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Act Math Exam 4

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Act Math Exam 4 - Quiz

Questions and Answers

1.

Evaluate the expression 1,004 + 110.
- A.
  
  2104
- B.
  
  1411
- C.
  
  1204
- D.
  
  1114
Correct Answer
D. 1114

Explanation
D. The correct solution is 1,114. Use the addition algorithm or note the two numbers never have nonzero digits in the same place. This fact allows addition by inspection.

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2.

If Professor Markham has 127 students in her calculus course but 37 drop out because it is too difficult, how many students remain?
- A.
  
  37
- B.
  
  90
- C.
  
  127
- D.
  
  164
Correct Answer
B. 90

Explanation
B. The correct solution is 90. This situation requires finding the difference between 127 and 37. Use the subtraction algorithm if necessary: 127 – 37 = 90.

See Lesson: Basic Addition and Subtraction.

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3.

Evaluate the expression (-224) ÷ 14.
- A.
  
  -210
- B.
  
  -16
- C.
  
  16
- D.
  
  210
Correct Answer
B. -16

Explanation
B. When dividing signed numbers, remember that if the dividend and divisor have different signs, the quotient is negative. Other than the sign, the process is the same as dividing whole numbers. Use the division algorithm to divide 224 by 14. See Lesson: Basic Multiplication and Division.

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4.

Which statement about multiplication is true?
- A.
  
  Multiplication is impossible.
- B.
  
  Multiplication is repeated division.
- C.
  
  Multiplication is repeated addition.
- D.
  
  Multiplication is repeated subtraction.
Correct Answer
C. Multiplication is repeated addition.

Explanation
C. Instead of adding the same number over and over (for example, 5 + 5 + 5 + 5 + 5 + 5), multiplication enables a more concise expression. In this example, because the expression adds 6 terms of 5, it becomes 6 x 5, or 30. See Lesson: Basic Multiplication and Division.

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5.

A rug is shaped in a half circle. The curved edge of the rug has a circumference of 74 inches. Find the area of the rug to the nearest tenth of a square inch. Use 3.14 for π.
- A.
  
  296.0
- B.
  
  874.4
- C.
  
  1,113.9
- D.
  
  1,748.9
Correct Answer
B. 874.4
6.

Identify the diameter of the circle.
- A.
- B.
- C.
- D.
Correct Answer
B.
7.

Find the circumference in centimeters of a circle with a radius of 11 centimeters. Use 3.14 for π.
- A.
  
  3.14
- B.
  
  6.28
- C.
  
  34.54
- D.
  
  69.08
Correct Answer
D. 69.08

Explanation
D. The correct solution is 69.08 because C = 2πr ≈ (2)3.14(11) ≈ 69.08 centimeters. See Lesson: Circles.

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8.

Select the figure that is rotated 90° counterclockwise about the origin.
- A.
- B.
- C.
- D.
Correct Answer
C.

Explanation
C. The correct solution is C. This is a rotation of 90° counterclockwise because the point (x, y) becomes (–y, x). See Lesson: Congruence.

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9.

DDEF has points D (–3, 6), E (–2, –4), and F (5, 0). After a transformation, the points are D’ (6, 3), E’ (–4, 2), and F’ (0, –5). What is the transformation between the points?
- A.
  
  Reflection across the x-axis
- B.
  
  Reflection across the y-axis
- C.
  
  Rotation of 90° counterclockwise
- D.
  
  Rotation of 270° counterclockwise
Correct Answer
D. Rotation of 270° counterclockwise

Explanation
D. The correct solution is a rotation of 270° counterclockwise because the points (x, y) become (y, –x). See Lesson: Congruence.

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10.

Select the figure that is translated (x + 2, y + 1).
- A.
- B.
- C.
- D.
Correct Answer
A.

Explanation
A. The correct solution is A. The translation for the points is (x + 2, y + 1). The points of the original square, (–4, –4), (–4, 2), (2, 2), and (2, –4), become (–2, –3), (–2, 3), (4, 3), and (4, –3). See Lesson: Congruence.

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11.

Write 1.5 as a percent.
- A.
  
  0.15%
- B.
  
  1.5%
- C.
  
  15%
- D.
  
  150%
Correct Answer
D. 150%

Explanation
D. The correct answer is 150% because 1.5 as a percent is 1.5 × 100 = 150%. See Lesson: Decimals and Fractions.

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12.

Write 290% as a fraction.
- A.
- B.
- C.
- D.
Correct Answer
D.
13.
- A.
  
  7.55
- B.
  
