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Act Math Exam 2

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Act Math Exam 2 - Quiz

Questions and Answers

1.

What is 604 - 561?
- A.
  
  34
- B.
  
  43
- C.
  
  53
- D.
  
  143
Correct Answer
B. 43

Explanation
B. The correct solution is 43. Use the subtraction algorithm, which will require borrowing once. See Lesson: Basic Addition and Subtraction.

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2.

A biologist has captured only two kinds of snakes, ringnecks and garters. If she has 6 ringneck snakes and 13 snakes total, how many garter snakes does she have?
- A.
  
  6
- B.
  
  7
- C.
  
  13
- D.
  
  19
Correct Answer
B. 7

Explanation
B. The correct solution is 7. Since the biologist only has ringnecks and garters, any snake in her possession is a garter if it is not a ringneck. Because she has 13 snakes but 6 ringneck snakes, the number of garter snakes is the difference: 13 – 6 = 7. See Lesson: Basic Addition and Subtraction.

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3.

Evaluate the expression. (3 x (4 + 9) ÷ 13 - 2) + 1
- A.
  
  -2
- B.
  
  0
- C.
  
  2
- D.
  
  5
Correct Answer
C. 2

Explanation
C. Follow the order of operations (the PEMDAS mnemonic). Begin with the innermost parentheses and work outward, multiplying and dividing from left to right before adding and subtracting from left to right.
(3 × (4 + 9) ÷ 13 – 2) + 1
(3 × 13 ÷ 13 – 2) + 1
(39 ÷ 13 – 2) + 1
(3 – 2) + 1
1 + 1
2
See Lesson: Basic Multiplication and Division.

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4.

What is 762 ÷ 127
- A.
  
  4
- B.
  
  6
- C.
  
  8
- D.
  
  9
Correct Answer
B. 6

Explanation
B. Use the division algorithm. Because 127 is greater than 7 and 76, the process begins with all three digits in the dividend.

See Lesson: Basic Multiplication and Division.

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5.

The area of a half circle is 48 square centimeters. Find the circumference of the curved portion of the half circle to the nearest tenth of a centimeter. Use 3.14 for π.
- A.
  
  17.3
- B.
  
  24.5
- C.
  
  34.5
- D.
  
  49.0
Correct Answer
A. 17.3

Explanation
A. The correct solution is 17.3.

See Lesson: Circles.

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6.

A dime has a radius of 8.5 millimeters. Find the circumference in millimeters of the dime. Use 3.14 for π.
- A.
  
  11.64
- B.
  
  26.69
- C.
  
  53.38
- D.
  
  106.76
Correct Answer
C. 53.38

Explanation
C. The correct solution is 53.38 because C=2πr≈(2)3.148.5≈53.38 millimeters.

See Lesson: Circles.

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7.

The area of a circular drum top is 175 square inches. Find the diameter to the nearest tenth of an inch. Use 3.14 for π.
- A.
  
  7.5
- B.
  
  15.0
- C.
  
  22.5
- D.
  
  30.0
Correct Answer
B. 15.0

Explanation
B. The correct solution is 15.0 because A = πr2 ; 175 = 3.14r2 ; 55.73=r2; r ≈ 7.5. The diameter is twice the radius, or about 15.0 inches. See Lesson: Circles.

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8.

Identify the coplanar points in the diagram.
- A.
  
  Points S, T, U, and Y
- B.
  
  Points X, V, S, and z
- C.
  
  Points X, Y, U, and V
- D.
  
  Points U, Y, Z, and T
Correct Answer
A. Points S, T, U, and Y

Explanation
A. The correct solution is points S, T, U, and Y because these four points are in plane Z. See Lesson: Congruence.

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9.

What is the number of symmetry lines for a regular hexagon?
- A.
  
  2
- B.
  
  4
- C.
  
  6
- D.
  
  8
Correct Answer
C. 6

Explanation
C. The correct solution is six lines of symmetry. There are three lines of symmetry through opposite vertices and three lines through the midpoints of opposite segments. See Lesson: Congruence.

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10.
- A.
- B.
- C.
- D.
Correct Answer
B.

Explanation
B. The correct solution is B. The two lines intersect at point Z. See Lesson: Congruence.

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11.

Which decimal is the least?
- A.
  
  2.22
- B.
  
  2.02
- C.
  
  2.002
- D.
  
  2.2
Correct Answer
C. 2.002

Explanation
C. The correct solution is 2.002 because 2.002 contains the smallest values in the tenths and hundredths places. See Lesson: Decimals and Fractions.

