Free Printable ACT MATH

1.

a)

A

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C

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E

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F

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G

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a)

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12.

a)

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H

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J

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K

13.

Tom works for a manufacturing plant and makes $7.00 per hours. Last week he worked 49 hours. For the hours above 40, he receives time and a half. What did Tom earn last week?

a)

$311.50

b)

$343.00

c)

$374.50

d)

$514.50

e)

$794.50

14.

Cara's stock portfolio is summarized in the table. What is the overall average value of each share she owns?

a)

$17.00

b)

$17.10

c)

$18.00

d)

$18.10

e)

$18.20

15.

Solve for the variable.

$\frac{x}{0.5}=2.5$

a)

1.25

b)

2

c)

2.5

d)

3

e)

5

16.

Find A + B

a)

b)

c)

d)

e)

17.

Where is the function increasing?

a)

$1<x<\infty$

b)

$3<x<\infty$

c)

$-\infty<x<1$

d)

$-\infty<x<3$

e)

$-\infty<x<-1$

18.

If lines a and b are parallel, which of the statements is true?

a)

$m\angle1\ \cong\ m\angle6$

b)

$m\angle1\ \cong\ m\angle7$

c)

$m\angle1\ \cong\ m\angle8$

d)

$m\angle3\ \cong\ m\angle5$

e)

All of these statements are false.

19.

Diego has one red due and one blue die. He will roll both dice at the same time. How many outcomes are possible?

a)

6

b)

8

c)

12

d)

18

e)

36

20.

Which boxplot correctly displays the data in the set?

a)

b)

c)

d)

e)

None

21.

If a point on or inside the square is chose at random, what is the probability that it is also on or inside the circle?

a)

$\frac{8-\pi}{8}$

b)

$\frac{\pi}{8}$

c)

$\frac{4-\pi}{8}$

d)

$\frac{\pi}{4}$

e)

$\frac{4-\pi}{4}$

22.

Which expression represents how many years are in x months?

a)

12x

b)

12 + x

c)

$\frac{x}{12}$

d)

$\frac{12}{x}$

e)

x - 12

23.

Alison bought 12 shares in The Toy Company when it cost $27. She is planning on selling her shares and they currently cost $39.50. What is the percent increase in sale price (round to the nearest whole percent)?

a)

13%

b)

32%

c)

46%

d)

68%

e)

72%

24.

Simplify.

$2x^2\left(4x^3-3x^2+6x\right)$

a)

$6x^5-5x^4+8x^3$

b)

$6x^6-5x^4+8x^2$

c)

$8x^5-3x^4+12x^2$

d)

$8x^3-6x^4+12x^3$

e)

$8x^6-6x^4+6x^2$

25.

The graph of the equation $y\ =\ x^2-3$ is shown. Which equation will shift the graph up 6 units.

a)

$y\ =\ x^2+3$

b)

$y\ =x^2-6$

c)

$y=x^2+6$

d)

$y=\left(x+6\right)^2$

e)

$y\ =\ x^2+9$

26.

Simplify $\frac{12}{148}$ by reducing to lowest form.

a)

$\frac{1}{12}$

b)

$\frac{12}{37}$

c)

$\frac{3}{37}$

d)

$\frac{6}{74}$

e)

$\frac{2}{37}$

27.

You are multiplying the two matrices A and B to find matrix C, what is the formula you use to find $C_{2,1}$ ?

a)

$\left(3\right)\left(8\right)\left(1\right)\left(6\right)\left(5\right)\left(-3\right)$

b)

$\left(1\right)\left(-4\right)\left(0\right)\left(11\right)\left(8\right)\left(4\right)$

c)

$\left(3\right)\left(8\right)+\left(1\right)\left(6\right)+\left(5\right)\left(-3\right)$

d)

$\left(1\right)\left(-4\right)+\left(0\right)\left(11\right)+\left(8\right)\left(4\right)$

e)

$\left(5\right)\left(-4\right)+\left(0\right)\left(11\right)+\left(-2\right)\left(4\right)$

28.

Solve the equation 3x + 5 = 17 for x.

a)

4

b)

8

c)

6

d)

2

29.

Find the slope of the line passing through the points (2, 4) and (6, 10).

4 lines

30.