  7.6
- C.
  
  7.65
- D.
  
  7.7
Correct Answer
C. 7.65
14.

Solve the inequality for the unknown, 2(3x - 1) +5 ≥ 3x - 4 - 4x.
- A.
  
  X ≥ -7
- B.
  
  X ≥ -4
- C.
  
  X ≥ -1
- D.
  
  X ≥ 0
Correct Answer
C. X ≥ -1
15.

Solve the equation for the unknown.
- A.
- B.
- C.
  
  6
- D.
  
  26
Correct Answer
C. 6
16.

Solve the equation for c. 2a(b + c) = c
- A.
- B.
- C.
- D.
Correct Answer
A.
17.

Solve for the system of equations. -4x + 3y = 30 3x + 4y = 15
- A.
  
  (3, -6)
- B.
  
  (-3, 6)
- C.
  
  (-3, -6)
- D.
  
  (3, 6)
Correct Answer
B. (-3, 6)
18.

Solve the system of equations. y = -2x x² + y² = 5
- A.
  
  (1, -2) and (-1, 2)
- B.
  
  (1, 2) and (-1, -2)
- C.
  
  (2, -1) and (-2, 1)
- D.
  
  (2, 1) and (-2, -1)
Correct Answer
A. (1, -2) and (-1, 2)
19.

Solve the system of equations by graphing. y = -x + 7 y = 2x - 8
- A.
- B.
- C.
- D.
Correct Answer
D.

Explanation
D. The correct graph has the two lines intersect at (5, 2).

See Lesson: Equations with Two Variables.

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20.

If a number has 3 and 5 as factors, which statement best describes that number?
- A.
  
  The number is 15.
- B.
  
  The number is prime.
- C.
  
  The number has 15 as a factor.
- D.
  
  The number has only two prime factors.
Correct Answer
C. The number has 15 as a factor.

Explanation
C. Because 3 and 5 are prime factors of the number, its prime factorization includes them. Furthermore, because a number is the product of all its prime factors, the number in this question must either be 15 or have 15 as a factor. It may or may not be 15, so it may have more than two prime factors. See Lesson: Factors and Multiples.

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21.

The dot plot shows the results of rolling a dice for a game. Which statement is true for the dot plot?
- A.
  
  There were 60 turns in the game.
- B.
  
  More than half of the turns were 3 or less.
- C.
  
  1 and 6 occurred the same number of times.
- D.
  
  The difference between the lowest and highest frequency is 3.
Correct Answer
A. There were 60 turns in the game.

Explanation
A. The correct solution is there were 60 turns in the game. The sum of the results is 12 + 9 + 8 + 13 + 7 + 11, which is 60 turns. See Lesson: Interpreting Categorical and Quantitative Data.

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22.

Which number is not a factor of 1,155?
- A.
  
  22
- B.
  
  33
- C.
  
  55
- D.
  
  77
Correct Answer
A. 22

Explanation
A. To determine whether a number is a factor of another number, divide the second number by the first number. If the quotient is whole, the first number is a factor. In this case, 1,155 is not divisible by 22. See Lesson: Factors and Multiples.

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23.

The last 8 transactions at a shoe store in dollars are 5, 39, 49, 50, 52, 35, 44, 100. What is the effect of removing the outliers on the mean and median?
- A.
  
  The mean and median increase.
- B.
  
  There is no effect on the mean or median.
- C.
  
  The mean decreases, but the median does not change.
- D.
  
  The median decreases, but the mean does not change.
Correct Answer
C. The mean decreases, but the median does not change.

Explanation
C. The correct solution is the mean decreases, but the median does not change. The mean decreases from 46.75 to 44.83, but the median does not change from 46.5. See Lesson: Interpreting Categorical and Quantitative Data.

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24.

Identify the variables from a study on cereal that is quantitative.
- A.
  
  Fat calories
- B.
  
  Cereal name
- C.
  
  Manufacturer
- D.
  
  Target audience
Correct Answer
A. Fat calories

Explanation
A. The correct solution is fat calories because this is a numerical value. See Lesson: Interpreting Categorical and Quantitative Data.

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25.

A gymnastics team has the following scores for an event: 12.3, 12.7, 14.1, 14.5, 13.8, 13.6, 14.2, 15.2, 14.8, 13.9, 15.4, 14.3. Find the mean score for the team to the nearest hundredth.
- A.
  
  14.07
- B.
  
  14.15
- C.
  
  14.57
- D.
  
