Tasc Math Exam 3

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1.

Solve the equation for the unknown. 3(x + 4) - 1 = 2(x + 3) - 2
- A.
  
  -7
- B.
  
  -2
- C.
  
  2
- D.
  
  7
Correct Answer
A. -7
2.

The temperature on Monday was -7°F, and it increased by 18°F by Tuesday afternoon. What is the temperature in F° on Tuesday afternoon?
- A.
  
  -25
- B.
  
  -11
- C.
  
  11
- D.
  
  25
Correct Answer
C. 11

Explanation
C. The correct solution is 11 because -7 + 18 = 11°F. See Lesson: Solving Real World Mathematical Problems.

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3.

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
Correct Answer
C. 22.5

Explanation
C. The correct solution is 22.5. The data set written in order is 20, 20, 20, 21, 22, 22, 22, 22, 23, 23, 24, 24, 25, 25, 25 and 26. The middle two numbers are 22 and 23, and the mean of these numbers is 22.5. See Lesson: Interpreting Graphics.

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4.

Which decimal is the least?
- A.
  
  0.786
- B.
  
  0.876
- C.
  
  0.687
- D.
  
  0.768
Correct Answer
C. 0.687

Explanation
C. The correct solution is 0.687 because 0.687 contains the smallest value in the tenths place.

See Lesson: Decimals and Fractions.

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5.

Which decimal is the greatest?
- A.
  
  4.04
- B.
  
  4.404
- C.
  
  4.44
- D.
  
  4.044
Correct Answer
C. 4.44

Explanation
C. The correct solution is 4.44 because 4.44 contains the largest values in the tenths and hundredths places.

See Lesson: Decimals and Fractions.

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6.

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
7.

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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8.

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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9.

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
10.

Which best describes the number of multiples of 10?
- A.
  
  1
- B.
  
  10
- C.
  
  100
- D.
  
  An unlimited number
Correct Answer
D. An unlimited number

Explanation
D. The multiples of 10 are the set {…, –30, –20, –10, 0, 10, 20, 30,…}. Therefore, the number of multiples is unlimited. See Lesson: Factors and Multiples.

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11.

Multiply.
- A.
  
  1
- B.
  
  2
- C.
  
  3
- D.
  
  4
Correct Answer
C. 3
12.

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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13.

What is the difference between natural numbers and whole numbers?
- A.
  
  They are the same.
- B.
  
  The whole numbers include zero, but the natural numbers exclude zero.
- C.
  
  The natural numbers only go to 10, but the whole numbers have no limit.
- D.
  
  The whole numbers include negative numbers, but the natural numbers do not.
Correct Answer
B. The whole numbers include zero, but the natural numbers exclude zero.

Explanation
B. The correct solution is the whole numbers include zero, but the natural numbers exclude zero. The natural or “counting” numbers are 1, 2, 3, 4,…. To get the whole numbers, just include 0 with the natural numbers. See Lesson: Basic Addition and Subtraction.

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14.

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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15.

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?
- A.
- B.
- C.
- D.
Correct Answer
A.
16.

Identify the diameter of the circle.
- A.
- B.
- C.
- D.
Correct Answer
B.
17.

Solve the equation by factoring. x² + 15x + 54 = 0
- A.
  
  -6, -9
- B.
  
  -6, 9
- C.
  
  6, -9
- D.
  
  6, 9
Correct Answer
A. -6, -9
18.

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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19.

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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20.

A circle has an area of 240 square centimeters. Find the radius to the nearest tenth of a centimeter. Use 3.14 for π.
- A.
  
  8.7
- B.
  
  15.5
- C.
  
  17.4
- D.
  
  38.2
Correct Answer
A. 8.7

Explanation
A. The correct solution is 8.7 because A = πr2; 240 = 3.14r2; 76.43 = r2; r ≈ 8.7 centimeters. See Lesson: Circles.

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21.

At the grocery store, a researcher asks random people about the number of text messages they send daily. What type of study is this?
- A.
  
  Census
- B.
  
  Survey
- C.
  
  Experiment
- D.
  
  Observational study
Correct Answer
B. Survey

Explanation
B. The correct solution is a survey because the sampling is convenient and only the results are recorded. See Lesson: Statistical Measures.

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22.

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

Explanation
D. The correct graph has the two lines intersect at (0, 3). See Lesson: Equations with Two Variables.

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23.

Convert 4 tons to pounds.
- A.
  