What is the equation of the line with a slope of -2 and a y-intercept of 3?

a)

y = -2x + 3

b)

y = 2x + 3

c)

y = -2x - 3

d)

y = -2x + 2

31.

Find the area of a triangle with base 8 units and height 6 units.

a)

14

b)

24

c)

30

d)

48

32.

Simplify the expression (2x^2 + 3x - 5) + (4x^2 - 2x + 7).

a)

6x^2 + 3x + 2

b)

6x^2 + 4x + 2

c)

6x^2 + 5x + 2

d)

6x^2 + x + 2

33.

What is the domain of the function f(x) = sqrt(x + 3)?

a)

x <= -3

b)

x > -3

c)

x < -3

d)

x >= -3

34.

Find the value of x in the equation 2x + 3 = 7x - 5.

a)

1.6

b)

2.5

c)

4.8

d)

3.2

35.

Determine the equation of a circle with center (2, -3) and radius 5.

a)

(x-2)^2 + (y+3)^2 = -25

b)

(x-2)^2 + (y+3)^2 = 5

c)

(x+2)^2 + (y-3)^2 = 25

d)

(x-2)^2 + (y+3)^2 = 25

36.

Calculate the perimeter of a rectangle with length 10 units and width 6 units.

a)

60 units

b)

16 units

c)

32 units

d)

22 units

37.

Solve the system of equations: 2x + y = 5 and 3x - 2y = 8.

a)

x = 18/7, y = -1/7

b)

x = 3/2, y = -1/2

c)

x = 5/2, y = 1/2

d)

x = 2/7, y = 1/7

38.

You and five friends are dividing a $1500 jackpot equally. How much will each person receive?

a)

250

b)

300

c)

500

d)

750

e)

1500

39.

$\left(2x+5\right)^2$

a)

$4x^2+25$

b)

$4x^2+20x+25$

c)

$4x^2+10x+25$

d)

$4x+10$

e)

$4x+25$

40.

$2\left(6x+3\right)-3\left(2x-4\right)$

a)

$6x-6$

b)

$6x+18$

c)

$2x-2$

d)

$2\left(3x-1\right)$

e)

$6\left(x-2\right)$

41.

Which describes the picture?

a)

$x<-2\ AND\ x>4$

b)

$x\le-2\ and\ x\ge4$

c)

$x\le-2\ OR\ x\ge4$

d)

$x\ge-2\ OR\ x\ge4$

e)

$x<-2\ or\ x>4$

42.

if $8c^4d^5=c^7d$ , then what is c in terms of d?

a)

$d^{\frac{4}{3}}$

b)

$2d^{\frac{3}{4}}$

c)

$8d^{\frac{3}{4}}$

d)

$2d^{\frac{4}{3}}$

e)

$8d^{\frac{4}{3}}$

43.

Suppose $0<m<1,$ which of the following has the largest value?

a)

$m^2$

b)

$m^3$

c)

$m^{-1}$

d)

$\left|m\right|$

e)

$\sqrt[]{m}$

44.

Matt has the following long distance plan: 0.10 per minute on weekdays from 7pm to 7am, Saturdays and holidays; 0.05 per minute on Sundays; 0.25 per minute all other times. If the table represents his long distance calls, what was the total cost?

a)

$4.70

b)

$5.50

c)

$6.20

d)

$7.40

e)

$8.25

45.

$\left(i+2\right)\left(i+4\right)$

a)

$i+6$

b)

$i+8$

c)

$6i+6$

d)

$6i+7$

e)

$6i+8$

46.

For the following functions, find $f\left(g\left(1\right)\right)$

a)

0

b)

2

c)

3

d)

5

e)

6

47.

if x = 65, what is y?

a)

70

b)

75

c)

100

d)

105

e)

110

48.

What is the formula for the circumference of a circle?

a)

C = πd, where C is the circumference and d is the diameter.

b)

C = 2πr, where C is the circumference and r is the radius.

c)

C = πr^2, where C is the area and r is the radius.

d)

C = 2r, where C is the circumference and r is the radius.

49.

What does a line with a slope of 0 look like?

a)

A vertical line.

b)

A diagonal line sloping upwards.

c)

A horizontal line.

d)

A diagonal line sloping downwards.

50.