  14.71
Correct Answer
A. 14.07

Explanation
A. The correct solution is 14.07. The sum of the scores is 168.8, and the average is 14.07 for the 12 scores. See Lesson: Interpreting Graphics.

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26.

The double line chart shows the number of points scored and points given up by a basketball team over the first 10 games. Which statement is true?
- A.
  
  The team scored more than 62 points in a majority of games and gave up fewer than 62 points in a majority of games.
- B.
  
  The team scored more than 65 points in a majority of games and gave up fewer than 65 points in a majority of games.
- C.
  
  The team scored more than 68 points in a majority of games and gave up fewer than 68 points in a majority of games.
- D.
  
  The team scored more than 70 points in a majority of games and gave up fewer than 65 points in a majority of games.
Correct Answer
B. The team scored more than 65 points in a majority of games and gave up fewer than 65 points in a majority of games.

Explanation
B. The correct solution is the team scored more than 65 points in a majority of games and gave up fewer than 65 points in a majority of games. From the graph, there are 6 games during which the team scored more than 65 points and 6 games during which it gave up fewer than 65 points.

See Lesson: Interpreting Graphics.

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27.

A mixture for a cake has various parts. Select the correct circle graph for the data.
- A.
- B.
- C.
- D.
Correct Answer
C.
28.

A basketball has a diameter of 10 inches. What is the volume in cubic inches inside the ball? Use 3.14 for π.
- A.
  
  261.67
- B.
  
  523.33
- C.
  
  1,046.67
- D.
  
  2,093.33
Correct Answer
B. 523.33
29.

The volume of a hemi-sphere is cubic feet. What is the diameter in feet?
- A.
  
  1
- B.
  
  2
- C.
  
  3
- D.
  
  4
Correct Answer
D. 4
30.

A jar of salsa has a diameter of 12 centimeters and a height of 10 centimeters. There are 4 centimeters of salsa left in the jar. How much salsa was used if the jar was originally filled to the top? State the answer in cubic centimeters in terms of π.
- A.
  
  216π
- B.
  
  360π
- C.
  
  864π
- D.
  
  1,440π
Correct Answer
A. 216π

Explanation
A. The correct solution is 216π. The radius is one-half of the diameter, 6 centimeters. The height of the used salsa is 10 – 4, or 6 centimeters. Substitute the values into the formula and simplify using the order of operations, V = πr2h = π62(6) = π(36)(6) = 216π cubic centimeters. See Lesson: Measurement and Dimension.

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31.
- A.
- B.
- C.
- D.
Correct Answer
C.
32.

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

Divide.
- A.
- B.
- C.
- D.
Correct Answer
B.
34.

Multiply. (2y² - 1)(y² - 3y + 5)
- A.
  
  2y⁴ - 6y³ + 10y² + 3y - 5
- B.
  
  2y⁴ - 6y³ + 9y² + 3y - 5
- C.
  
  2y⁴ - 6y³ + 11y² + 3y - 5
- D.
  
  2y⁴ - 6y³ + 8y² + 3y - 5
Correct Answer
B. 2y⁴ - 6y³ + 9y² + 3y - 5
35.

Apply the polynomial identity to rewrite x² - 100.
- A.
  
  (x - 10)²
- B.
  
  (x - 10)(x + 10)
- C.
  
  (x + 10)²
- D.
  
  X² - 10²
Correct Answer
B. (x - 10)(x + 10)

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

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36.

Simplify.
- A.
- B.
- C.
  
  Y⁴
- D.
  
  X⁴y⁴
Correct Answer
C. Y⁴
37.

Perform the operation. (-2x² + 8x) + (3x³ - 4x² + 1)
- A.
  
  3x³ - 6x² + 8x + 1
- B.
  
  3x³ - 2x² + 8x + 1
- C.
  
  3x³ + 6x² + 8x + 1
- D.
  
  3x³ + 2x² + 8x + 1
Correct Answer
A. 3x³ - 6x² + 8x + 1
38.

The land area of Colorado is about 1 x 10⁵ square miles, and the land area of Ohio is about 4 x 10⁴ square miles. How many times larger is the land area of Colorado?
- A.
  
  2
- B.
  
  3
- C.
  
  4
- D.
  
  5
Correct Answer
B. 3

Explanation
B. The correct solution is 3 because the land area of Colorado is about 100,000 square miles and the land area of Ohio is about 40,000 square miles. So, the land area is about 3 times larger. See Lesson: Powers, Exponents, Roots, and Radicals.

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39.

Solve. x³ = -8
- A.
  
  -4
- B.
  
