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Act Math Exam 1 (In Book)

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Questions and Answers

1.

How many whole numbers are less than 3 but greater than –3?
- A.
  
  2
- B.
  
  3
- C.
  
  4
- D.
  
  5
Correct Answer
B. 3

Explanation
B. The correct solution is 3. The whole numbers include 0, 1, 2, 3,…. All whole numbers are greater than –3, but only 0, 1, and 2 are less than 3. See Lesson: Basic Addition and Subtraction.

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2.

Which procedure is impossible?
- A.
  
  Adding two negative numbers
- B.
  
  Subtracting a negative number from zero
- C.
  
  Adding two quantities with different units
- D.
  
  Placing negative numbers on the number line
Correct Answer
C. Adding two quantities with different units

Explanation
C. The correct solution is adding two quantities with different units. To add quantities, they must have the same unit. For instance, adding a quantity of meters to a quantity of grams is impossible. See Lesson: Basic Addition and Subtraction.

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3.

Evaluate the expression. 15 x (-15)
- A.
  
  -225
- B.
  
  -30
- C.
  
  -1
- D.
  
  0
Correct Answer
A. -225

Explanation
A. When multiplying signed numbers, remember that the product of a negative and a positive is negative. Other than the sign, the process is the same as multiplying whole numbers. See Lesson: Basic Multiplication and Division.

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4.

Evaluate the expression 26 ÷ 9.
- A.
  
  2
- B.
  
  2R8
- C.
  
  3R1
- D.
  
  35
Correct Answer
B. 2R8

Explanation
B. Because 26 is not evenly divisible by 9, the best answer in this case has a remainder. The division algorithm is used to obtain this result. See Lesson: Basic Multiplication and Division.

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5.

A circle has an area of 12 square feet. Find the diameter to the nearest tenth of a foot. Use 3.14 for π.
- A.
  
  1.0
- B.
  
  2.0
- C.
  
  3.0
- D.
  
  4.0
Correct Answer
D. 4.0

Explanation
D. The correct solution is 4.0 because A = πr2; 12 = 3.14r2; 3.82 = r2; r ≈ 2.0. The diameter is twice the radius, or about 4.0 feet. See Lesson: Circles.

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6.

A circular dinner plate has a diameter of 13 inches. A ring is placed along the edge of the plate. Find the circumference of the ring in inches. Use 3.14 for π.
- A.
  
  31.4
- B.
  
  40.82
- C.
  
  62.8
- D.
  
  81.64
Correct Answer
B. 40.82

Explanation
B. The correct solution is 40.82 because C = πd ≈ 3.14(13) ≈ 40.82 inches. See Lesson: Circles.

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7.

Select the square with the correct lines of symmetry.
- A.
- B.
- C.
- D.
Correct Answer
D.

Explanation
D. The correct solution is the square with four lines of symmetry. There is a horizontal line, a vertical line, and two diagonals of symmetry that map the rectangle onto itself. See Lesson: Congruence.

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8.

Find the area in square centimeters of a circle with a diameter of 16 centimeters. Use 3.14 for π.
- A.
  
  25.12
- B.
  
  50.24
- C.
  
  100.48
- D.
  
  200.96
Correct Answer
D. 200.96

Explanation
D. The correct solution is 200.96. The radius is 8 centimeters and A = πr2 ≈ 3.1482 ≈ 3.14(64) ≈ 200.96 square centimeters. See Lesson: Circles.

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9.
- A.
- B.
- C.
- D.
Correct Answer
C.

Explanation
C. The two rays intersect at point D. See Lesson: Congruence.

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10.

⌂JKL has points J (5, -3), K (-2,4), and L (3, 0). After a transformation the points are J' (5, 3), K' (-2, -4), and L' (3, 0). What is the transformation between the points?
- A.
  
  Reflection across the x-axis
- B.
  
  Reflection across the y-axis
- C.
  
  Reflection across the y = x
- D.
  
  Reflection across the y = –x
Correct Answer
A. Reflection across the x-axis

Explanation
A. The correct solution is a reflection across the x-axis because the points (x, y) become (x, –y). See Lesson: Congruence.

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11.

Change 0.375 to a fraction. Simplify completely.
- A.
- B.
- C.
- D.
Correct Answer
A.
12.

Write as a percent.
- A.
  
  15%
- B.
  
  20%
- C.
  
  25%
- D.
  
  30%
Correct Answer
B. 20%

Explanation
B. The correct answer is 20% because 1/5 as a percent is 0.2 × 100 = 20%. See Lesson: Decimals and Fractions.

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13.

$Change the following fraction to a decimal and simplify completely. - ProProfs$

Change the following fraction to a decimal and simplify completely.
- A.
- B.
- C.
- D.
Correct Answer
B.
14.

