Act Math Exam 3

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1/60 Questions

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.)
- 347
- 437
- 3,047
- 3,407

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2.

What is 96 ÷ 12?
- 8
- 84
- 960
- 1,512
Correct Answer

A. 8

Explanation

A. Use the division algorithm. Knowing the multiplication table well helps you recognize these numbers. See Lesson: Basic Multiplication and Division.

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3.

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?
- Translation right 3 units and up 4 units
- Translation left 3 units and up 4 units
- Translation right 3 units and down 4 units
- Translation left 3 units and down 4 units
Correct Answer

A. Translation left 3 units and down 4 units

Explanation

D. The correct solution is a translation left 3 units and down 4 units because the points (x, y) become (x – 3, y – 4). See Lesson: Congruence.

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4.

Change the following to a decimal and simplify completely.
- 5.275
- 5.325
- 5.375
- 5.425
Correct Answer

A. 5.375

Explanation

C. The correct answer is 5.375 because 3.000 ÷ 8 = 0.375. See Lesson: Decimals and Fractions.

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5.

Write 12.5% as a fraction.
Correct Answer

A.
6.

Write 0.21 as a percent.
- 2.1%
- 20%
- 20.1%
- 21%
Correct Answer

A. 21%

Explanation

D. The correct answer is 21% because 0.21 as a percent is 0.21 × 100 = 21%. See Lesson: Decimals and Fractions.

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7.

Solve the equation for the unknown.
- -20
- -10
- 10
- 20
Correct Answer

A. -20
8.

Solve the equation for the unknown, 6x - 12 = -24.
- -4
- -2
- 2
- 4
Correct Answer

A. -2

Explanation

B. The correct solution is –2.
6x = –12 Add 12 to both sides of the equation.
x= –2 Divide both sides of the equation by 6.
See Lesson: Equations with One Variable.

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9.

Solve the system of equations. x = -3y + 10 x = 3y - 8
- (-1, 3)
- (-3, 1)
- (1, 3)
- (3, 1)
Correct Answer

A. (1, 3)
10.

Solve the system of equations. x + 3y = 34 -3x + y = -12
- (-7, -9)
- (-9, -7)
- (7, 9)
- (9, 7)
Correct Answer

A. (7, 9)
11.

Solve the system of equations by graphing.
Correct Answer

A.

Explanation

C. The correct graph has the two lines intersect at (-9, -1). See Lesson: Equations with Two Variables.

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12.

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.
Correct Answer

A.

Explanation

B. The correct response is B. The median value is 12.5, the first quartile value is 8, and the third quartile value is 17. The minimum is 5, and the maximum is 20. See Lesson: Interpreting Categorical and Quantitative Data.

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13.

The histogram below shows the number of text messages between a group of friends in a week. Which statement is true for the histogram?
- There are 30 friends in the group.
- The highest frequency is 8 friends.
- The bin size is 1,000 text messages.
- Two bins have the same frequency.
Correct Answer

A. Two bins have the same frequency.

Explanation

D. The correct solution is two bins have the same frequency. The bins 400–600 and 800–1,000 have three friends. See Lesson: Interpreting Categorical and Quantitative Data.

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14.

The bar chart shows the number of boys and girls who participate in sports. What year had the most participants?
- 2013
- 2014
- 2016
- 2017
Correct Answer

A. 2016

Explanation

C. The correct solution is 2016 because there were 155 total participants.

See Lesson: Interpreting Graphics.

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15.

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.
Correct Answer

A.

Explanation

C. The correct solution is C. The line graph has the correct values for each roller coaster. See Lesson: Interpreting Graphics.

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16.
Correct Answer

A.
17.
- 9
- 18
- 36
- 72
Correct Answer

A. 36
18.

Multiply. (4x + 5)(3x - 2)
- 12x² - 7x + 10
- 12x² + 7x + 10
- 12x² + 7x - 10
- 12x² - 7x - 10
Correct Answer

A. 12x² + 7x - 10

Explanation

C. The correct solution is 12x2+7x-10.
(4x + 5)(3x - 2) = 4x(3x - 2) + 5(3x-2) = 12x2 - 8x + 15x - 10 = 12x2 + 7x - 10
See Lesson: Polynomials.

