage of the multiple-choice format and
try each answer until you find the one that works.
WARNING Doing it this way will take more time.
The greatest common divisor of 84, 90, and 66
(that is, the largest exact divisor of all three
numbers) is

1. 6
2. 12
3. 18
4. 36
5. 90

90 does not go into 84 eliminate answer E 36
does not go into 84 eliminate answer D 18 does
not go into 84 eliminate answer C 12 does not
go into 90 eliminate answer B 6 must be the
correct answer and it checks
84 2?2?3?7 90 2?3?3?5 66 2?3?11 2?3
6
CORRECT ANSWER A
11
BACKSOLVE (cont)

• F. 0
• G. 2
• 4
• J. 8
• K. 10

12
BACKSOLVE (cont)

• F. 0
• G. 2
• 4
• J. 8
• K. 10

Correct AnswerJ
13
GUESSTIMATE
If you can estimate the correct answer, then you
should be able to eliminate at least one or two
answer choices.
What is 2 of 60?
60 x 0.02 1.2

1. 120
2. 12
3. 1.2
4. 0.12
5. 0.012

120 is greater than 60 eliminate answer A
12 is too large eliminate answer B
CORRECT ANSWER C
0.012 is too small eliminate answer E
14
GUESSTIMATE (cont.)
A
? 4 meters
B 3 meters C
12, 7, and 5 are longer than the hypotenuse
eliminate answers F, G, and H
15
GUESSTIMATE (cont.)
A
? 4 meters
B 3 meters C
CORRECT ANSWER K
16
EYEBALL
By looking at the figure X looks too big to be
5- eliminate answer A X looks too small to be
either 60 or 55 - eliminate answers E and D
On the ACT, the diagrams are not necessarily
drawn to scale, but usually theyre quite
accurate, so you could eliminate certain answer
choices by sizing things up with your eyes
In the figure below, what is the value of x?

1. 5
2. 30
3. 40
4. 55
5. 60

x
125 85
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EYEBALL (cont.)
In the figure below, what is the value of x?
x

1. 5
2. 30
3. 40
4. 55
5. 60

125 85
55
95
180 125 55
180 - 85 95
180 55 95 30
CORRECT ANSWER B
18
EYEBALL (cont.)
By looking at the figure ?A looks larger than
99 eliminate answer F ?A looks smaller than
240 eliminate answer K
Lola is making the circle graph below showing the
number of students at each grade level in her
high school. What should be the measure of ?A?
F. 99 G. 120 H. 133 J. 167 K. 240
240 freshmen
A
200 sophomores
130 seniors
150 juniors
19
EYEBALL (cont.)
Total number of students 720 Total number of
freshmen 240 Total number of degrees in a
circle 360
CORRECT ANSWER G
20
PICK NUMBERS
Some problems are hard because theyre general or
abstract, so replace variables with specific
numbers
If kx k 0, and kgt1, then x ?
Pick a value for k that is greater than 1

1. 0
2. -1
3. 1
4. -k
5. k

Let k 2 kx k 0 2x 2 0 2x -2 x -1
Let k 5 kx x 0 5x 5 0 5x -5 x -1
21
PICK NUMBERS (cont.)
If kx k 0, and kgt1, then x ?

1. 0
2. -1
3. 1
4. -k
5. k

kx k 0 k(x1) 0 k 0 OR x1 0 k 0
OR x -1
CORRECT ANSWERB
22
PICK NUMBERS (cont.)
For all a ? 0, what is the slope of the line
segment connecting (a,b) and (-a,b) in the usual
(x,y) coordinate plane?
23
PICK NUMBERS (cont.)
For all a ? 0, what is the slope of the line
segment connecting (a,b) and (-a,b) in the usual
(x,y) coordinate plane?
CORRECT ANSWER F
24
Practice
Questions
25
Question 1
D
C

1. 13
2. 17
3. 19
4. 24
5. 25

4
12
A
3
B
26
CORRECT ANSWER A
13
D
C
5
4
12
A
3
B
ABC is a 3-4-5 right triangle and BCD is a
5-12-13 right triangle
27
Question 2
In the figure below, line m is parallel to line
n, and line t is a transversal crossing both m
and n. Which of the following lists has 3 angles
that are all equal in measure?