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12.

Change 2.5 to a fraction. Simplify completely.
- A.
- B.
- C.
- D.
Correct Answer
D.
13.
- A.
- B.
- C.
- D.
Correct Answer
C.

Explanation
See Lesson: Decimals and Fractions.

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14.

Solve the equation for the unknown. a - 10 = -20
- A.
  
  -30
- B.
  
  -10
- C.
  
  2
- D.
  
  200
Correct Answer
B. -10

Explanation
B. The correct solution is –10 because 10 is added to both sides of the equation. See Lesson: Equations with One Variable.

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15.

Solve the inequality for the unknown.
- A.
  
  X ≤ -45
- B.
  
  X ≥ -45
- C.
  
  X ≤ 90
- D.
  
  X ≥ 90
Correct Answer
C. X ≤ 90
16.

Solve the equation for the unknown. 3x - 8 + 5 + 2x = 4x - x + 6
- A.
- B.
- C.
- D.
Correct Answer
D.
17.

Solve the system of equations. -2x + 6y = -6 4x - 5y = 26
- A.
  
  (2, 3)
- B.
  
  (3, 6)
- C.
  
  (6, 9)
- D.
  
  (9, 2)
Correct Answer
D. (9, 2)
18.

Solve the system of equations. x + 2y = 5 -5x + 3y = -25
- A.
  
  (5, 0)
- B.
  
  (0, -5)
- C.
  
  (-5, 0)
- D.
  
  (0, 5)
Correct Answer
A. (5, 0)
19.

Solve the system of equations by graphing. 3x + 4y = -5 -2x +2y =8
- A.
- B.
- C.
- D.
Correct Answer
A.

Explanation
A. The correct graph has the two lines intersect at (-3, 1). See Lesson: Equations with Two Variables.

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20.

If the term of a mobile-phone contract is in multiples of a year, which duration can a customer choose?
- A.
  
  6 months
- B.
  
  18 months
- C.
  
  24 months
- D.
  
  32 months
Correct Answer
C. 24 months

Explanation
C. A year-long contract is also 12 months long. Multiples of 12 months are 24 months, 36 months, 48 months, and so on. See Lesson: Factors and Multiples.

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21.

How many unique prime factors does 75 have?
- A.
  
  1
- B.
  
  2
- C.
  
  3
- D.
  
  4
Correct Answer
B. 2

Explanation
B. The prime factorization—for example, using a factor tree—shows that 75 has the prime factors 3, 5, and 5, since 3 × 5 × 5 = 75. Because 5 repeats, 75 has only two unique prime factors. See Lesson: Factors and Multiples.

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22.

The data below show the number of cars that drove through an intersection on a Saturday. 1, 48, 60, 43, 41, 70, 75, 80, 101, 90, 121, 114, 99, 153, 205, 175, 222, 96, 201, 158, 141, 117, 74, 29 Select a histogram for the data.
- A.
- B.
- C.
- D.
Correct Answer
D.

Explanation
D. The correct solution is D. Each bin contains 50 cars, and the frequencies are 4, 8, 5, 3, and 3. See Lesson: Interpreting Categorical and Quantitative Data.

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23.

Find the values from the box plot.
- A.
  
  Minimum: 0, first quartile: 3, median: 5, third quartile: 7, maximum: 9
- B.
  
  Minimum: 0.5, first quartile: 3, median: 4.5, third quartile: 7, maximum: 9
- C.
  
  Minimum: 0, first quartile: 3, median: 5, third quartile: 7, maximum: 10
- D.
  
  Minimum: 0.5, first quartile: 3, median: 4.5, third quartile: 7, maximum: 10
Correct Answer
B. Minimum: 0.5, first quartile: 3, median: 4.5, third quartile: 7, maximum: 9

Explanation
B. The correct solution is minimum: 0.5, first quartile: 3, median: 4.5, third quartile: 7, maximum: 9, which are the values of the box plot. See Lesson: Interpreting Categorical and Quantitative Data.

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24.

The high temperatures in degrees Fahrenheit for the beginning of April are 45, 48, 53, 57, 52, 60, 58. The last temperature is 28. Compare the standard deviation and interquartile range before and after the last temperature.
- A.
  
  The standard deviation and interquartile range increase.
- B.
  
  The standard deviation and interquartile range decrease.
- C.
  
  The standard deviation increases, and the interquartile range decreases.
- D.
  