Solve the equation for the unknown,
- A.
  
  -16
- B.
  
  -8
- C.
  
  3
- D.
  
  48
Correct Answer
D. 48

Explanation
D. The correct solution is 48 because both sides of the equation are multiplied by –4. See Lesson: Equations with One Variable.

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15.

Solve the inequality for the unknown, 3(x + 1) + 2(x+1) > 5 (3 -x) + 4(x +2).
- A.
  
  X > 0
- B.
  
  X > 1
- C.
  
  X > 2
- D.
  
  X > 3
Correct Answer
D. X > 3

Explanation
D. The correct solution is x > 3.

3x + 3 + 2x +2 > 15 - 5x + 4x + 8 Apply the distributive property.
5x + 5 > -- x + 23 Combine like terms on both sides of the inequality.
6x + 5 > 23 Add x to both sides of the inequality.
6x > 18 Subtract 7 from both sides of the inequality.
x > 3 Divide both sides of the inequality by 6.

See Lesson: Equations with One Variable.

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16.

Solve the system of equations. 2y + x = -20 y = -x - 12
- A.
  
  (4, 8)
- B.
  
  (4, -8)
- C.
  
  (-4, 8)
- D.
  
  (-4, -8)
Correct Answer
D. (-4, -8)
17.

Solve the equation for P. A= P + Prt
- A.
- B.
- C.
- D.
Correct Answer
D.
18.

Solve the system of equations. -2x + 2y = 28 3x + y = -22
- A.
  
  (9, 5)
- B.
  
  (-9, -5)
- C.
  
  (9, -5)
- D.
  
  (-9, 5)
Correct Answer
D. (-9, 5)
19.

Solve the system of equations by graphing. 2x + y = 4 4x + y = 14
- A.
- B.
- C.
- D.
Correct Answer
B.

Explanation
B. The correct graph has the two lines intersect at (5, -6). See Lesson: Equations with Two Variables.

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20.

How many prime numbers are less than 20 but greater than 0?
- A.
  
  8
- B.
  
  9
- C.
  
  10
- D.
  
  11
Correct Answer
A. 8

Explanation
A. Start by eliminating 1, which is not a prime number. The number 2 is the only even prime; the other even numbers are composite. Therefore, consider only odd numbers greater than 2. The prime numbers less than 20 but greater than 2 are 3, 5, 7, 11, 13, 17, and 19. The total is eight. See Lesson: Factors and Multiples.

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21.

Which number is a multiple of 123?
- A.
  
  -123
- B.
  
  1
- C.
  
  247
- D.
  
  359
Correct Answer
A. -123

Explanation
A. Any product of a number and an integer is a multiple of that number. Since 123 x -1 is -123, one multiple of 123 is -123. See Lesson: Factors and Multiples.

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22.

A soccer team has scored 1, 1, 2, 2, 3, 3, 4, 4, 5 goals in its first 9 games. During the next game, the team scores 8 goals. Compare the mean and the standard deviation before and after the next game.
- A.
  
  The mean and standard deviation increase.
- B.
  
  The mean and standard deviation decrease.
- C.
  
  The mean increases, but the standard deviation does not change.
- D.
  
  The mean decreases, but the standard deviation does not change.
Correct Answer
A. The mean and standard deviation increase.

Explanation
A. The correct solution is the mean and standard deviation increase. The game with 8 goals increases the mean from 2.8 to 3.3 and increases the standard deviation from 1.315 to 2.002. See Lesson: Interpreting Categorical and Quantitative Data.

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23.

The histogram below shows the amount a family spent on groceries during the year. Which statement is true for the histogram?
- A.
  
  The lowest frequency is between $80 and $110.
- B.
  
  The highest frequency is between $140 and $170.
- C.
  
  More than half of the amount spent is greater than $140.
- D.
  
  More than half of the amount spent is between $110 and $170.
Correct Answer
D. More than half of the amount spent is between $110 and $170.

Explanation
D. The correct solution is more than half of the amount spent is between $110 and $170. There are 14 weeks where the amount spent is between $110 and $140 and 13 weeks where the amount spent is between $140 and $170. This is 27 weeks, which is more than half the data set. See Lesson: Interpreting Categorical and Quantitative Data.

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24.

The data below shows the number of minutes available to eat breakfast for a group of employees. 10, 20, 40, 30, 50, 60, 50, 40, 30, 20, 40, 30, 10, 20, 30, 50, 40, 10, 10, 20, 30, 40, 20, 50, 40, 30 Select a dot plot for the data.
- A.
- B.
- C.
- D.
Correct Answer
A.