  2,000 pounds
- B.
  
  4,000 pounds
- C.
  
  8,000 pounds
- D.
  
  10,000 pounds
Correct Answer
C. 8,000 pounds

Explanation
C. The correct solution is 8,000 pounds.

See Lesson: Standards of Measure.

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24.

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.
Correct Answer
D. 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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25.

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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26.

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
27.

Solve the inequality for the unknown.
- A.
- B.
- C.
- D.
Correct Answer
D.
28.

A research study aims to find the average age of all retail workers. A group asks all retail workers in Ohio their birth years. What is a name for this study?
- A.
  
  Census
- B.
  
  Survey
- C.
  
  Experiment
- D.
  
  Observational Study
Correct Answer
B. Survey

Explanation
B. The correct solution is survey because the group is focused on people in Ohio. See Lesson: Statistical Measures.

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29.

Simplify. 5⁶ x 5^-3
- A.
  
  5
- B.
  
  15
- C.
  
  125
- D.
  
  625
Correct Answer
C. 125
30.

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
31.

A mixture for a cake has various parts. Select the correct circle graph for the data.
- A.
- B.
- C.
- D.
Correct Answer
C.
32.

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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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.
- A.
  
  2 inches
- B.
  
  9 inches
- C.
  
  13 inches
- D.
  
  26 inches
Correct Answer
C. 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.

A bucket contains 4 bottles of apple juice, 6 bottles of orange juice, 5 bottles of grape juice, and 10 bottles of water. What is the probability of NOT selecting a bottle of water?
- A.
- B.
- C.
- D.
Correct Answer
C.
35.

Convert 6 meters to feet.
- A.
  
  1.52 feet
- B.
  
  1.72 feet
- C.
  
  18.68 feet
- D.
  
  19.68 feet
Correct Answer
D. 19.68 feet
36.

The top 5 leading scorers on a basketball team average 21.3, 19.8, 15.5, 13.9, and 12.4 points per game. What is the estimated average of these players?
- A.
  
  15
- B.
  
  16
- C.
  
  17
- D.
  
  18
Correct Answer
C. 17
37.

What shape is used to measure the distance between two cities on a map?
- A.
  
  A ray
- B.
  
  A line
- C.
  
  A point
- D.
  
  A line segment
Correct Answer
D. A line segment

Explanation
D. The correct solution is line segment because the cities represent the endpoints and the segment is the distance between the two points. See Lesson: Congruence.

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38.

A regular hexagonal pyramid has a base side length of 6 inches, an apothem of 3√3 inches, and a height of 15 inches. Find the volume in cubic inches.
- A.
  
  108√3
- B.
  
  216√3
- C.
  
  512√3
- D.
  
  1024√3
Correct Answer
A. 108√3
39.

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
Correct Answer
C. 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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40.

What is the sum of two negative numbers?
- A.
  
  Negative number
- B.
  
  Positive number
- C.
  
  Zero
- D.
  
  Not enough information
Correct Answer
A. Negative number

Explanation
A. The correct solution is a negative number. Try a few examples: (–1) + (–1), (–8) + (–2). By the rule (-x)+(-y)=-(x+y), the sum is always negative.

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41.

Benjamin buys of fabric at a store. How many total yards did he purchase?
- A.
- B.
- C.
- D.
Correct Answer
C.
42.

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
43.

Solve the system of equations. x = -y - 7 -x +4y = 22
- A.
  
  (10, -3)
- B.
  
  (-10, 3)
- C.
  
  (5, 7)
- D.
  
  (7, 5)
Correct Answer
B. (-10, 3)

Explanation
B. The correct solution is (-10, 3).

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44.

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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45.

Apply the polynomial identity to rewrite x³ + 125.
- A.
  
  (x + 5)(x² - 5x + 25)
- B.
  
  (x - 5)(x² - 10x + 25)
- C.
  
  (x + 5)(x² + 10x + 25)
- D.
  
  (x - 5)(x² + 10x + 25)
Correct Answer
A. (x + 5)(x² - 5x + 25)
46.

Identify 1920 in 12-hour clock time.
- A.
  
  6:20 p.m.
- B.
  
  7:20 p.m.
- C.
  
  6:20 a.m.
- D.
  
  7:20 a.m.
Correct Answer
B. 7:20 p.m.

Explanation
B. The correct solution is 7:20 p.m. Subtract 1200 from the time, 1920 - 1200 = 7: 20 p.m. See Lesson: Standards of Measure.

