Free TASC Math Exam

1. The bar chart shows the number of boys and girls who participate in sports. What year had the most participants?

2013

2014

2016

2017

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

See Lesson: Interpreting Graphics.

Explanation

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

See Lesson: Interpreting Graphics.

2. Evaluate the expression 1,004 + 110.

2104

1411

1204

1114

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.

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.

3. Ron is training for a marathon. If he trains by running 57.5 miles every 5 days, then about how many miles will he run in 43 days?

120

300

480

60

C. The correct solution is 480 because by estimation Ron runs about 60(8) = 480 miles. See Lesson: Solving Real World Mathematical Problems.

Explanation

C. The correct solution is 480 because by estimation Ron runs about 60(8) = 480 miles. See Lesson: Solving Real World Mathematical Problems.

4. Evaluate the expression 26 ÷ 9.

2

2R8

3R1

35

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.

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.

5. A diver was at 125 feet below sea level. The diver dove down another 350 feet. Where was the diver located?

475 feet below sea level

225 feet below sea level

225 feet above sea level

475 feet above sea level

A. The correct solution is 475 feet below sea level because -125 - 350 = -475 feet. See Lesson: Solving Real World Mathematical Problems.

Explanation

A. The correct solution is 475 feet below sea level because -125 - 350 = -475 feet. See Lesson: Solving Real World Mathematical Problems.

6. The bar chart shows the number of items collected for a charity drive. What is the total number of items collected for the three highest classes?

500

510

520

530

B. The correct solution is 510 items because the three largest classes collected 180, 170, and 160 items.

See Lesson: Interpreting Graphics.

Explanation

B. The correct solution is 510 items because the three largest classes collected 180, 170, and 160 items.

See Lesson: Interpreting Graphics.

7. Which fraction is the greatest?

Explanation

8. Solve the system of equations. x - 5y = -21 3x + y = 33

(4, 1)

(1, 4)

(9, 6)

(6, 9)

Explanation

9. Solve. x³ = -216

-6

-4

4

6

Explanation

10. Which procedure is impossible?

Adding two negative numbers

Subtracting a negative number from zero

Adding two quantities with different units

Placing negative numbers on the number line

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.

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.

11. Find the area in square millimeters of a circle with a radius of 9 millimeters. Round to the nearest hundredth. Use 3.14 for π.

56.52

254.34

508.68

1,017.36

B. The correct solution is 254.34 because A=πr²≈ 3.1492 ≈ 3.14(81) ≈ 254.34 square millimeters. See Lesson: Circles.

Explanation

B. The correct solution is 254.34 because A=πr²≈ 3.1492 ≈ 3.14(81) ≈ 254.34 square millimeters. See Lesson: Circles.

12. The data below shows a class's quiz scores out of 20 points. 5, 5, 6, 7, 8, 8, 9, 10, 11, 12, 13, 14, 15, 15, 16, 18, 18, 19, 20, 20 Select a box plot for the data.

B. The correct response is B. The median value is 12.5, the first quartile value is 8, and the third quartile value is 17. The minimum is 5, and the maximum is 20. See Lesson: Interpreting Categorical and Quantitative Data.

Explanation

B. The correct response is B. The median value is 12.5, the first quartile value is 8, and the third quartile value is 17. The minimum is 5, and the maximum is 20. See Lesson: Interpreting Categorical and Quantitative Data.

13. Perform the operation. (-3x + 5xy - 6y) - (4x + 2xy - 5y)

-7x + 7xy - y

-7x + 7xy - 11y

-7x + 3xy - y

-7x + 3xy - 11y

C. The correct solution is -7x + 3xy - y. (-3x + 5xy -6y) - (4x +2xy - 5y) = (-3x +5xy - 6y) + (-4x -2xy + 5y) = (-3x - 4x) + (5xy - 2xy) + (-6y + 5y) = -7x + 3xy -y See Lesson: Polynomials.

Explanation

C. The correct solution is -7x + 3xy - y. (-3x + 5xy -6y) - (4x +2xy - 5y) = (-3x +5xy - 6y) + (-4x -2xy + 5y) = (-3x - 4x) + (5xy - 2xy) + (-6y + 5y) = -7x + 3xy -y See Lesson: Polynomials.

14. A surveyor asked students if they are attending school after high school. The students who responded "No" were excluded. What type of sampling is used?

Quota sampling

Volunteer sampling

Purposive sampling

Convenience sampling

C. The correct solution is purposive sampling because the surveyor chose the sample based on “Yes” responses. See Lesson: Statistical Measures.