What is the formula for the area of a circle?

a)

A = πr², where A is the area and r is the radius.

b)

A = 2πr, where A is the area and r is the radius.

c)

A = πd², where A is the area and d is the diameter.

d)

A = r², where A is the area and r is the radius.

51.

What is the formula for the volume of a cylinder?

a)

V = 2πr²h

b)

V = πr²h

c)

V = πr² + h

d)

V = 4/3πr³

52.

What is the formula for the sum of the interior angles of a polygon?

a)

Sum = (n - 2) * 180°

b)

Sum = n * 180°

c)

Sum = (n + 2) * 90°

d)

Sum = (n - 1) * 180°

53.

What is the quadratic formula?

a)

x = (-b ± √(b² - 4ac)) / (2a) for the equation ax² + bx + c = 0.

b)

x = (b ± √(b² + 4ac)) / (2a) for the equation ax² + bx + c = 0.

c)

x = (-b ± √(b² + 4ac)) / (2a) for the equation ax² + bx + c = 0.

d)

x = (b ± √(b² - 4ac)) / (2a) for the equation ax² + bx + c = 0.

54.

What is the solution to the equation x² - x = 72?

a)

x = 7

b)

x = 8

c)

x = 9

d)

x = 10

55.

What is the definition of a function?

a)

A relation where each input has exactly one output.

b)

A set of ordered pairs with no restrictions.

c)

A collection of inputs and outputs that can be random.

d)

A mathematical expression that can be simplified.

56.

If 15 passengers share the cost of a bus rental and 7 have not paid, with $177.60 collected, what is the total cost?

a)

$250.00

b)

$300.00

c)

$333.00

d)

$400.00

57.

Solve for x: 2x + 3 = 3x - 4.

a)

x = 5

b)

x = 6

c)

x = 7

d)

x = 8

58.

What is the Pythagorean theorem?

a)

In a right triangle, a² + b² = c², where c is the hypotenuse.

b)

In any triangle, the sum of the angles equals 180 degrees.

c)

The area of a circle is πr².

d)

The square of the hypotenuse is equal to the sum of the squares of the other two sides.

59.

What is the definition of a prime number?

a)

A natural number greater than 1 that has no positive divisors other than 1 and itself.

b)

A natural number that is divisible by 2.

c)

Any number that ends with a 1 or 3.

d)

A number that can be expressed as the sum of two other natural numbers.

60.

What is the slope-intercept form of a linear equation?

a)

y = mx + b, where m is the slope and b is the y-intercept.

b)

y = ax^2 + bx + c, where a, b, and c are constants.

c)

y = mx^2 + b, where m is the coefficient of x squared and b is a constant.

d)

y = m + b, where m is the slope and b is the y-intercept.

61.

What is the formula for the area of a triangle?

a)

A = base * height

b)

A = 1/2 * base * height

c)

A = base + height

d)

A = base * height / 2

62.

What is the value of x in the equation 3x + 5 = 20?

a)

x = 3

b)

x = 4

c)

x = 5

d)

x = 6

63.

When x = 3 and y = 5, by how much does the value of 3x² – 2y exceed the value of 2x² – 3y ?

a)

4

b)

14

c)

16

d)

20

64.

What is the value of x when 2x + 3 = 3x – 4 ?

a)

-7

b)

-1/5

c)

1/5

d)

7

65.

What type of number is 5/8?

a)

Rational

b)

Irrational

c)

both

d)

neither

66.

What is 4% of 80?

a)

320

b)

32

c)

3.2

d)

0.032

67.

What is the value of the expression (y-x)³ when x =5 and y = 1?

a)

-64

b)

64

c)

-4

d)

16

68.

Given m and n are parallel lines, t is a transversal crossing both m and n, and m∡8 = 100 degrees, what is the measure of ∡3?

a)

50 degrees

b)

80 degrees

c)

100 degrees

d)

120 degrees

69.

What is the value of x when 2x + 3 = 3x – 4 ?

a)

-7

b)

-1/5

c)

1

d)

1/5

e)

7

70.

What is the greatest common factor of 42, 126, and 210 ?

a)

2

b)

6

c)

14

d)

21

e)

42

71.

The length, in inches, of a box is 3 inches less than twice its width, in inches. Which of the following gives the length, l inches, in terms of the width, w inches, of the box?

a)

l = (1/2)w + 3

b)

l = 2w + 3

c)

l = 2w - 3

d)

l = w - 3

72.

