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ACT Math Prep

Total questions: 121

Worksheet time: 2hrs 1mins

Name
Class
Date
1.

What are the basic operations in Math?

a)

Sum, difference and fractions

b)

Addition, subtraction, multiplication and division

c)

Product and Quotient

2.

Liam went to the doctor. There are 8 patients waiting. The nurse told him it will be his turn after 2 hours. How many minutes would the doctor use to see each patient?

a)

20 minutes

b)

8 minutes

c)

15 minutes

3.
Which operation does "times" represent?
a)
addition
b)
subtraction
c)
multiplication
d)
division
4.
Which operation does "the quotient of" represent?
a)
addition
b)
subtraction
c)
multiplication
d)
division
5.
What place value is the 7 in in the number:  4,521,735?
a)
thousands
b)
tens
c)
hundreds
d)
hundred thousands
6.
What is the value of the 9 in the number 293,672
a)
90,000
b)
900,000
c)
900
d)
9,000
7.
What is the standard form of the number  1,000 + 300 + 50 + 7
a)
10,357
b)
1,305
c)
1,357
d)
13, 507
8.
What is the expanded form of the number: 4,305
a)
4,000 + 300 + 5
b)
4,000 + 300 + 50
c)
40,000 + 3,000 + 5
d)
4,000 + 30 + 5
9.

754,987 ______ 754,987

a)

<

b)

>

c)

=

10.
three and three tenths
a)
3.10
b)
3.3
c)
310
11.
What is the standard form of Thirty-eight and seventy-two hundredths?
a)
38.72
b)
308.720
c)
3872
d)
308.27
12.
What is the standard form of Thirty-eight and seventy-two hundredths?
a)
38.72
b)
308.720
c)
3872
d)
308.27
13.
What is the standard form of three and six hundred fourteen thousandths?  
a)
3.614
b)
3.0614
c)
.3614
d)
30.614
14.
The area of a square is 36 cm2.  What is the length of one side?
a)
6 cm
b)
24 cm
c)
9 cm
d)
9 cm
15.
To find the square root of a number, you must divide it by 2.
a)
True
b)
False
16.
The √20 is between which two consecutive integers?
a)
2 & 3
b)
3 & 4
c)
4 & 5
d)
5 & 6
17.
Between which two consecutive whole numbers is the√200? 
a)
13 and 14
b)
15 and 16
c)
14 and 15
d)
11 and 12
18.
Write each product using an exponent. 
4 x 4 x 4 x 4 x 4 
a)
45
b)
54
c)
46
d)
46
19.
Find the value (standard form) of the power. 
33
a)
9
b)
6
c)
27
d)
12
20.
Evaluate this expression using the quotient rule.
a)
95
b)
99
c)
15
d)
9-5
21.
Simplify (-1/2)0
a)
1
b)
0
c)
-1
d)
-2
22.
(2x3y)6
a)
2x18y6
b)
64x18y6
c)
64x3y6
d)
2x3y6
23.

How would you write 5.6 x 10-3 in standard form?

a)

56,000

b)

5,600

c)

0.00056

d)

0.0056

24.
How do you write
8.317 x 106
in standard form?
a)
8, 371, 000
b)
83, 170, 000
c)
837, 100
d)
8, 317, 000
25.
Which of the following is correct scientific notation?
a)
20.35 x 104
b)
.2035 x 104
c)
2035 4
d)
2.035 x104
26.
Express the following in scientific notation:
.000457
a)
457 x 106
b)
457 x 10-6
c)
4.57 x104
d)
4.57 x 10-4
27.

Find ALL FACTORS of 24

a)

1, 2, 12, 24

b)

1, 2, 8, 24

c)

1, 2, 3, 4, 5, 6, 8, 12, 24

d)

1, 2, 3, 4, 6, 8, 12, 24

28.
Which number is a factor of 10
a)
3
b)
4
c)
5
d)
8
29.

[Use the table to find each ratio]

**white socks to brown socks**

a)

8:5

b)

5 to 8

c)

8:4

d)

6 to 5

30.

Earl runs 75 meters in 30 seconds. How many meters does Earl run per second?

a)

5.2

b)

6:6

c)

4.6

d)

2.5

31.

Danny charges $35 for 3 hours of swimming lessons. Martin charges $24 for 2 hours of swimming lessons. Who offers a better deal?

a)

Danny

b)

Martin

32.

45% of 20 is _______

a)

20

b)

12

c)

50%

d)

9

33.
Solve the equation: 
x + 7 = 12
a)
x = 5
b)
x = 19
c)
x = -5
d)
x = 84
34.

List the integers from least to greatest: -9, -3, 0, -7, 5

a)

-9, -7, -3, 0, 5

b)

-9, -3, -7, 0, 5

c)

5, 0, -3, -7, -9

d)

-7, -9, 0, -3, 5

35.

