ACT PREP

1
?
ACT PREP
MATH
Educational Talent Search and Upward
Bound Forward Service Corporation
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Question 15
CORRECT ANSWER E
3
2x5 ?
3x4y6
Calculator or Zoom?
34 ?
53
Calculator or Zoom?
4
73 ?
54
25 (33 43)
5
7x2y4
(2x2 7xy4 3xy)
(3x 5y2)2
6
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

ZOOM?
7
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
8
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
9
2x 4 8
10
2x 4 lt 8
11
2x 4 gt 8
12
v576 4v1296 6v64
13
A
Cos A Sin A Tan A Cos C Sin C Tan C
5
3
B
C
4
Will you be asked for Sin B?
14
A
Use Sin to find Angle A Use Cos to find Angle A
5
3
B
C
4
15
A
Use Sin to find Angle C Use Cos to find Angle C
13
5
B
C
12
16
A
Use Sin to find Angle A Use Cos to find Angle A
13
5
B
C
12
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Imaginary Numbers

• i14 Calculator or zoom?
• i7
• i20
• i21

18

1. i(2 i)
2. 6i(5 4i)
3. (2 8i) (-3 9i)
4. (6 5i) (3 12i)
5. (2 i)(4 3i)

19
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
20
Geometry Section
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GUESSTIMATE (cont.)
A
? 4 meters
B 3 meters C
12, 7, and 5 are longer than the hypotenuse
eliminate answers F, G, and H
22
GUESSTIMATE (cont.)
A
? 4 meters
B 3 meters C
CORRECT ANSWER K
23
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
One 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
25
Practice
Questions
26
Question 1
D
C

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

4
12
A
3
B
27
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
28
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
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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
30
Question 4
What is the slope of the line x 2y 3?
CORRECT ANSWER A
y mx b
31
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
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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?
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Question 8
Regular calculator or ZOOM?
CORRECT ANSWER C
34
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
35
Question 10
C

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

D
100?
30?
A B
36
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
37
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
38
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
39
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
40
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
41
Question 13
A
6

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

O
60?
B
42
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
43
Question 14
A
13
C 12 B
44
a2 b2 c2 122 b2 132 144 b2 169 b2
25 b 5
CORRECT ANSWER A
A
13
5
C 12 B
45
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
46
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

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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
48
Question 18
Which of the following is equal to 3.14 x 106?
Regular calculator or ZOOM or NEITHER?

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

3.1400000000
3140000.0000
CORRECT ANSWER E
49
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
50
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
51
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
52
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
53
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
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Question 24
B A
1 C
CORRECT ANSWER C
55
Question 25
B E
C
D A
56
CORRECT ANSWER E
B 20-x E x
C
20
4 D 6 A
10
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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)
58
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