1. ?a,?b,?d
2. ?a,?c,?d
3. ?a,?c,?e
4. ?b,?c,?d
5. ?b,?c,?e

a
m n
b c
d
e
t
CORRECT ANSWER A
28
Question 3
A shirt that originally cost 35 is on sale at
20 off. If the sales tax on shirts is 5 of the
purchase price, how much would it cost to buy the
shirt at its sale price?
35 (.20) 7
CORRECT ANSWER D
35 7 28

1. 7.35
2. 20.00
3. 26.60
4. 29.40
5. 29.75

28 (.05) 1.40
28 1.40 29.40
35 (.80) 28 28 (1.05) 29.40
29
Question 4
What is the slope of the line x 2y 3?
CORRECT ANSWER A
y mx b
30
Question 5
In the figure below, A, C, and D are collinear.
If the measure of ?A is 30? and the measure
of?BCD is 120?, what is the measure of ?B?

1. 30?
2. 60?
3. 90?
4. 120?
5. 150?

B
A
C D
31
In the figure below, A, C, and D are collinear.
If the measure of ?A is 30? and the measure of
?BCD is 120?, what is the measure of ?B?
CORRECT ANSWER C
B
180 30 60 90?
90
30
120
60
A
C D
180 120 60?
32
Question 6
If the area of a circle is ?, what is the length
of its circumference?

• 1
• 2
• ?
• 2?
• 3?

Areacircle ?r2 Circumference 2?r
? ?r2 1 r2 1 r
C 2?(1) C 2?
CORRECT ANSWER D
33
Question 7
What is the value of x in the solution for the
system of equations below? 2x 5y 20 6x ½ y
29

1. 4
2. 5
3. 6
4. 15
5. 20

34
What is the value of x in the solution for the
system of equations below? 2x 5y 20 6x ½ y
29
2x 5y 20 6x ½ y 29
2x 5y 20 60x - 5y 290
multiply by 10
add equations together 62x 310
solve for x x 5
35
What is the value of x in the solution for the
system of equations below?
CORRECT ANSWER B
2x 5y 20 6x ½ y 29
12x y 58
solve for y
-y 58 12x
y -58 12x
substitute into 1st equation
2x 5(-5812x) 20
solve for x
2x -290 60x 20 62x -290 20 62x 310 x
5
36
Question 8
CORRECT ANSWER C
37
Question 9
For all y, 26y (-10y) 3y(-y3) ?

1. 10y
2. -3y2 25y
3. 3y2 7y
4. 3y2 25y
5. 3y2 27y

26y (-10y) 3y(-y3) 26y 10y 3y2 9y 3y2
27y
CORRECT ANSWER E
38
Question 10
C

1. 65?
2. 70?
3. 75?
4. 80?
5. 85?

D
100?
30?
A B
39
C
D

1. 65?
2. 70?
3. 75?
4. 80?
5. 85?

80
100?
50?
50?
30?
A B
180 30 50 100
180 100 80 m? BDC 80?
CORRECT ANSWER D
40
Question 11
In the figure below, ?S is a right angle, RS is 3
units long, and ST is 4 units long. If the
measure of ?R is x, then sin x ?
T
4
x
R 3 S
41
In the figure below, ?S is a right angle, RS is 3
units long, and ST is 4 units long. If the
measure of? R is x, then sin x ?
T
a2 b2 c2 32 42 c2 9 16 c2 25 c2 5
c
5
4
x
CORRECT ANSWER C
R 3 S
RST is a 3-4-5 right triangle
42
Question 12
In the figure below, the lengths of DE, EF, and
FG are given, in units. What is the area, in
square units, of triangle DEG?
G
10
D 12 E 7
F
43
In the figure below, the lengths of DE, EF, and
FG are given, in units. What is the area, in
square units, of triangle DEG?
G
10
D 12 E 7
F
AreaTriangle ½ base x height ½ (12)
(10) 60
CORRECT ANSWER C
44
Question 13
A
6

1. ?
2. 2?
3. 6?
4. 12?
5. 36?