Order the decimals from least to greatest: 1.5, 15, 8.5, -10.2, -12.3

a)

15, 8.5, 1.5, -10.2, -12.3

b)

-10.2, -12.3, 1.5, 8.5, 15

c)

-12.3, -10.2, 1.5, 8.5, 15

d)

15, 8.5, -10.2, -12.3, 1.5

36.

Order the fractions from greatest to least: 1/2, -1/2, -3/4, 7/8, 8/9

a)

8/9, 7/8, 1/2, -1/2, -3/4

b)

7/8, 8/9, 1/2, -1/2, -3/4

c)

-3/4, -1/2, 1/2, 7/8, 8/9

d)

8/9, 7/8, 1/2, -3/4, -1/2

37.

What inequality should be used to compare the absolute value of the two rational numbers? ∣−4.5∣        ∣−3∣\left|-4.5\right|\ \ \ \ \ \ \ \ \left|-3\right|  

a)

>

b)

<

c)

=

38.

What rational numbers can 'x' be when:  ∣x∣=56\left|x\right|=\frac{5}{6}  

a)

5/6

b)

-5/6

c)

0.87

d)

-0.87

39.
What is the probability of spinning a red if we spin 30 times?
a)
1/5
b)
1/30
c)
3/30
d)
1/10
40.
If you choose from the following M & M colors, what is the probability that you choose blue?
5 green
6 yellow
8 blue
7 brown
a)
8/26
b)
4/13
c)
8/25
d)
1/3
41.

What is the symbolic representation for Budget?

a)

y = $15x + $0.15

b)

y = $0.15x - $15

c)

y = $0.15x + $15

d)

y = $15

42.
According to a random telephone survey of 200 adults, 75% of all working adults in the U.S. are satisfied with their current job. What is the population in this survey?
a)
200 adults
b)
adults in the U.S.
c)
75% of adults
43.
A recent survey of 800 seventh graders from across the state shows 4 out of 10 like to play paper football. How many students said they like to play paper football?
a)
40 students
b)
200 students 
c)
320 students
d)
8,000 students
44.
Ana wants to know the average student’s opinion of the tardy policy at her school. Which group of students should she survey in order to achieve the most accurate results?
a)
thirty students who are often tardy
b)
thirty students who are rarely tardy
c)
thirty of her friends
d)
thirty randomly selected students from her school
45.
The entire group studied is called the
a)
sample
b)
population
46.
5³⋅5⁴
a)
5⁷
b)
5⁻¹
c)
5¹²
d)
5
47.

Which of the following is a square of an even number?

a)

144

b)

169

c)

441

d)

625

48.

Which of the following is not a perfect square?

a)

841

b)

529

c)

198

d)

All of the above

49.

If  a=3a=3 , find  7−a7-a  

a)

2

b)

3

c)

4

d)

5

50.

If b=10b=10 , find  40b\frac{40}{b}  .

a)

10

b)

2

c)

30

d)

4

51.

Which graph best represents the following situation: Nancy first walked toward the car and then away from it.

a)
b)
c)
d)
52.

Emma drove at a constant speed.

a)
b)
c)
d)
53.

Identify the independent variable.

Lana practices cello for 15 minutes each day. How many minutes does she practice in 3 days?

a)

number of minutes

b)

number of days

c)

45 days

d)

practicing cello

54.

What is the dependent variable?

Lana practices the cello for 15 minutes each day. How many minutes does she practice in 3 days?

a)

number of days

b)

45 minutes

c)

number of minutes

d)

practicing cello

55.

How would I isolate the variable? x-3=10

a)

add 3

b)

subtract 3

c)

divide by 3

d)

multiply by 3

56.

What do you need to do to solve for f? 4f=44

a)

multiply by 4

b)

subtract 4

c)

add 4

d)

divide by 4

57.
Solve by factoring: x2 - 9x + 20 = 0
a)
x = -4 and x = -5
b)
x = 20 and x = -9
c)
x = 4 and x = 5
d)
x = -4 and x = 5
58.
Factor: 49x2 - 100
a)
(49x + 100)(x - 1)
b)
(7x - 10)(7x + 10)
c)
(49x - 10)(x + 10)
d)
(7x -10)(7x - 10)
59.
Factor:   3x2- 6x - 24
a)
(3x - 8)(x + 3)
b)
(3x + 4)(x - 6)
c)
3(x - 2)(x + 4)
d)
3(x + 2)(x - 4)
60.
Solve Using the Quadratic Formula
 x2 + 4x - 40 = -8
a)
-10 & -4
b)
-4 & 10
c)
-8 & 4
d)
8 & -4
61.
In the equation
y = x2 +5x +7, match each leading coefficient with its correct letter 
a)
a=0, b=5, c=7
b)
a=1, b=5, c=7
c)
a=7, b=5, c=1
62.
a)
5x5/4
b)
5x-5/4
c)
(5x)-5/4
d)
(5x)-4/5
63.

