Act Math Exam 3

How many millimeters are in a measurement that is 4 centimeters, 3 meters, and 7 millimeters long? (Note that a centimeter is 10 millimeters and a meter is 1,000 millimeters.)

• A.

  347

• B.

  437

• C.

  3,047

• D.

  3,407

Which statement is true?

• A.

  The sum of a positive number and a negative number is always negative.

• B.

  The sum of a positive number and a negative number is always positive.

• C.

  The sum of a positive number and a negative number is always zero.

• D.

  None of the above.

Evaluate the expression 462 ÷ 53.

• A.

  1R3

• B.

  8R0

• C.

  8R38

• D.

  8R53

What is 96 ÷ 12?

• A.

  8

• B.

  84

• C.

  960

• D.

  1,512

A half circle has an area of 45 square centimeters. Find the diameter to the nearest tenth of a centimeter. Use 3.14 for π.

• A.

  2.7

• B.

  5.4

• C.

  10.8

• D.

  16.2

Half of a circular garden with a radius of 11.5 feet needs weeding. Find the area in square feet that needs weeding. Round to the nearest hundredth. Use 3.14 for π.

• A.

  207.64

• B.

  415.27

• C.

  519.08

• D.

  726.73

The circumference of a circle is 92 centimeters. Find the area of the circle to the nearest tenth of a square centimeter. Use 3.14 for π.

• A.

  669.3

• B.

  858.5

• C.

  1,338.6

• D.

  2,695.7

Select the figure that is translated (x – 4, y + 4).

• A.
• B.
• C.
• D.

Select the statement that is true for the angles.

• A.

  Points X and Y are vertices of angles.

• B.

  Points X and U are vertices of angles.

• C.

  Points W and Y are vertices of angles.

• D.

  Points W and U are vertices of angles.

ΔMNO has points M (2, 6), N (3, –1), and O (0, –2). After a transformation, the points are M’ (–1, 2), N’ (0, –5), and O’ (–3, –6). What is the transformation between the points?

• A.

  Translation right 3 units and up 4 units

• B.

  Translation left 3 units and up 4 units

• C.

  Translation right 3 units and down 4 units

• D.

  Translation left 3 units and down 4 units

Change the following to a decimal and simplify completely.

• A.

  5.275

• B.

  5.325

• C.

  5.375

• D.

  5.425

Write 12.5% as a fraction. 

• A.
• B.
• C.
• D.

Write 0.21 as a percent.

• A.

  2.1%

• B.

  20%

• C.

  20.1%

• D.

  21%

Solve the inequality for the unknown, 3(4x - 1) > 5(2x + 3).

• A.

  > 2

• B.

  X > 9

• C.

  X > 10

• D.

  X > 18

Solve the equation for the unknown. 

• A.

  -20

• B.

  -10

• C.

  10

• D.

  20

Solve the equation for the unknown, 6x - 12 = -24.

• A.

  -4

• B.

  -2

• C.

  2

• D.

  4

Solve the system of equations.  x = -3y + 10 x = 3y - 8

• A.

  (-1, 3)

• B.

  (-3, 1)

• C.

  (1, 3)

• D.

  (3, 1)

Solve the system of equations. x + 3y = 34 -3x + y = -12

• A.

  (-7, -9)

• B.

  (-9, -7)

• C.

  (7, 9)

• D.

  (9, 7)

Solve the system of equations by graphing. 

• A.
• B.
• C.
• D.

What are the unique prime factors of 56?

• A.

  2, 7

• B.

  1, 2, 7

• C.

  2, 5, 7

• D.

  2, 4, 7, 8, 14, 16, 28

Which number is composite?

• A.

  2

• B.

  11

• C.

  73

• D.

  91

The data below shows a class’s quiz scores out of 20 points. 5, 5, 6, 7, 8, 8, 9, 10, 11, 12, 13, 14, 15, 15, 16, 18, 18, 19, 20, 20 Select a box plot for the data.

• A.
• B.
• C.
• D.

The histogram below shows the number of text messages between a group of friends in a week. Which statement is true for the histogram?

• A.

  There are 30 friends in the group.

• B.

  The highest frequency is 8 friends.

• C.

  The bin size is 1,000 text messages.

• D.

  Two bins have the same frequency.

The test scores in a class are 82, 83, 84, 84, 85, 86, 88, 89, 90. The last test is a score of 105. Compare the mean and median before and after the last test score is included.

• A.

  The mean and median increase.

• B.

  The mean and median decrease.

• C.

  The mean increases, and the median does not change.

• D.

  The mean decreases, and the median does not change.

The bar chart shows the number of boys and girls who participate in sports. What year had the most participants?