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47.

Select the figure that is rotated 90° 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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48.

An ice cream cone is filled with ice cream, and then one-half of a spherical scoop of ice cream is added on top of the cone. The diameter of the top of the cone is 8 centimeters, and the height of the cone (not including the half scoop on top) is 6 centimeters. What is the amount of ice cream to the nearest cubic centimeter? Use 3.14 for π.
- A.
  
  168
- B.
  
  200
- C.
  
  234
- D.
  
  268
Correct Answer
D. 268
49.

Which option results in the greatest gain on an investment?
- A.
  
  60% of gaining $5,000 and 40% of gaining $0
- B.
  
  70% of gaining $4,500 and 30% of gaining $0
- C.
  
  80% of gaining $4,000 and 20% of gaining $0
- D.
  
  90% of gaining $3,500 and 10% of gaining $0
Correct Answer
C. 80% of gaining $4,000 and 20% of gaining $0

Explanation
C. The correct solution is 80% of gaining $4,000 and 20% of gaining $0. The expected value is 0.80(40) =$3,200. See Lesson: Statistics & Probability: The Rules of Probability.

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50.

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

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Tasc Math Exam 3

Solve the equation for the unknown. 3(x + 4) - 1 = 2(x + 3) - 2

The temperature on Monday was -7°F, and it increased by 18°F by Tuesday afternoon. What is the temperature in F° on Tuesday afternoon?

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

Which decimal is the least?

Which decimal is the greatest?

Solve the equation by any method. x2 + 17x + 20 = 0

Evaluate the expression. (3 x (4 + 9) ÷ 13 - 2) + 1

What is the number of symmetry lines for a regular hexagon?

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.

Which best describes the number of multiples of 10?

Multiply.

How many men does a company employ if it has 420 employees and 35% are women?

What is the difference between natural numbers and whole numbers?

The number 22 is what percent of 54?

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?

Identify the diameter of the circle.

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

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?

If a number has 3 and 5 as factors, which statement best describes that number?

A circle has an area of 240 square centimeters. Find the radius to the nearest tenth of a centimeter. Use 3.14 for π.

At the grocery store, a researcher asks random people about the number of text messages they send daily. What type of study is this?

Solve the system of equations by graphing. y = -2x +3 y = 3

Convert 4 tons to pounds.

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

What is 762 ÷ 127

Solve the equation by the quadratic formula. 12x2 + x - 3 = 0

Solve the inequality for the unknown.

A research study aims to find the average age of all retail workers. A group asks all retail workers in Ohio their birth years. What is a name for this study?

Simplify. 56 x 5-3

A trapezoid has bases of 8 inches and 12 inches and a height of 6 inches. Find the area in square inches.

A mixture for a cake has various parts. Select the correct circle graph for the data.

The dot plot shows the results of rolling a dice for a game. Which statement is true for the dot plot?

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 bucket contains 4 bottles of apple juice, 6 bottles of orange juice, 5 bottles of grape juice, and 10 bottles of water. What is the probability of NOT selecting a bottle of water?

Convert 6 meters to feet.

The top 5 leading scorers on a basketball team average 21.3, 19.8, 15.5, 13.9, and 12.4 points per game. What is the estimated average of these players?

What shape is used to measure the distance between two cities on a map?

A regular hexagonal pyramid has a base side length of 6 inches, an apothem of 3√3 inches, and a height of 15 inches. Find the volume in cubic inches.

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?

What is the sum of two negative numbers?

Benjamin buys of fabric at a store. How many total yards did he purchase?

Multiply. (2y2 - 1)(y2 - 3y + 5)

Solve the system of equations. x = -y - 7 -x +4y = 22

Given the coordinates for a rectangle (-4, -1), (-9, -1), (-9,-8), and (-4,-8), find the length of each side of the rectangle.

Apply the polynomial identity to rewrite x3 + 125.

Identify 1920 in 12-hour clock time.

Select the figure that is rotated 90° about the origin.

Which option results in the greatest gain on an investment?

Divide.

Solve the equation by any method. x² + 17x + 20 = 0

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

Solve the equation by the quadratic formula. 12x² + x - 3 = 0

Simplify. 5⁶ x 5^-3

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?

Multiply. (2y² - 1)(y² - 3y + 5)

Apply the polynomial identity to rewrite x³ + 125.