  The standard deviation decreases, but the interquartile range increases.
Correct Answer
A. The standard deviation and interquartile range increase.

Explanation
A. The correct solution is the standard deviation and interquartile range increase. The standard deviation increases from 5.06 to 9.61, and the interquartile range increases from 9.5 to 11. See Lesson: Interpreting Categorical and Quantitative Data.

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25.

The data set represents the number of weekly pop-up ads for 12 families: 125, 145, 150, 130, 150, 120, 170, 165, 175, 145, 150, and 130. Find the median.
- A.
  
  145
- B.
  
  145.5
- C.
  
  147
- D.
  
  147.5
Correct Answer
D. 147.5

Explanation
D. The correct solution is 147.5. The data set written in order is 120, 125, 130, 130, 145, 145, 150, 150, 150, 165, 170, 175. The middle two numbers are 145 and 150, and the mean of the numbers is 147.5. See Lesson: Interpreting Graphics.

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26.

Find the mode for the data set 42, 45, 44, 44, 45, 42, 45, 44, 45, 46, 42, 44, 41, 48, 47, 46, 45, 42, 42, and 44.
- A.
  
  42, 43
- B.
  
  44, 45
- C.
  
  42, 44, 45
- D.
  
  42, 43, 44, 45
Correct Answer
C. 42, 44, 45

Explanation
C. The correct solution is 42, 44, and 45. The modes are 42, 44, and 45 because these values appear four times in the data set. See Lesson: Interpreting Graphics.

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27.

Find the mean for the data set. 16, 18, 17, 15, 19, 14, 12, 11, 10, 16, 18, and 17.
- A.
  
  14.25
- B.
  
  15.25
- C.
  
  16
- D.
  
  17
Correct Answer
B. 15.25

Explanation
B. The correct solution is 15.25. The sum of all items is 183, and 183 divided by 12 gives a mean of 15.25. See Lesson: Interpreting Graphics.

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28.

A package of a toy is a cylinder with a cone on top. The radius of the figure is 2 feet, the height of the cylinder is 3 feet, and the height of the cone is 3 feet. Find the volume to the nearest cubic foot. Use 3.14 for π.
- A.
  
  12
- B.
  
  38
- C.
  
  50
- D.
  
  76
Correct Answer
C. 50

Explanation
See Lesson: Measurement and Dimension.

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29.

Find the radius in meters of a cone with a volume of cubic meters and a height of 8 meters.
- A.
  
  2
- B.
  
  4
- C.
  
  6
- D.
  
  8
Correct Answer
D. 8
30.

A square pyramid has a volume of 189 cubic feet and a height of 7 feet. Find the length in feet of a side of the base.
- A.
  
  3
- B.
  
  9
- C.
  
  12
- D.
  
  18
Correct Answer
B. 9
31.
- A.
- B.
- C.
- D.
Correct Answer
A.
32.

Divide.
- A.
- B.
- C.
- D.
Correct Answer
D.
33.
- A.
- B.
- C.
- D.
Correct Answer
B.
34.

Multiply. (4y² + 3)(2y + 5)
- A.
  
  8y³+ 10y² + 16y +15
- B.
  
  8y³+ 20y² + 16y +15
- C.
  
  8y³+ 10y² + 6y +15
- D.
  
  8y³+ 20y² + 6y +15
Correct Answer
D. 8y³+ 20y² + 6y +15
35.

Perform the operation. (8x2 - 6x - 3) - (4x2 - 5x + 4)
- A.
  
  4x² - 11x - 7
- B.
  
  4x² - 11x + 1
- C.
  
  4x² - x - 7
- D.
  
  4x² - x + 1
Correct Answer
C. 4x² - x - 7
36.

Apply the polynomial identity to rewrite 27x³ - 8.
- A.
  
  (3x - 2)(9x² - 6x + 4)
- B.
  
  (3x - 2)(9x² + 6x + 4)
- C.
  
  (3x - 2)(9x² + 6x - 4)
- D.
  
  (3x - 2)(9x² - 6x - 4)
Correct Answer
B. (3x - 2)(9x² + 6x + 4)
37.

Simplify.
- A.
  
  -343
- B.
  
  -49
- C.
  
  -21
- D.
  
  -7
Correct Answer
A. -343
38.

Solve x² = 225.
- A.
  
  -5, 5
- B.
  
  -10, 10
- C.
  
  -15, 15
- D.
  