• A.

  2013

• B.

  2014

• C.

  2016

• D.

  2017

Find the median for the data set 20, 22, 23, 24, 25, 21, 20, 22, 24, 25, 23, 22, 25, 26, 22, and 20.

• A.

  22

• B.

  22.25

• C.

  22.5

• D.

  22.75

The table shows the speed in miles per hour of different roller coasters at an amusement park. Select the correct line graph for this data.  

• A.
• B.
• C.
• D.

The base of an equilateral triangular pyramid has side lengths of 9 centimeters. The height of the triangular base is 3√3 centimeters, and the pyramid has a height of 10 centimeters. Find the volume of the pyramid in cubic centimeters.

• A.

  45√3

• B.

  90√3

• C.

  135√3

• D.

  180√3

A paper cup in the shape of a cone has a diameter of 8 centimeters and a height of 11 centimeters. How much liquid does the cup hold if filled to the top? Use 3.14 for π.

• A.

  92.11 cubic centimeters

• B.

  184.21 cubic centimeters

• C.

  368.42 cubic centimeters

• D.

  736.84 cubic centimeters

A cylinder has an outer radius of 6 inches. There is a hole cut out of the center with a radius of 4 inches. The volume of the solid part is 260π cubic inches. Find the height of the cylinder.

• A.

  2 inches

• B.

  9 inches

• C.

  13 inches

• D.

  26 inches

• A.
• B.
• C.
• D.

• A.
• B.
• C.
• D.

• A.

  9

• B.

  18

• C.

  36

• D.

  72

Multiply. (4x + 5)(3x - 2)

• A.

  12x² - 7x + 10

• B.

  12x² + 7x + 10

• C.

  12x² + 7x - 10

• D.

  12x² - 7x - 10

Perform the operation.  (-3x + 5xy - 6y) - (4x + 2xy - 5y)  

• A.

  -7x + 7xy - y

• B.

  -7x + 7xy - 11y

• C.

  -7x + 3xy - y

• D.

  -7x + 3xy - 11y

Apply the polynomial identity to rewrite x²+ 20x + 100.

• A.

  X² + 100

• B.

  (x + 10)²

• C.

  (x² + 10)²

• D.

  (10x)²

The error on one manufacturing machine is 2 × 10^-4, and the error on a second machine is 8 × 10^-5. How many times larger is the error on the first machine?

• A.

  1

• B.

  2

• C.

  3

• D.

  4

• A.
• B.
• C.
• D.

Solve. x³ = 64

• A.

  2

• B.

  3

• C.

  4

• D.

  5

If a company’s automobile fleet includes 132 cars of brand A and 48 cars of brand B, what is the fleet’s ratio of brand B to brand A?

• A.

  4: 11

• B.

  11: 15

• C.

  15: 11

• D.

  11: 4

What is 36% as a ratio?

• A.

  9:25

• B.

  36:100

• C.

  18:40

• D.

  25:9

If 1 out of every 250 people will contract a certain disease, what percent of people will contract it?

• A.

  0.004%

• B.

  0.4%

• C.

  2.5%

• D.

  25%

A stop sign is a regular octagon with an area of 27,000 square centimeters and an apothem of 90 centimeters. What is the length in centimeters of one side?

• A.

  38

• B.

  75

• C.

  300

• D.

  600

Three vertices of a parallelogram are (8, 5), (-2, 5), and (-1, 1). What is the fourth coordinate?

• A.

  (9, 1)

• B.

  (8, 1)

• C.

  (9, -1)

• D.

  (8, -1)

A right triangular prism has a triangular base with legs of 5 centimeters and 12 centimeters and a hypotenuse of 13 centimeters. What is the surface area in square centimeters if the height is 2 centimeters?

• A.

  60

• B.

  120

• C.

  180

• D.

  240

Solve the equation by any method. x² + 16x + 33 = 0

• A.

  -8 ± √31

• B.

  8 ± √31

• C.

  -8 ± √33

• D.

  8 ± √33

Solve the equation by the square  root method.  2x² = 162

• A.

  ±8

• B.

  ±9

• C.

  ±10

• D.

  ±11

Solve the equation by factoring. x² + 15x + 54 = 0

• A.

  -6, -9

• B.

  -6, 9

• C.

  6, -9

• D.

  6, 9

Karida has a part-time job. She works 4.25 hours on Thursday and Friday and 6.5 hours on Saturday and Sunday. What is her hourly rate if her check is $268.75?

• A.

  $8.50

• B.

  $12.50

• C.

  $14.50

• D.

  $21.50

Eric buys   pounds of apples each week for four weeks. How many total pounds does he buy?

• A.
• B.
• C.
• D.