O
60?
B
45
Circumference 2?r C 2?6
C 12?
degrees arc
60(12?) 360 x 720? 360 x 2? x
A
6
O
60?
CORRECT ANSWER B
B
46
Question 14
A
13
C 12 B
47
a2 b2 c2 122 b2 132 144 b2 169 b2
25 b 5
CORRECT ANSWER A
A
13
5
C 12 B
48
Question 15
CORRECT ANSWER E
49
Question 16
What is the cost in dollars to carpet a room x
yards long and y yards wide if the carpet costs
two dollars per square foot?
x yards 3x feet
y yards 3y feet

1. xy
2. 2xy
3. 3xy
4. 6xy
5. 18xy

Arearectangle length x width
3x(3y) 9xy square feet
Total Cost area x price 9xy
(2) 18xy
CORRECT ANSWER E
50
Question 17
In the figure below, the largest possible circle
is cut out of a square piece of tin. The area of
the remaining piece of tin is approximately (in
square inches)
2 inches

1. 0.14
2. 0.75
3. 0.86
4. 1.0
5. 3.14

51
Question 17
In the figure below, the largest possible circle
is cut out of a square piece of tin. The area of
the remaining piece of tin is approximately (in
square inches)
2 inches
Areacircle ? r2

1. 0.14
2. 0.75
3. 0.86
4. 1.0
5. 3.14

? 12 ? 3.14
1
Areasquare s2
22 4
Areapiece Areasquare - Areacircle
4 3.14 0.86
CORRECT ANSWER C
52
Question 18
Which of the following is equal to 3.14 x 106?

1. 314
2. 3140
3. 31,400
4. 314,000
5. 3,140,000

3.1400000000
3140000.0000
CORRECT ANSWER E
53
Question 19
Find the last number in the series 8, 4, 12, 6,
18, 9,?
8?4 8-44 or 8?24 4?12 4812 or
4x312 12?6 12-66 or 12?2 6 6
?18 61218 or 6x318 18?9 18-99 or
18?2 9

1. 19
2. 20
3. 22
4. 24
5. 27

9x327
CORRECT ANSWER E
54
Question 20
Lyndsey receives grades of 91, 88, 86, and 78 on
four tests. What grade must she receive on her
fifth test to have an average test score of 85?

1. 82
2. 83
3. 84
4. 85
5. 86

Let x the fifth test score (91 88 86
78 x ) ? 5 85 343 x 425 x 82
CORRECT ANSWER A
55
Question 21
One angle, ?A, has 3 times the measure of its
supplement, ?B. What is the degree measure of ?A?
Let x the measure of ?B then 3x the measure
of ?A

1. 112 ½
2. 120
3. 135
4. 150
5. 157 ½

x 3x 180 4x 180 x 45
?B 45 ?A 135
CORRECT ANSWER C
56
Question 22
A bag contains 4 red jelly beans, 5 green jelly
beans, and 3 white jelly beans. If a jelly bean
is selected at random from the bag, what is the
probability that the jelly bean selected is green?
Probability of drawing a green jelly bean
CORRECT ANSWER D
57
Question 23
For all positive values of a, b, and c with altb
and agtc, which of the following MUST be true? I.
abgtc II. 2agtc III. acgtb
c lt a lt b

1. a and b are both greater than c, so their sum
   will also be TRUE

1. I only
2. II only
3. I and II only
4. II and III only
5. I, II, and III

II. agtc, so 2agtc TRUE
III. If c2, a4, and b10, then acltb - FALSE
CORRECT ANSWER C
58
Question 24
B A
1 C
CORRECT ANSWER C
59
Question 25
B E
C
D A
60
CORRECT ANSWER E
B 20-x E x
C
20
4 D 6 A
10
61
Things to Remember on the Math ACT
Dont read the directions
Bring a calculator that you know how to use
Read the question carefully
Pay attention to what the question asks you to
find
Watch for unnecessary information
Draw a picture
Pace yourself (60 questions/60 minutes)
62
Things to Remember on the Math ACT
Do the easy questions first, then try the hard
ones
Show some work and circle your answers in your
test booklet
Dont waste too much time on one problem
Eliminate wrong answers before guessing
Answer every question
Check your work
Work for the whole 60 minutes