  -2
- C.
  
  2
- D.
  
  4
Correct Answer
B. -2

Explanation
B. The correct solution is -2 because the cube root of -8 is -2. See Lesson: Powers, Exponents, Roots, and Radicals.

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40.

Which percent is closest to the ratio 7 : 3?
- A.
  
  23%
- B.
  
  43%
- C.
  
  73%
- D.
  
  233%
Correct Answer
D. 233%

Explanation
D. To convert a ratio to a percent, divide the numbers in the ratio (noting that its equivalent fraction is 7/3) to get approximately 2.33. Then, multiply by 100%. See Lesson: Ratios, Proportions, and Percentages.

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41.

If a company’s revenue changes from $123 million to $118 million in a month, how quickly is it increasing in a year?
- A.
  
  –$60 million
- B.
  
  –$5 million
- C.
  
  $5 million
- D.
  
  $60 million
Correct Answer
A. –$60 million
42.

The number 36 is what percent of 16?
- A.
  
  31%
- B.
  
  44%
- C.
  
  69%
- D.
  
  225%
Correct Answer
D. 225%

Explanation
D. The fraction 36/16 is 225%, meaning 36 is 225% of 16. See Lesson: Ratios, Proportions, and Percentages.

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43.

Given the coordinates for a rectangle (-4, -1), (-9, -1), (-9,-8), and (-4,-8), find the length of each side of the rectangle.
- A.
  
  2 units and 3 units
- B.
  
  2 units and 7 units
- C.
  
  5 units and 3 units
- D.
  
  5 units and 7 units
Correct Answer
D. 5 units and 7 units

Explanation
D. The correct solution is 5 units and 7 units. The difference between the x-coordinates is -4 - (-9) = 5 units, and the difference between the y-coordinates is -1 - (-8) = 7 units. See Lesson: Similarity, Right Triangles, and Trigonometry.

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44.

A box in the shape of a right rectangular prism has dimensions of 6 centimeters by 7 centimeters by 8 centimeters. What is the volume in cubic centimeters?
- A.
  
  280
- B.
  
  336
- C.
  
  560
- D.
  
  672
Correct Answer
B. 336

Explanation
B. The correct solution is 336. Substitute the values into the formula and simplify using the order of operations, V = lwh = 6(7)(8) cubic centimeters. See Lesson: Similarity, Right Triangles, and Trigonometry.

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45.

A sign stating “Do Not Enter” is in the shape of a square with side lengths of 75 centimeters. What is the area in square centimeters?
- A.
  
  150
- B.
  
  300
- C.
  
  5,325
- D.
  
  5,625
Correct Answer
D. 5,625

Explanation
D. The correct solution is 5,625. Substitute the values into the formula and simplify using the order of operations, A = s2 = 752 = 5,625 square centimeters. See Lesson: Similarity, Right Triangles, and Trigonometry.

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46.

Solve the equation by any method. x² + 4x - 15 = 0
- A.
  
  2 ± √19
- B.
  
  -2 ± √19
- C.
  
  2 ± √15
- D.
  
  -2 ± √15
Correct Answer
B. -2 ± √19
47.

Solve the equation by the quadratic formula. 12x² + x - 3 = 0
- A.
  
  -0.46 and -0.54
- B.
  
  0.46 and -0.54
- C.
  
  -0.46 and 0.54
- D.
  
  0.46 and 0.54
Correct Answer
B. 0.46 and -0.54
48.

Solve the equation by the square root method. x² + 10 = 110
- A.
  
  ± 8
- B.
  
  ± 9
- C.
  
  ± 10
- D.
  
  ± 11
Correct Answer
C. ± 10
49.

The level of a river during a flood was 39.45 feet. After a week, the water level declined to 18.97 feet. What was the amount of decrease in feet?
- A.
  
  20.38
- B.
  
  20.48
- C.
  
  21.38
- D.
  
  21.48
Correct Answer
B. 20.48

Explanation
B. The correct solution is 20.48 because 39.45 - 18.97 = 20.48 feet. See Lesson: Solving Real World Mathematical Problems.

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50.

An even roll of a number cube results in +2 points, and an odd roll of a number cube is -3 points. If there are 14 even numbers and 11 odd numbers, then how many points are scored?
- A.
  
  -61
- B.
  
  -5
- C.
  
  5
- D.
  
  61
Correct Answer
B. -5

Explanation
B. The correct solution is -5 because 14(2) + 11(-3) = 28+(-33) = -5 points. See Lesson: Solving Real World Mathematical Problems.

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