Explanation

C. The correct solution is purposive sampling because the surveyor chose the sample based on “Yes” responses. See Lesson: Statistical Measures.

15. Solve the equation by any method. x² - 23x + 125 = 0

-8.81 and -14.2

8.81 and 14.2

8.81 and -14.2

-8.81 and 14.2

Explanation

16. Change 2.5 to a fraction. Simplify completely.

Explanation

17. Find the mean for the data set. 16, 18, 17, 15, 19, 14, 12, 11, 10, 16, 18, and 17.

14.25

15.25

16

17

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.

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.

18. A dime has a radius of 8.5 millimeters. Find the circumference in millimeters of the dime. Use 3.14 for π.

11.64

26.69

53.38

106.76

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

See Lesson: Circles.

Explanation

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

See Lesson: Circles.

19. Solve the equation by factoring. x² + 3x - 88 = 0.

-8, -11

-8, 11

8, -11

8, 11

Explanation

20. Which option is the greatest gain on a sale?

50% of gaining $8 million and 50% of gaining $7 million

60% of gaining $9 million and 40% of gaining $6 million

70% of gaining $10 million and 30% of gaining $5 million

80% of gaining $11 million and 20% of gaining $4 million

D. The correct solution is 80% of gaining $11 million and 20% of gaining $4 million. The expected value is 0.80(11) + 0.20(4) = 8.8 + 0.8 = $9.6 million. See Lesson: Statistics & Probability: The Rules of Probability.

Explanation

D. The correct solution is 80% of gaining $11 million and 20% of gaining $4 million. The expected value is 0.80(11) + 0.20(4) = 8.8 + 0.8 = $9.6 million. See Lesson: Statistics & Probability: The Rules of Probability.

21. 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?

The mean and median increase.

There is no effect on the mean or median.

The mean decreases, but the median does not change.

The median decreases, but the mean does not change.

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.

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.

22. What is the quotient of a number divided by itself?

-1

0

1

Not enough information

C. Since division yields a positive quotient when the signs of the dividend and divisor are the same, the answer must be positive. Pick any nonzero number: 231 ÷ 231, for example. The quotient is always 1. See Lesson: Basic Multiplication and Division.

Explanation

C. Since division yields a positive quotient when the signs of the dividend and divisor are the same, the answer must be positive. Pick any nonzero number: 231 ÷ 231, for example. The quotient is always 1. See Lesson: Basic Multiplication and Division.

23. Given the coordinates for a square (-3, -5), (-3, 4), (6, 4), and (6, 5), find the length of each side of the square.

3 unites

6 units

9 units

12 units

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.

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.

24. A half circle has an area of 45 square centimeters. Find the diameter to the nearest tenth of a centimeter. Use 3.14 for π.

2.7

5.4

10.8

16.2

C. The correct solution is 10.8 because A=12πr²; 45=(12)3.14r²; 45=1.57r²= 28.66 = r²; r≈5.4.The diameter is twice the radius, or about 10.8 centimeters. See Lesson: Circles.

Explanation

C. The correct solution is 10.8 because A=12πr²; 45=(12)3.14r²; 45=1.57r²= 28.66 = r²; r≈5.4.The diameter is twice the radius, or about 10.8 centimeters. See Lesson: Circles.

25. Multiply.

1

2

3

4

Explanation

26. Simplify.

Y4

X4y4

Explanation

27. Convert 9 meters to yards.

4.09 yards

8.23 yards

9.84 yards

12.28 yards

Explanation

28.

Explanation

29. Convert 0.75 kilograms to grams.

0.0075 grams

0.075 grams

75 grams

750 grams

Explanation

30. Apply the polynomial identity to rewrite x² - 100.

(x - 10)2

(x - 10)(x + 10)

(x + 10)2

X2 - 102

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.

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.

31. Multiply. (4y² + 3)(2y + 5)

8y3 + 10y2 + 16y +15

8y3 + 20y2 + 16y +15

8y3 + 10y2 + 6y +15

8y3 + 20y2 + 6y +15

Explanation

32. A house is located at (15,30). The next house is 100 meters away. What could be the coordinate of the second house?

(15,30)

(30,15)

(115,15)

(115,30)

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.

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.

33. 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.

12

38

50

76

See Lesson: Measurement and Dimension.

Explanation

See Lesson: Measurement and Dimension.

34. Siobhan walks 1.45 miles to school and then back home each day Monday through Friday. How many miles does she walk each week?

