TASC Math Exam 3

1. Divide.

Explanation

2. 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.

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.

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.

3. Which decimal is the least?

0.786

0.876

0.687

0.768

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

See Lesson: Decimals and Fractions.

Explanation

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

See Lesson: Decimals and Fractions.

4. What is 762 ÷ 127

4

6

8

9

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.

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.

5. Identify 1920 in 12-hour clock time.

6:20 p.m.

7:20 p.m.

6:20 a.m.

7:20 a.m.

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.

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.

6. Identify the diameter of the circle.

Explanation

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

Explanation

8. 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?

15

16

17

18

Explanation

9. Simplify. 5⁶ x 5^-3

5

15

125

625

Explanation

10. The number 22 is what percent of 54?

22%

29%

41%

76%

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

Explanation

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

11. Multiply.

1

2

3

4

Explanation

12. Which decimal is the greatest?

4.04

4.404

4.44

4.044

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.

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.

13. Convert 6 meters to feet.

1.52 feet

1.72 feet

18.68 feet

19.68 feet

Explanation

14. 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?

-25

-11

11

25

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

Explanation

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

15. What is the sum of two negative numbers?

Negative number

Positive number

Zero

Not enough information

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.

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.

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

Explanation

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

2 units and 3 units

2 units and 7 units

5 units and 3 units

5 units and 7 units

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.

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.

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

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

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.

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

Census

Survey

Experiment

Observational study

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

Explanation

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

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

35

147

273

420

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.

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.

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

-7

-2

2

7

Explanation

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

-2

0

2

5

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.

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.

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

2

4

6

8

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.

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.

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

22

22.25

22.5

22.75

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.

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.

25. Multiply. (2y² - 1)(y² - 3y + 5)

2y4 - 6y3 + 10y2 + 3y - 5

2y4 - 6y3 + 9y2 + 3y - 5

2y4 - 6y3 + 11y2 + 3y - 5

2y4 - 6y3 + 8y2 + 3y - 5

Explanation

26. Which best describes the number of multiples of 10?

1

10

100

An unlimited number

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.

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.

27. 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?

Explanation

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

18

20

60

72

Explanation

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

8.7

15.5

17.4

38.2

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

Explanation

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

30. Which option results in the greatest gain on an investment?

60% of gaining $5,000 and 40% of gaining $0

70% of gaining $4,500 and 30% of gaining $0

80% of gaining $4,000 and 20% of gaining $0

90% of gaining $3,500 and 10% of gaining $0

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.

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.

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

There were 60 turns in the game.

More than half of the turns were 3 or less.

1 and 6 occurred the same number of times.

The difference between the lowest and highest frequency is 3.

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.

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.

32. 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?

Census

Survey

Experiment

Observational Study

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

Explanation

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

33. What is the difference between natural numbers and whole numbers?

They are the same.

The whole numbers include zero, but the natural numbers exclude zero.

The natural numbers only go to 10, but the whole numbers have no limit.

The whole numbers include negative numbers, but the natural numbers do not.

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.

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.

34. 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

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.

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.

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

A ray

A line

A point

A line segment

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.

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.

36. Solve the inequality for the unknown.

Explanation

37. Convert 4 tons to pounds.

2,000 pounds

4,000 pounds

8,000 pounds

10,000 pounds

C. The correct solution is 8,000 pounds.

See Lesson: Standards of Measure.

Explanation

C. The correct solution is 8,000 pounds.

See Lesson: Standards of Measure.

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

-0.46 and -0.54

0.46 and -0.54

-0.46 and 0.54

0.46 and 0.54

Explanation

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

(10, -3)

(-10, 3)

(5, 7)

(7, 5)

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

Explanation

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

40. 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?

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.

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.

41. 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.

296.0

874.4

1,113.9

1,748.9

Explanation

42. 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?

Explanation

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

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

Explanation

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

44. Apply the polynomial identity to rewrite x³ + 125.

(x + 5)(x2 - 5x + 25)

(x - 5)(x2 - 10x + 25)

(x + 5)(x2 + 10x + 25)

(x - 5)(x2 + 10x + 25)

Explanation

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

The number is 15.

The number is prime.

The number has 15 as a factor.

The number has only two prime factors.

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.

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.

46. 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.

168

200

234

268

Explanation

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

-15.73 and -1.27

15.73 and -1.27

-15.73 and 1.27

15.73 and 1.27

Explanation

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

-6, -9

-6, 9

6, -9

6, 9

Explanation

49. 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.

108√3

216√3

512√3

1024√3

Explanation

50. The error on one manufacturing machine is 2 m 10^-4, and the error on a second machine is 8 m 10^-5. How many times larger is the error on the first machine?

1

2

3

4

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.

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.

Tasc Math Exam 3

1. Divide.

2.

What first name or nickname would you like us to use?

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

3. Which decimal is the least?

4. What is 762 ÷ 127

5. Identify 1920 in 12-hour clock time.

6. Identify the diameter of the circle.

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

8. 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?

9. Simplify. 56 x 5-3

10. The number 22 is what percent of 54?

11. Multiply.

12. Which decimal is the greatest?

13. Convert 6 meters to feet.

14. 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?

15. What is the sum of two negative numbers?

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

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

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

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

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

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

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

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

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

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

26. Which best describes the number of multiples of 10?

27. 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?

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

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

30. Which option results in the greatest gain on an investment?

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

32. 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?

33. What is the difference between natural numbers and whole numbers?

34. 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.

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

36. Solve the inequality for the unknown.

37. Convert 4 tons to pounds.

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

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

40. 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?

41. 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.

42. 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?

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

44. Apply the polynomial identity to rewrite x3 + 125.

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

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

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

49. 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.

50. The error on one manufacturing machine is 2 m 10-4, and the error on a second machine is 8 m 10-5. How many times larger is the error on the first machine?

9. Simplify. 5⁶ x 5^-3

25. Multiply. (2y² - 1)(y² - 3y + 5)

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

44. Apply the polynomial identity to rewrite x³ + 125.

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

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

50. The error on one manufacturing machine is 2 m 10^-4, and the error on a second machine is 8 m 10^-5. How many times larger is the error on the first machine?