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19.

Perform the operation. (-3x + 5xy - 6y) - (4x + 2xy - 5y)
- -7x + 7xy - y
- -7x + 7xy - 11y
- -7x + 3xy - y
- -7x + 3xy - 11y
Correct Answer

A. -7x + 3xy - y

Explanation

C. The correct solution is -7x + 3xy - y. (-3x + 5xy -6y) - (4x +2xy - 5y) = (-3x +5xy - 6y) + (-4x -2xy + 5y) = (-3x - 4x) + (5xy - 2xy) + (-6y + 5y) = -7x + 3xy -y See Lesson: Polynomials.

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20.

Apply the polynomial identity to rewrite x^²+ 20x + 100.
- X² + 100
- (x + 10)²
- (x² + 10)²
- (10x)²
Correct Answer

A. (x + 10)²

Explanation

B. The correct solution is (x + 10)2. The expression x2+ 20x + 100 is rewritten as (x + 10)2 because the value of a is x and the value of b is 10. See Lesson: Polynomials.

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21.
Correct Answer

A.
22.

Solve. x³ = 64
- 2
- 3
- 4
- 5
Correct Answer

A. 4

Explanation

C. The correct solution is 4 because the cube root of 64 is 4. See Lesson: Powers, Exponents, Roots, and Radicals.

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23.

If 1 out of every 250 people will contract a certain disease, what percent of people will contract it?
- 0.004%
- 0.4%
- 2.5%
- 25%
Correct Answer

A. 0.4%

Explanation

B. If 1 out of every 250 contract a disease, the fraction of people is 1/250, which is equal to 0.004. Multiply by 100% to get 0.4%. See Lesson: Ratios, Proportions, and Percentages.

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24.

Solve the equation by the square root method. 2x² = 162
- ±8
- ±9
- ±10
- ±11
Correct Answer

A. ±9

Explanation

B. The correct solution is ±9.

See Lesson: Solving Quadratic Equations.

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25.

Which statement is true?
- The sum of a positive number and a negative number is always negative.
- The sum of a positive number and a negative number is always positive.
- The sum of a positive number and a negative number is always zero.
- None of the above.
Correct Answer

A. None of the above.

Explanation

D. The correct solution is none of the above. Try some test cases. For example, –1 + 5 = 4, but –5 + 1 = –4. Also, –5 + 5 = 0. Counterexamples therefore show that statements A, B, and C are false. See Lesson: Basic Addition and Subtraction.

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26.

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.
- 207.64
- 415.27
- 519.08
- 726.73
Correct Answer

A. 207.64

Explanation

A. The correct solution is 207.64 because A = ½πr2 ≈ ½(3.14)(11.5)2 ≈ 12(3.14)(132.25) ≈ 207.64 square feet. See Lesson: Circles.

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27.

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.
- 669.3
- 858.5
- 1,338.6
- 2,695.7
Correct Answer

A. 669.3

Explanation

A. The correct solution is 669.3. C = 2πr; 92 = 2(3.14)r; 92 = 6.28r; r ≈ 14.6 centimeters. A = πr2 ≈ 3.14 (14.6)2 ≈ 3.14(213.16) ≈ 669.3 square centimeters. See Lesson: Circles.

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28.

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

A.

Explanation

D. The correct solution is D. The translation for the points is (x – 4, y + 4). The points of the original square, (–1, 5), (–1, –1), (5, –1) and (5, 5), become (–5, 9), (–5, 3), (1, 3) and (1, 9). See Lesson: Congruence.

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29.

Select the statement that is true for the angles.
- Points X and Y are vertices of angles.
- Points X and U are vertices of angles.
- Points W and Y are vertices of angles.
- Points W and U are vertices of angles.
Correct Answer

A. Points X and U are vertices of angles.

Explanation

B. The correct solution is points X and U are vertices of angles because these points are the intersection of two rays. See Lesson: Congruence.

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30.