  -20, 20
Correct Answer
C. -15, 15

Explanation
C. The correct solution is -15, 15 because the square root of 225 is 15. The values of -15 and 15 make the equation true. See Lesson: Powers, Exponents, Roots, and Radicals.

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39.

A lysosome has a length of 1×10^-6 meter, and measles virus has a length of 2×10^-9 meter. How many times longer is the lysosome?
- A.
  
  5
- B.
  
  50
- C.
  
  500
- D.
  
  5,000
Correct Answer
C. 500

Explanation
C. The correct solution is 500 because 1×10-6 is 0.000001 and 2×10-9 is about 0.000000002. So, the lysosome is 500 times longer. See Lesson: Powers, Exponents, Roots, and Radicals.

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40.

How many dogs are necessary to make a cat-to-dog ratio of 3:2 in an area with 1,425 cats?
- A.
  
  285
- B.
  
  950
- C.
  
  2,138
- D.
  
  2,375
Correct Answer
B. 950

Explanation
B. The correct answer is B. Set up the proportion of dogs to cats (or vice versa):

Since 1,425 ÷ 3 = 475, the number of dogs is the product of 2 and 475, or 950. See Lesson: Ratios, Proportions, and Percentages.

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41.

How many men does a company employ if it has 420 employees and 35% are women?
- A.
  
  35
- B.
  
  147
- C.
  
  273
- D.
  
  420
Correct Answer
C. 273

Explanation
C. The company employs 273 men. If 35% of the company’s employees are women, 65% are men. Set up a proportion using 65%, which is equal to

The unknown number is the product of 13 and 420 ÷ 20 = 21, which is 273. See Lesson: Ratios, Proportions, and Percentages.

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42.

If a truck’s initial speed is 60 mph and its final speed is 100 mph, what is its percent change in speed
- A.
  
  17%
- B.
  
  33%
- C.
  
  40%
- D.
  
  67%
Correct Answer
D. 67%
43.

Given the coordinates for a square (-3, -5), (-3, 4), (6, 4), and (6, -5), find the length of each side of the square.
- A.
  
  3 unites
- B.
  
  6 units
- C.
  
  9 units
- D.
  
  12 units
Correct Answer
C. 9 units

Explanation
C. The correct solution 9 units. The difference between the x-coordinates is 6 - (-3) = 9 units, and the difference between the y-coordinates is 4 - (-5) = 9 units. See Lesson: Similarity, Right Triangles, and Trigonometry.

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44.

A trapezoid has bases of 8 inches and 12 inches and a height of 6 inches. Find the area in square inches.
- A.
  
  18
- B.
  
  20
- C.
  
  60
- D.
  
  72
Correct Answer
C. 60
45.

Draw a square with the coordinates (-3, 4), (-3, -2), (3, -2), (3, 4).
- A.
- B.
- C.
- D.
Correct Answer
B.

Explanation
B. The first point is in the second quadrant, the second point is in the third quadrant, the third point is in the fourth quadrant, and the last point is in the first quadrant. See Lesson: Similarity, Right Triangles, and Trigonometry.

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46.

Solve the equation by completing the square. x² + 12x + 10 = 0
- A.
  
  6 ± √26
- B.
  
  -6 ± √26
- C.
  
  6 ± √10
- D.
  
  -6 ± √10
Correct Answer
B. -6 ± √26
47.

Solve the equation by factoring. x² + 3x - 88 = 0.
- A.
  
  -8, -11
- B.
  
  -8, 11
- C.
  
  8, -11
- D.
  
  8, 11
Correct Answer
C. 8, -11
48.

Solve the equation by any method. 9x² - 48x + 64 = 0
- A.
- B.
- C.
- D.
Correct Answer
D.
49.

John spends $21.25 at the movies. His ticket is $7.75, and he buys popcorn, a pretzel, and a drink. If each snack costs the same, what is the price of the pretzel?
- A.
  
  $3.58
- B.
  
  $4.50
- C.
  
  $6.00
- D.
  
  $7.08
Correct Answer
B. $4.50

Explanation
B. The correct solution is $4.50 because 21.25 - 7.75 = 13.50 ÷ 3 = $4.50. See Lesson: Solving Real World Mathematical Problems.

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50.

One recipe calls for ¾ cup of sugar, and another calls for 2 ½ cups of sugar. The first recipe is tripled, and the second recipe is halved. How many cups of sugar are needed?
- A.
  
  1
- B.
  
  1¾
- C.
  
  3
- D.
  
  3½
Correct Answer
D. 3½

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