Free Printable ACT Boot Camp Quiz

1.

In parallelogram ABCD below, $\overline{AC}$ is a diagonal, the measure of $\angle ACD$ is $57\degree$ . What is the measure of $\angle CAD$ ?

a)

40

b)

57

c)

77

d)

83

e)

97

2.

For what value of x is the equation $2^{\left(2x+7\right)}=2^{15}$ true?

a)

2

b)

4

c)

11

d)

16

e)

44

3.

Let the function f be defined as $f\left(x\right)=5x^2-7\left(4x+3\right).\ \$ What is the value of $f\left(3\right)$ ?

a)

-18

b)

-26

c)

-33

d)

-60

e)

-75

4.

a)

-18

b)

-2

c)

0

d)

2

e)

18

5.

What is the slope of the line through (-2,1) and (2,-5) in the standard (x,y) coordinate plane?

a)

$\frac{3}{2}$

b)

1

c)

-1

d)

$\frac{-3}{2}$

e)

-4

6.

The length of a rectangle is 5 inches longer than the width. The perimeter of the rectangle is 40 inches. What is the width of the rectangle, in inches?

a)

7.5

b)

8

c)

15

d)

16

e)

17.5

7.

In the standard (x,y) coordinate place, what is the slope of the line given by the equation $4x\ =\ 7y\ +\ 5$

a)

$\frac{-4}{7}$

b)

$\frac{4}{7}$

c)

$\frac{7}{4}$

d)

4

e)

7

8.

$8\%\$ of $60$ is $\frac{1}{5}$ of what number?

a)

0.96

b)

12

c)

24

d)

240

e)

3750

9.

The lengths of the 2 legs of right triangle $\Delta ABC$ shown below are given in inches. The midpoint of $\overline{AB}$ is how many inches from A?

a)

16

b)

20

c)

21

d)

28

e)

40

10.

$\frac{4.8\ \times\ 10^{-7}}{1.6\ \times\ 10^{-11}}$

a)

$3\ \times\ 10^4$

b)

$3\ \times\ 10^{-4}$

c)

$3\ \times\ 10^{-18}$

d)

$3.2\ \times\ 10^{18}$

e)

$3.2\ \times\ 10^4$

11.

Which of the following expressions is a factor $x^{3\ }-64$

a)

$x-4$

b)

$x+4$

c)

$x+64$

d)

$x^2+16$

e)

$x^{2\ }-4x+16$

12.

What is the area, in square inches, of the scale drawing of the park?

a)

448

b)

544

c)

640

d)

672

e)

1088

13.

Mikea's proposal include installing a fence on the perimeter of the park. What is the perimeter, in feet, of the park?

a)

84

b)

88

c)

104

d)

126

e)

156

14.

The length of the south side of the park is what percent of the length of the north side?

a)

$112\%$

b)

$124\%$

c)

$142\ \frac{6}{7\ }\%$

d)

$175\%$

e)

$250\%$

15.

Mr. Smith plans to build a 3-foot wide walkway around the outside of the cabin, as shown in the floor plan. What will be the area, in square feet, of the top surface of the walkway?

a)

171

b)

324

c)

360

d)

396

e)

720

16.

Mr. & Mrs. Smith plan to roof the cabin on 2 consecutive days. Assuming that the chance of rain is independent of the day, what is the probability that it will rain both days?

a)

0.04

b)

0.08

c)

0.16

d)

0.20

e)

0.40

17.

A line through the origin and $\left(10,4\right)$ is shown in the standard $\left(x,\ y\right)$ coordinate plane below. The acute angle between the line and the positive x-axis has measure $\theta$ . What is the value of $\tan\theta$ ?

a)

$\frac{\sqrt{29}}{2}$

b)

$\frac{2}{\sqrt{29}}$

c)

$\frac{5}{\sqrt{29}}$

d)

$\frac{2}{5}$

e)

$\frac{5}{2}$

18.