Explanation
A. The correct solution is A. There are 4 employees who have 10 minutes and 50 minutes, 5 employees who have 20 minutes, 6 employees who have 30 minutes and 40 minutes, and 1 employee who has 60 minutes. See Lesson: Interpreting Categorical and Quantitative Data.

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25.

Find the median for the data set 34, 31, 37, 35, 38, 33, 39, 32, 36, 35, 37, and 33.
- A.
  
  34
- B.
  
  35
- C.
  
  36
- D.
  
  37
Correct Answer
B. 35

Explanation
B. The correct solution is 35. The data set in order is 31, 32, 33, 33, 34, 35, 35, 36, 37, 37, 38, 39, and the middle numbers are both 35. Therefore, the median is 35. See Lesson: Interpreting Graphics.

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26.

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
Correct Answer
C. 2016

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

See Lesson: Interpreting Graphics.

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27.

Find the range for the data set 34, 45, 27, 29, 36, 60, 52, 48, 41, 65, 44, 50, 64, 58, 47, and 31.
- A.
  
  3
- B.
  
  5
- C.
  
  36
- D.
  
  38
Correct Answer
D. 38

Explanation
D. The correct solution is 38. The difference between the highest value of 65 and the lowest value of 27 is 38. See Lesson: Interpreting Graphics.

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28.

A rectangular pyramid has a length of 10 centimeters, a width of 11 inches, and a height of 12 inches. Find the volume in cubic inches.
- A.
  
  220
- B.
  
  440
- C.
  
  660
- D.
  
  880
Correct Answer
B. 440
29.

A sphere has a volume of 972π cubic millimeters. Find the radius in millimeters.
- A.
  
  3
- B.
  
  9
- C.
  
  27
- D.
  
  81
Correct Answer
B. 9

Explanation
B. The correct solution is 9 millimeters. Substitute the values into the formula, , then multiply by the reciprocal, 729 = r3, and apply the cube root, r = 9 millimeters. See Lesson: Measurement and Dimension.

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30.

Find the height in centimeters of a cylinder with a volume of 800π cubic centimeters and a radius of 10 centimeters.
- A.
  
  8
- B.
  
  10
- C.
  
  40
- D.
  
  80
Correct Answer
A. 8

Explanation
A. The correct solution is 8. Substitute the values into the formula, 800π = π102h, and apply the exponent, 800π = π(100)h. Then, divide both sides of the equation by 100π, h = 8 centimeters. See Lesson: Measurement and Dimension.

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31.

Divide.
- A.
- B.
- C.
- D.
Correct Answer
A.
32.

Multiply.
- A.
- B.
- C.
- D.
Correct Answer
C.
33.

Multiply.
- A.
  
  1
- B.
  
  2
- C.
  
  3
- D.
  
  4
Correct Answer
B. 2
34.

Multiply. (5x - 3)(5x + 3)
- A.
  
  25x² - 9
- B.
  
  25x² + 9
- C.
  
  25x² + 30x - 9
- D.
  
  25x² + 30x + 9
Correct Answer
A. 25x² - 9
35.

Perform the operation. (-3x² - 2xy + 4y²) + (5x² + 3xy -3y²)
- A.
  
  2x² - xy + y²
- B.
  
  -2x² - xy +y²
- C.
  
  -2x² + xy + y²
- D.
  
  2x² + xy + y²
Correct Answer
D. 2x² + xy + y²

Explanation
D. The correct solution is 2x2 + xy + y2.
(-3x2 - 2xy + 4y2) + (5x2 + 3xy - 3y2)
= (-3x2 + 5x2) + (-2xy + 3xy) + (4y2 - 3y2)
= 2x2 + xy +y2
See Lesson: Polynomials

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36.

Apply the polynomial identity to rewrite x³ + 125.
- A.
- B.
- C.
- D.
Correct Answer
A.
37.

Simplify.
- A.
- B.
- C.
- D.
Correct Answer
C.
38.

One athlete had a salary of about 3×10⁷ dollars per year and another athlete had a salary of about 2×10⁶ dollars per year. How many times larger is the salary of the first athlete?
- A.
  
  2
- B.
  
  5
- C.
  
  10
- D.
  
  15
Correct Answer
D. 15

Explanation
D. The correct solution is 15 because the first athlete’s salary is about $30,000,000 and the second athlete’s salary is about $2,000,000. So, the first athlete’s salary is about 15 times larger. See Lesson: Powers, Exponents, Roots, and Radicals.

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39.

Solve. x³ = -216
- A.
  
  -6
- B.
  
  -4
- C.
  
  4
- D.
  
  6
Correct Answer
A. -6

Explanation
A. The correct solution is -6 because the cube root of -216 is -6. See Lesson: Powers, Exponents, Roots and Radicals.

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40.