Rewrite and Evaluate:

a)

1

b)

7.22

c)

45

d)

243

64.
|v + 8| − 5 = 2 
a)
{-1,-15}
b)
{-1,-5}
c)
{-15,15}
d)
No Solution
65.
|2a - 10| = 6
a)
a = 8, a = 5
b)
a = 2
c)
a = 8
d)
a = 8, a = 2
66.
| 2w - 1 | < 11
a)
No Solution
b)
All Real Numbers
c)
-5 < w < 6
d)
-6 < w < 5
67.
| x + 3 | ≤ 2
a)
No Solution
b)
All Real Numbers
c)
-5 ≤ x ≤ -1
d)
1 ≤ x ≤ 5
68.

What is the rule for this pattern?

32, 36, 40, 44

a)

add 4

b)

multiply 2

c)

subtract 4

d)

divide by 2

69.
What are the missing numbers in this pattern?
12, 15, ___, 21, ____, 27
a)
18,23
b)
18, 24
c)
17, 25
d)
17, 24
70.
What is the rule?
a)
Add 2
b)
Add 3
c)
Multiply by 3
d)
Multiply by 4
71.
If a system of equations has no solution, what does the graph look like? 
a)
intersecting lines
b)
parallel lines
c)
skew lines
d)
intersecting lines
72.
What is the solution?
a)
(1, -1)
b)
(-1, 1)
c)
(0, -2)
d)
(0, 1)
73.
Solve the system of equations.
y = 4x+1
3x + 2y = 13
a)
(1, 5)
b)
(5, 1)
c)
(0.25, 2)
d)
∅
74.

Solve: 5x - 10x2 < 0

a)

(0, ½)

b)

[0, ½]

c)

(−∞, 0) U (½, ∞)

d)

(- ½ , 0)

75.
Which inequality is shown?
a)
y< -x2
b)
y≤ -x2
c)
y> -x2
d)
y≥ -x2
76.

Which function does the equation represent?

a)

Linear

b)

Exponential

c)

Quadratic

d)

Cubic

77.

Which Table best represents a exponential relationship?

a)
b)
c)
d)
78.
Find B-A
a)
-3     1
7     -1
b)
1     0
1     -4
c)
4       0
-6     0
d)
not possible because rows do not match columns
79.
What are the dimensions of this matrix?
a)
2 x 3
b)
3 x 2
c)
6 x 1
d)
1 x 6
80.

Given the polynomial below, how many roots will it have?
 y=x2−25y=x^2-25  

a)

2

b)

1

c)

3

d)

0

81.

What are the roots of the quadratic function?

a)

-4 and -2

b)

4 and 2

c)

-4 and 2

d)

4 and -2

82.
i7
a)
i
b)
-i
c)
1
d)
-1
83.
Simplify:
(4 + 7i) - (3 + 2i)
a)
1 + 5i
b)
7 + 9i
c)
1 + 9i
d)
-1 + 5i
84.

What does (h,k) stand for in the standard circle equation?

a)

(h,k) is the center of the circle

b)

(h,k) is a point on the circle.

c)

(h,k) is a point that we guess and find

d)

(h,k) is the distance of the circle

85.
What is the equation of the circle?
a)
(x+1)2 + (y +1)2 = 3
b)
(x+1)2 + (y -1)2 = 3
c)
(x+1)2 + (y +1)2 = 9
d)
(x-1)2 + (y -1)2 = 9
86.
What is the y-intercept of the line?
a)
y = 1/2
b)
y = 1
c)
y = -1/2
d)
y = -1
87.

Which graph represents the table?

a)
b)
c)
d)
88.
Select the correct graph for each inequality.
a)
A
b)
B
c)
C
d)
D
89.
Select the correct graph for each inequality.
a)
A
b)
B
c)
C
d)
D
90.
Find the slope of the line.
a)
-5/4
b)
5/4
c)
-4/5
d)
4/5
91.
What type of slope?
a)
zero slope
b)
undefined
c)
negative
d)
positive
92.

Two lines that are parallel will have ...

a)

Slope that is opposite reciprocals

b)

No slope

c)

Slope that is the same

d)

none of the above

93.