Solve the inequality for the unknown, 3(4x - 1) > 5(2x + 3).
- > 2
- X > 9
- X > 10
- X > 18
Correct Answer

A. X > 9
31.

What are the unique prime factors of 56?
- 2, 7
- 1, 2, 7
- 2, 5, 7
- 2, 4, 7, 8, 14, 16, 28
Correct Answer

A. 2, 7

Explanation

A. The prime factorization of 56—for example, using a factor tree—yields the numbers 2, 2, 2, and 7. Ignoring repeats of 2, the unique prime factors are 2 and 7. See Lesson: Factors and Multiples.

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32.

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.
- The mean and median increase.
- The mean and median decrease.
- The mean increases, and the median does not change.
- The mean decreases, and the median does not change.
Correct Answer

A. The mean and median increase.

Explanation

A. The correct solution is the mean and median increase. The test score of 105 increases the mean from 85.67 to 87.6 and increases the median from 85 to 85.5. See Lesson: Interpreting Categorical and Quantitative Data.

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33.

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.
- 2 inches
- 9 inches
- 13 inches
- 26 inches
Correct Answer

A. 13 inches

Explanation

C. The correct solution is 13 inches. Substitute the values into the formula, 260π = π62h - π42h. Apply the exponent and combine like terms, 260π = π36h - π16h; 260π = 20πh. Divide both sides of the equation by 20π, h=13 inches. See Lesson: Measurement and Dimension.

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34.
Correct Answer

A.

Explanation

See Lesson: Multiplication and Division of Fractions.

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35.

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?
- 1
- 2
- 3
- 4
Correct Answer

A. 3

Explanation

C. The correct solution is 3 because 2 × 10-4 is 0.0002 and 8 × 10-5 is 0.00008. So, the error on the first machine is about 3 times larger. See Lesson: Powers, Exponents, Roots, and Radicals.

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36.

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?
- 38
- 75
- 300
- 600
Correct Answer

A. 75

Explanation

B. The correct solution is 75. Substitute the values into the formula, 27,000 = ½(90)p and simplify using the order of operations, 27,000 = 45p. Divide both sides of the equation by 45 to find the perimeter, p = 600 centimeters. Divide the perimeter by 8 to find the length of 75 centimeters for each side. See Lesson: Similarity, Right Triangles, and Trigonometry.

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37.

Three vertices of a parallelogram are (8, 5), (-2, 5), and (-1, 1). What is the fourth coordinate?
- (9, 1)
- (8, 1)
- (9, -1)
- (8, -1)
Correct Answer

A. (9, 1)

Explanation

A. The correct solution is (9, 1) because this point shows a parallelogram with a base length of 10 units. See Lesson: Similarity, Right Triangles, and Trigonometry.

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38.

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?
- 60
- 120
- 180
- 240
Correct Answer

A. 120

Explanation

B. The correct solution is 120. Substitute the values into the formula and simplify using the order of operations, SA = (2)(½)(5)(12) + (2)(5) + 2(12) + 2(13) = 60 + 10 + 26 + 24 = 120 square centimeters. See Lesson: Similarity, Right Triangles, and Trigonometry.

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39.

Solve the equation by factoring. x² + 15x + 54 = 0
- -6, -9
- -6, 9
- 6, -9
- 6, 9
Correct Answer

A. -6, -9
40.

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?
- $8.50
- $12.50
- $14.50
- $21.50
Correct Answer

A. $12.50

Explanation

B. The correct solution is $12.50 because she worked a total of 4.25(2) + 6.5(2) = 8.5 + 13 = 21.5 hours. The hourly rate is 268.75 ÷ 21.50 = $12.50. See Lesson: Solving Real World Mathematical Problems.

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41.

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

A.
42.

Convert 0.75 kilograms to grams.
- 0.0075 grams
- 0.075 grams
- 75 grams
- 750 grams
Correct Answer

A. 750 grams
43.

A teacher wants to know if seat location affects test scores. What data needs to be collected for an experiment?
- The teacher should collect data on one seat for every class.
- The teacher should collect data on one student for every class.
- The teacher should collect data on a random sample of students for the final exam.
- The teacher should collect data on a random sample of students of test scores and seat location.
Correct Answer

A. The teacher should collect data on a random sample of students of test scores and seat location.

Explanation

D. The correct solution is that the teacher should collect data on a random sample of students of test scores and seat location because there are specific groups based on seat location. See Lesson: Statistical Measures.