Toby wants to find the volume of a solid toy soldier. He fills a rectangular container 8 cm long, 6 cm wide, and 10 cm high with water to a depth of 4 cm. Toby totally submerges the toy soldier in the water. The height of the water with the submerged toy soldier is 6.6 cm. Which of the following is closest to the volume, in cubic centimeters, of the toy soldier?

a)

125

b)

156

c)

192

d)

208

e)

317

19.

Mario plays basketball on a town league team. The table below gives Mario's scoring statistics for last season. How many points did Mario score playing basketball last season?

a)

129

b)

190

c)

213

d)

330

e)

380

20.

The graph of a function $y\ =\ f\left(x\right)$ consists of 3 line segments. The graph and the coordinates of the endpoints of the 3 line segments are shown in the standard $\left(x,y\right)$ coordinate plane below. What is the area, in square coordinate units, of the region bounded by the graph $y\ =\ f\left(x\right)$ , the positive y-axis, and the positive x-axis?

a)

10

b)

13

c)

14

d)

15

e)

20

21.

The sum of 2 positive numbers is 151. The lesser number is 19 more than the square root of the greater number. What is the value of the greater number minus the lesser number?

a)

19

b)

66

c)

85

d)

91

e)

121

22.

The frequency chart below shows the cumulative number of Ms. Hernandez's science students whose test scores fell within certain score ranges. All test scores are whole numbers.

How many students have a test score in the interval 71-80?

a)

1

b)

6

c)

8

d)

12

e)

13

23.

Maria ordered a pizza. She ate only $\frac{2}{9}$ of it and gave the remaining pizza to her 3 brothers. What fraction of hte whole pizza will each of Maria's brothers receive, if they share the remaining pizza equally?

a)

$\frac{7}{9}$

b)

$\frac{3}{7}$

c)

$\frac{1}{3}$

d)

$\frac{7}{27}$

e)

$\frac{2}{27}$

24.

A circle in the standard $\left(x,y\right)$ coordinate plane has a center at $C\left(-1,2\right)$ and passes through $A\left(2,6\right)$ . Line segment $\overline{AB}$ is a diameter of this circle. What are the coordinates of point B?

a)

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

b)

$\left(-5,\ -1\right)_{ }$

c)

$\left(-4,-2\right)$

d)

$\left(5,10\right)$

e)

$\left(4,2\right)$

25.

When $x=\frac{1}{2}$ , what is the value of $\frac{8x-3}{x}$ ?

a)

$\frac{1}{2}$

b)

2

c)

$\frac{5}{2}$

d)

5

e)

10

26.

(A2 Bonus)

One of the following graphs in the standard (x,y) coordinate plane is the graph of $y=\sin^{2\ }x\ +\ \cos^{2\ }x$ over the domain of $\frac{-\pi}{2}\le x\le\frac{\pi}{2}$ . Which one?

a)

b)

c)

d)

e)

27.

(A2 Bonus)

For $-\frac{\pi}{2}\le x\le\frac{\pi}{2}$ , $\left|\sin\theta\right|\ge1$ is true for all and only the value of $\theta$ in which of the following sets?

a)

$\left\{-\frac{\pi}{2},\frac{\pi}{2}\right\}$

b)

$\left\{\frac{\pi}{2}\right\}$

c)

$-\frac{\pi}{2}<\theta<\frac{\pi}{2}$

d)

$\left\{-\frac{\pi}{2}\le\theta\le\frac{\pi}{2}\right\}$

e)

The Empty Set

28.

(A2 Bonus)

The number of decibels, d, produced by an audio source can be modeled by the equation $d=10\log\ \left(\frac{1}{K}\right)$ , where I is the sound intensity of the audio source and K is a constant. How many decibels are produced by an audio source whose sound intensity is 1,000 times the value of K?

a)

4

b)

30

c)

40

d)

100

e)

10,000

ACT Boot Camp Quiz

Total questions: 28

Worksheet time: 28mins

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