If a survey finds that 120 people are in group X and 230 people are in group Y, what is the ratio of people in group Y to people in group X or group Y?
- A.
  
  12:35
- B.
  
  12:23
- C.
  
  23:35
- D.
  
  35:23
Correct Answer
C. 23:35

Explanation
C. The ratio is 23:35. The first part of the ratio is the number of people in group Y, which is 230. The second part is the number of people in either group, which is the sum 120 + 230 = 350. The ratio is therefore 230:350 = 23:35. See Lesson: Ratios, Proportions, and Percentages.

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41.

The number 22 is what percent of 54?
- A.
  
  22%
- B.
  
  29%
- C.
  
  41%
- D.
  
  76%
Correct Answer
C. 41%

Explanation
C. The fraction 22/54 is 41%, meaning 22 is 41% of 54. See Lesson: Ratios, Proportions, and Percentages.

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42.

If 35% of a cattle herd is Ayrshire and the rest is Jersey, and it has 195 Jerseys, how many cattle are in the herd?
- A.
  
  230
- B.
  
  263
- C.
  
  300
- D.
  
  557
Correct Answer
C. 300

Explanation
C. There are 300 cattle in the herd. Because the herd is only Ayrshire or Jersey, it is 65% Jersey. The equivalent decimals are 0.35 Ayrshire and 0.65 Jersey. Set up a proportion that relates these decimals to the number of cattle of each type:

One approach is to divide 195 by 0.65 to get 300, then multiply by 0.35 to get the number of Ayrshires: 105. Add 195 and 105 to get the total number of cattle in the herd. See Lesson: Ratios, Proportions, and Percentages.

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43.

A regular hexagon has a side length of 5 inches and an apothem of 2 inches. Find the area in square inches.
- A.
  
  30
- B.
  
  40
- C.
  
  50
- D.
  
  60
Correct Answer
A. 30

Explanation
A. The correct solution is 30. Substitute the values into the formula and simplify using the order of operations, A = ½ap = ½(2)(6(5)) = 30 square inches. See Lesson: Similarity, Right Triangles, and Trigonometry.

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44.

A wedge of cheese is in the shape of a right triangular prism. The area of the base is 30 square inches. What is the height in inches of the cheese if the volume is 150 cubic inches?
- A.
  
  2.5
- B.
  
  5
- C.
  
  7.5
- D.
  
  10
Correct Answer
B. 5

Explanation
B. The correct solution is 5. Substitute the values into the formula, 150 = 30h. Divide both sides of the equation by 30, h = 5 inches. See Lesson: Similarity, Right Triangles, and Trigonometry.

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45.

A house is located at (15,30). The next house is 100 meters away. What could be the coordinate of the second house?
- A.
  
  (15,30)
- B.
  
  (30,15)
- C.
  
  (115,15)
- D.
  
  (115,30)
Correct Answer
D. (115,30)

Explanation
D. The correct solution is (115,30) because 100 can be added to the x-coordinate, 15+100=115. See Lesson: Similarity, Right Triangles, and Trigonometry.

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46.

Solve the equation by completing the square. x² - 2x - 37 = 0
- A.
  
  -1 ± √37
- B.
  
  1 ± √37
- C.
  
  -1 ± √38
- D.
  
  1 ± √38
Correct Answer
D. 1 ± √38
47.

Solve the equation by factoring. x² - 5x - 50 = 0
- A.
  
  -10, -5
- B.
  
  -10, 5
- C.
  
  10, -5
- D.
  
  10, 5
Correct Answer
B. -10, 5
48.

Solve the equation by any method. x² + 17x + 20 = 0
- A.
  
  -15.73 and -1.27
- B.
  
  15.73 and -1.27
- C.
  
  -15.73 and 1.27
- D.
  
  15.73 and 1.27
Correct Answer
A. -15.73 and -1.27
49.

A service group collects trash from area roadways for four straight weeks. The amount of trash they pick up is about . Estimate the total number of pounds collected.
- A.
  
  70
- B.
  
  71
- C.
  
  72
- D.
  
  73
Correct Answer
D. 73

Explanation
D. The correct solution is 73. The estimated weights are 20, 15, 21, and 17 pounds, and the total weight is about 73 pounds. See Lesson: Solving Real World Mathematical Problems.

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50.

In a game, positive and negative points can be scored. For 10 turns, the point total is - 5, + 4, - 7, - 2, 0, +3, +5, - 6, - 4, +2. What is the average point total?
- A.
  
  -2
- B.
  
  -1
- C.
  
  1
- D.
  
  2
Correct Answer
B. -1

Explanation
B. The correct solution is -1 because the sum of the scores is -10. The average is -10 divided by 10, or -1 point. See Lesson: Solving Real World Mathematical Problems.

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