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44.

A bag contains 10 red marbles, 8 black marbles, and 7 white marbles. What is the probability of selecting a white marble twice in a row without replacement?
Correct Answer

A.
45.

In a deck of 20 number cards, cards 1–5 are green, cards 6–10 are red, cards 11–15 are yellow, and cards 16–20 are blue. Describe the union of the first 10 cards.
- Green cards
- Cards 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
- Green cards and Red cards; 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
- Green cards 1, 2, 3, 4, 5; Red cards 6, 7, 8, 9, 10
Correct Answer

A. Green cards 1, 2, 3, 4, 5; Red cards 6, 7, 8, 9, 10

Explanation

D. The correct solution is Green cards 1, 2, 3, 4, 5; Red cards 6, 7, 8, 9, 10. The union is listing out all options of the sample space. See Lesson: Statistics & Probability: The Rules of Probability.

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46.

A club wants to meet once a week. The available times are Tuesday, Wednesday, and Thursday at 2:00 p.m., 3:00 p.m., and 4:00 p.m. How many outcomes are there for the sample space?
- 3
- 6
- 9
- 12
Correct Answer

A. 9

Explanation

C. The correct solution is 9 possible outcomes. There are three days and three times available, or 3 times 3, which is 9 times. See Lesson: Statistics & Probability: The Rules of Probability.

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47.

Evaluate the expression 462 ÷ 53.
- 1R3
- 8R0
- 8R38
- 8R53
Correct Answer

A. 8R38

Explanation

C. Because 462 is not evenly divisible by 53, remainder division is necessary. Use the division algorithm to obtain 8R38. See Lesson: Basic Multiplication and Division.

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48.

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.
- 2.7
- 5.4
- 10.8
- 16.2
Correct Answer

A. 10.8

Explanation

C. The correct solution is 10.8 because A = ½πr2; 45 = (½)3.14r2; 45 = 1.57r2 = 28.66 = r2; r ≈ 5.4.The diameter is twice the radius, or about 10.8 centimeters. See Lesson: Circles.

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49.

Which number is composite?
- 2
- 11
- 73
- 91
Correct Answer

A. 91

Explanation

D. A composite number has factors other than 1 and itself. Note that 2 is prime by definition: it only has itself and 1 as factors. Answer B is easy to confirm as prime. That leaves answers C and D. One approach is to start at 2 and test each successive whole number to determine whether it is a factor by dividing. If the quotient is a whole number, it is a factor. In this case, 91 has 7 as a factor. Therefore, it is composite. See Lesson: Factors and Multiples.

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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.)

Quiz Preview

What is 96 ÷ 12?

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?

Change the following to a decimal and simplify completely.

Write 12.5% as a fraction.

Write 0.21 as a percent.

Solve the equation for the unknown.

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

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

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

Solve the system of equations by graphing.

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.

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

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

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.

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

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

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

Solve. x3 = 64

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

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

Which statement is true?

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.

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.

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

Select the statement that is true for the angles.

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

What are the unique prime factors of 56?

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 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.

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 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?

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

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?

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

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?

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

Convert 0.75 kilograms to grams.

A teacher wants to know if seat location affects test scores. What data needs to be collected for an experiment?

A bag contains 10 red marbles, 8 black marbles, and 7 white marbles. What is the probability of selecting a white marble twice in a row without replacement?

In a deck of 20 number cards, cards 1–5 are green, cards 6–10 are red, cards 11–15 are yellow, and cards 16–20 are blue. Describe the union of the first 10 cards.

A club wants to meet once a week. The available times are Tuesday, Wednesday, and Thursday at 2:00 p.m., 3:00 p.m., and 4:00 p.m. How many outcomes are there for the sample space?

Evaluate the expression 462 ÷ 53.

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.

Which number is composite?

Apply the polynomial identity to rewrite x^²+ 20x + 100.

Solve. x³ = 64

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

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?

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