7.25

10.15

14.5

20.3

C. The correct solution is 14.5 because 1.45(10)=14.5 miles. See Lesson: Solving Real World Mathematical Problems.

Explanation

C. The correct solution is 14.5 because 1.45(10)=14.5 miles. See Lesson: Solving Real World Mathematical Problems.

35. In which of the following situations is probability sampling used?

Qualitative research

Studies with specific goals

Randomly selected samples

Studies with limited functions

C. The correct solution is randomly selected samples because random sampling techniques are used. See Lesson: Statistical Measures.

Explanation

C. The correct solution is randomly selected samples because random sampling techniques are used. See Lesson: Statistical Measures.

36. If the multiple of some positive number is prime, which statement about that positive number is true?

The positive number is prime.

The positive number is equal to 0.

The positive number is composite.

None of the above.

D. If the positive number is 1, then one of its multiples is 3—a prime number. Answer A is therefore false, as is answer C. If the positive number is 0, all of its multiples are 0. Therefore, it has no prime multiples, eliminating answer B. See Lesson: Factors and Multiples.

Explanation

D. If the positive number is 1, then one of its multiples is 3—a prime number. Answer A is therefore false, as is answer C. If the positive number is 0, all of its multiples are 0. Therefore, it has no prime multiples, eliminating answer B. See Lesson: Factors and Multiples.

37. Identify the coplanar points in the diagram.

Points S, T, U, and Y

Points X, V, S, and z

Points X, Y, U, and V

Points U, Y, Z, and T

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

Explanation

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

38. Divide.

Explanation

39. 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?

150

300

5,325

5,625

Explanation

40. Select the square with the correct lines of symmetry.

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.

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.

41. Solve the system of equations by graphing. y = 4x - 3 y = x

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

Explanation

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

42. Solve the equation for the unknown. 3x - 8 + 5 + 2x = 4x - x + 6

Explanation

43. Which proportion yields a number for the unknown that is different from the others?

D. The correct answer is D. Although solving each proportion is one approach, the easiest approach is to compare them as they are. The proportions in answers A and B yield the same number for the unknown because they keep the same numbers in either the numerators or the denominators. Answer C just reverses the order of the equation in answer A, which does not yield a different number for the unknown. Answer D flips one fraction without flipping the other, which changes the proportion. See Lesson: Ratios, Proportions, and Percentages.

Explanation

D. The correct answer is D. Although solving each proportion is one approach, the easiest approach is to compare them as they are. The proportions in answers A and B yield the same number for the unknown because they keep the same numbers in either the numerators or the denominators. Answer C just reverses the order of the equation in answer A, which does not yield a different number for the unknown. Answer D flips one fraction without flipping the other, which changes the proportion. See Lesson: Ratios, Proportions, and Percentages.

44. 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?

12:35

12:23

23:35

35:23

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.

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.

45. Solve the equation by completing the square. x² + 12x + 10 = 0

6 ± √26

-6 ± √26

6 ± √10

-6 ± √10

Explanation

46. In a deck of 20 number cards, cards 1–5 are green, cards 6–10 are red, cards 11–15 are yellow, and cards 16–20 are blue. Describe the complement of even cards.

Odd number cards

Even number cards

Green and red cards

Yellow and blue cards

A. The correct solution is odd number cards. The complement of even number cards is odd. See Lesson: Statistics & Probability: The Rules of Probability.

Explanation

A. The correct solution is odd number cards. The complement of even number cards is odd. See Lesson: Statistics & Probability: The Rules of Probability.

47. A sphere has a radius of 14 centimeters. Find the volume in cubic centimeters. Use 3.14 for π.

1,436

2,872

5,744

11,488

Explanation

48. What are the prime factors of 30?

5, 6

2, 3, 5

1, 3, 10

2, 3, 5, 6, 10, 15

B. Answers A, C, and D all contain composite numbers (6, 10, and 15). Therefore, answer B is correct. See Lesson: Factors and Multiples.

Explanation

B. Answers A, C, and D all contain composite numbers (6, 10, and 15). Therefore, answer B is correct. See Lesson: Factors and Multiples.

49. 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.

The standard deviation and interquartile range increase.

The standard deviation and interquartile range decrease.

The standard deviation increases, and the interquartile range decreases.

The standard deviation decreases, but the interquartile range increases.

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.

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.

50. Solve the system of equations. 2y + x = -20 y = -x - 12

(4, 8)

(4, -8)

(-4, 8)

(-4, -8)

Explanation

Free Tasc Math Exam