When x = 3 and y = 5, by how much does the value of

3x^2-2y

exceed the value of

2x^2-3y

??

a)

4

b)

14

c)

16

d)

20

e)

50

73.

In quadrilateral PQRS below, sides PS and QR are parallel for what value of x ?

a)

158

b)

132

c)

120

d)

110

e)

70

74.

What is the value of $\frac{8}{y^2}-\frac{x^2}{y}$ when x = - 3 and y = - 4 ?

a)

$-\frac{11}{4}$

b)

$-\frac{7}{4}$

c)

$\frac{7}{4}$

d)

$\frac{11}{4}$

e)

$\frac{56}{9}$

75.

Given that $f\left(x\right)\ =\ 4x^2$ and $g\left(x\right)\ =3-\frac{x}{2}$ , what is the value of $f\left(g\left(4\right)\right)$ ?

a)

1

b)

4

c)

8

d)

16

e)

64

76.

What is the value of
$y^x+\left(2x-2y\right)$ when x= 2 and y = -3

a)

-10

b)

1

c)

7

d)

16

e)

19

77.

Trey attended a New Year's Eve event and watched a ball drop at midnight. Prior to midnight, the bottom of the ball was 150 feet above the ground. If Trey’s horizontal line of sight is 6 feet above the ground and he stands 80 feet from the base of the pole the ball is on, what is the angle of elevation, x?

a)

60.9 degrees

b)

45 degrees

c)

30 degrees

d)

75.3 degrees

78.

Placing in a single layer, edge to edge, what is the maximum number of snowballs with area 4π in² that Jill can fit in a 12” x 12” box lid?

a)

4

b)

9

c)

16

d)

12

79.

As part of his New Year’s resolution to be more active, Mike plans to go to the gym to play handball every 3rd day. Jay makes a similar resolution, but plans to go to the gym for handball every 4 days. If they are both at the gym today, what is the next time (in number of days) they will both be at the gym?

a)

6 days

b)

12 days

c)

9 days

d)

15 days

80.

In years past, the Time’s Square New Year’s Eve crystal ball dropped 141 ft in 60 seconds. Let’s assume a taller pole is made for this year. If the drop rate is increased by 0.15 ft/sec, how many feet have been added to the pole given the ball still drops over a 60 second time period?

a)

9 feet

b)

12 feet

c)

18 feet

d)

15 feet

81.

When graphed, the cos(x) function resembles a snowy ski slope!

Is f(x) = cos(x) even, odd, or neither? How do you know?

a)

Even

b)

Odd

c)

Neither

d)

Both

82.

If the daily low temperatures (°F) over a 10 day period are 34, 35, 30, 24, 18, 30, 34, 30, 28, and 29, what are the mean, median, mode, and standard deviation of these 10 low temperatures?

a)

Mean: 29.2, Median: 30, Mode: 30, Standard Deviation: 5.2

b)

Mean: 30.2, Median: 29, Mode: 30, Standard Deviation: 4.5

c)

Mean: 29.2, Median: 30, Mode: 30, Standard Deviation: 4.85

d)

Mean: 30.2, Median: 30, Mode: 29, Standard Deviation: 5.2

83.

Given the 2 cities plotted on a coordinate plane below, what is the midpoint of the line connecting these 2 cities?

a)

(4, 3.5)

b)

(3, 3.5)

c)

(4, 2)

d)

(3, 2)

84.

Write the equation that represents the situation and solve: The circumference of the snowball Patty made is ⅔ as large as the one Sarah made. If Patty’s snowball has a circumference of 20π, what is Sarah’s snowball’s circumference? What is the diameter of each snowball?

a)

Sarah's circumference: 30π,

Patty's diameter: 10,

Sarah's diameter: 15

b)

Sarah's circumference: 30π,

Patty's diameter: 15,

Sarah's diameter: 10

c)

Sarah's circumference: 20π,

Patty's diameter: 10,

Sarah's diameter: 10

d)

Sarah's circumference: 25π,

Patty's diameter: 10,

Sarah's diameter: 12.5

85.