Which is the equation of the line that is parallel to the graph of y = 5x + 7 and has a y-intercept at (0, -2)?

a)

y = 5x - 2

b)

y = -2x + 7

c)

y = 5(x - 2)

d)

y = -1/5x - 2

94.
What slope is perpendicular to:  
m = 5/8
a)
-5/8
b)
5/8
c)
-8/5
d)
8/5
95.
Find the distance between the two points: (2, -1) and (2, 5)
a)
0
b)
8.3
c)
6
d)
5.5
96.
What is the midpoint between (3, -1) and (7, -5)
a)
(5, -2)
b)
(10, -6)
c)
(5, -3)
d)
(2, -2)
97.
What are the coordinates of the center and the radius of the circle with equation:
(x - 4)2 + (y - 3)2 = 25 ?
a)
Center (4,3)
Radius = 5 units
b)
Center (4,3)
Radius = 25 units
c)
Center (-4,-3)
Radius = 25 units
d)
Center (-4,-3)
Radius = 5 units
98.
Which is the equation of a circle with center (2, 1) that passes through (2, 4)?
a)
(x – 2)2 + (y – 1)2 = 9
b)
(x – 2)2 + (y – 1)2 = 3
c)
(x + 2)2 + (y + 1)2 = 9
d)
(x + 2)2 + (y + 1)2 = 3
99.

A ___________is any closed, two-dimensional shape.

a)

quadrilateral

b)

figure

c)

plane figure

d)

solid figure

100.

The point at which two or more lines, line segments, or rays meet to form an angle. In solid figures, a _______ is the point at which three or more faces meet.

a)

face

b)

edge

c)

vertex

101.

What shape am I?

I have two congruent circles that are joined by a curved surface. I have no edges or vertices, but I can roll.

a)

Cylinder

b)

Sphere

c)

Cone

d)

Cube

102.
How many sets of parallel lines are in this shape?
a)
0
b)
1
c)
2
d)
5
103.
Does a rectangle have right angles?
a)
yes
b)
no
104.
Are these two lines parallel?
a)
yes
b)
no
105.
Identify the transformation from ABC to A'B'C'.
a)
90o clockwise rotation
b)
90o counter clockwise rotation
c)
Reflection across the y-axis
d)
Reflection across the x-axis
106.
Identify the transformation from C to D.
a)
90o Counter Clockwise Rotation
b)
180o Rotation
c)
270o Counter clockwise Rotation
d)
360o Rotation
107.
What is the justification (reason)?
a)
Reflexive Property
b)
Symmetric Property
c)
Transitive Property
d)
Substitution
108.
What is the justification (reason)?
a)
reflexive property
b)
definition of segment bisect
c)
definition of a midpoint
d)
substitution property
109.
A cereal box is 12cm tall.  The area of the base is 7cm.  What is the volume?
a)
84 cm2
b)
84 cm3
c)
83 cm
d)
84
110.
Find the volume of the following cone.
a)
156 ∏ m3
b)
702∏ m3
c)
2,106∏ m3
d)
78∏ m3
111.

A solid figure with 6 flat surfaces, all of the faces are squares

a)

cube

b)

rectangular prism

c)

triangular prism

d)

square based pyramid

112.
What shape is this?
a)
Cube
b)
Triangular Prism
c)
Rectangular Pyramid
d)
Cone
113.
Which trigonometric ratio is correct?
a)
cosC= adj/hyp
b)
sinC= adj/hyp
c)
tanC= adj/hyp
d)
tanC=adj/opp
114.
Fill in the blank...
SOH ___ TOA
a)
COH
b)
CAH
c)
COA
d)
CHA
115.
If you are given the opposite side and hypotenuse, which trig function should you use?
a)
sine
b)
cosine
c)
tangent
d)
cotangent
116.
A trig function has an amplitude of 4 and a minimum value of 5.  What is its maximum value?
a)
7
b)
9
c)
11
d)
13
117.
What is the equation of graph? 
a)
y = sin 5x
b)
y =  cos 5x
c)
y = 5 sin x
d)
y = 5 cos x 
118.

What is the period of the function shown in the given graph?

a)

7

b)

8

c)

15

d)

16

119.
What is csc(x) equivalent to?
a)
1/sin(x)
b)
1/tan(x)
c)
sin(x)
d)
1/cos(x)
120.
Please select the correct solution
a)
csc x
b)
sec x
c)
cot x
d)
tan x
121.
Which of the following is NOT
a solution to
sin θ = √(3) / 2 ?
a)
π / 3
b)
2π / 3
c)
5π / 3
d)
7π / 3

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