Packing away holiday decorations, Abby uses a box with dimensions 8” x 6” x 12”. What is the volume of this box?

a)

576 $in^3$

b)

512 $in^3$

c)

648 $in^3$

d)

432 $in^3$

86.

What is the probability of randomly choosing a student whose favorite item is a snowboard?

a)

12/31

b)

8/31

c)

5/31

d)

6/31

87.

What is the probability of randomly choosing a student whose favorite item is either skis or sled?

a)

13/31

b)

8/31

c)

5/31

d)

6/31

88.

What is the probability of randomly choosing a student whose favorite item is NOT a snowboard?

a)

19/31

b)

12/31

c)

8/31

d)

5/31

89.

Simplify the expression: $\frac{\left(4x^3\right)\left(3x^4\right)y^2}{6x^2y^3}$

a)

$\frac{2x^5}{y}$

b)

$\frac{2x^7}{y}$

c)

$12x^5y$

d)

$12x^7y$

90.

Erin has found that her new scarf making business has a profit function of P(x) = 20x - 50 - 4x.

Simplify this function.

If Erin sells 55 scarves, what is her profit?

Erin later updates her profit function to the following:

P(x) = 16x - 50, x ≤ 50

P(x) = 17.25x - 60, x ≥ 51

Now, if Erin sells 55 scarves, what is her profit?

a)

$P\left(x\right)=16x-50$ 55 scarves = $830

b)

$P\left(x\right)=80x-50$ 55 scarves = $825.00

c)

$P\left(x\right)=24x-50$ 55 scarves = $888.75

d)

$P\left(x\right)=16x-50$ 55 scarves = $900.00

91.

Erin later updates her profit function to the following:

P(x) = 16x - 50, x ≤ 50

P(x) = 17.25x - 60, x ≥ 51

Now, if Erin sells 55 scarves, what is her profit?

a)

55 scarves = $830.50

b)

55 scarves = $825.25

c)

55 scarves = $888.75

d)

55 scarves = $900.00

92.

12. If $pq\ =\ 3$ , then $p^3q^{4\ }+\ p^4q^5\ =$

a)

12q

b)

7p+ 9q

c)

12p+ 20q

d)

96p

e)

108q

93.

1. A parking meter in downtown Seattle takes dollar coins and quarters only. When the machine was last emptied, there were 250 coins in it, with a total value of $137.50. Which of the following systems of equations gives the number of quarters, q, and the number of dollar coins, d ?

a)

d + q = 250 and 100d + 25q = 137.50

b)

d + q = 250 and 0.1d + 0.25q = 137.50

c)

d + q = 250 and d + 0.25q = 137.50

d)

d + q = 137.50 and d + 0.25q = 250

94.

For two consecutive integers, the result of adding double the smaller integer and triple the larger integer is 153. What are the two integers?

a)

29, 30

b)

30, 31

c)

49, 50

d)

50, 51

95.

In a certain triangle, the longest side is twice as long as the shortest side, and the shortest side is 4 inches shorter than the middle side. If the perimeter of the triangle is 52 inches, how long is the longest side? A. 10 inches B. 12 inches C. 16 inches D. 20 inches E. 24 inches

a)

10 inches

b)

12 inches

c)

20 inches

d)

24 inches

96.

How many minutes are you given on the ACT math exam?

a)

40

b)

50

c)

60

d)

70

97.

How many question are on the Math ACT?

a)

70

b)

60

c)

50

d)

40

98.

Where do the most difficult questions appear?

a)

first 15 questions

b)

middle 15 questions

c)

last 15 questions

d)

randomly mixed

99.

What is a scaled score?

a)

The score you would like to make on the ACT

b)

The score you get when you answer one question correctly

c)

The super score of all ACT test taken

d)

The score you receive on the actual ACT test

100.

Identify the correct Trig ratios: SIN

a)

OPP/HYP

b)

ADJ/HYP

c)

OPP/ADJ

d)

ADJ/OPP

101.

Identify the correct Trig ratios: COS

a)

OPP/HYP

b)

ADJ/HYP

c)

OPP/ADJ

d)

ADJ/OPP

102.

Identify the correct Trig ratios: TAN

a)

OPP/HYP

b)

ADJ/HYP

c)

OPP/ADJ

d)

ADJ/OPP

ACT MATH

Total questions: 102

Worksheet time: 3hrs 36mins

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