TASC Math Exam 4

1. What is 1,078 + 0?

1,078

1,079

2,156

None of the above

A. The correct solution is 1,078. Adding any number to 0 yields that number. On a number line, starting at a certain number and taking no steps in either direction yields the same number.

See Lesson: Basic Addition and Subtraction.

Explanation

A. The correct solution is 1,078. Adding any number to 0 yields that number. On a number line, starting at a certain number and taking no steps in either direction yields the same number.

See Lesson: Basic Addition and Subtraction.

2. Which expression yields a quotient with no remainder?

5 ÷ 5

26 ÷ 5

81 ÷ 40

365 ÷ 87

A. By inspection, 5 ÷ 5 = 1, so it has no remainder. Using the division algorithm on the other expressions produces a remainder. See Lesson: Basic Multiplication and Division.

Explanation

A. By inspection, 5 ÷ 5 = 1, so it has no remainder. Using the division algorithm on the other expressions produces a remainder. See Lesson: Basic Multiplication and Division.

3. Write 29% as a decimal.

29

2.9

0.29

0.029

C. The correct answer is 0.29 because 29% as a decimal is 29 ÷ 100 = 0.29. See Lesson: Decimals and Fractions.

Explanation

C. The correct answer is 0.29 because 29% as a decimal is 29 ÷ 100 = 0.29. See Lesson: Decimals and Fractions.

4. Solve the equation for the unknown, -6d = 36.

-216

-6

30

42

B. The correct solution is –6 because both sides of the equation are divided by –6.
See Lesson: Equations with One Variable.

Explanation

B. The correct solution is –6 because both sides of the equation are divided by –6.
See Lesson: Equations with One Variable.

5. Solve the system of equations. x + 2y = 10 x + y = 5

(5, 0)

(0, 5)

(-5, 0)

(0, -5)

Explanation

6. Solve x² = 225.

-5, 5

-10, 10

-15, 15

-20, 20

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.

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.

7. Solve the equation by the square root method. 2x² = 162

±8

±9

±10

±11

B. The correct solution is ±9.

See Lesson: Solving Quadratic Equations.

Explanation

B. The correct solution is ±9.

See Lesson: Solving Quadratic Equations.

8. Convert 1,000 fluid ounces to gallons.

7.8125 gallons

15.625 gallons

31.25 gallons

62.5 gallons

A. The correct solution is 7.8125 gallons.

See Lesson: Standards of Measure.

Explanation

A. The correct solution is 7.8125 gallons.

See Lesson: Standards of Measure.

9. Which math statement is true?

3 ÷ 1 = 0

0 ÷ 3 = 1

3 ÷ 0 = 3

None of the above

D. Division by 0 is undefined, and dividing a number by one yields that number. Also, 0 divided by any number is 0. See Lesson: Basic Multiplication and Division.

Explanation

D. Division by 0 is undefined, and dividing a number by one yields that number. Also, 0 divided by any number is 0. See Lesson: Basic Multiplication and Division.

10. The test scores in a class are 82, 83, 84, 84, 85, 86, 88, 89, 90. The last test is a score of 105. Compare the mean and median before and after the last test score is included.

The mean and median increase.

The mean and median decrease.

The mean increases, and the median does not change.

The mean decreases, and the median does not change.

A. The correct solution is the mean and median increase. The test score of 105 increases the mean from 85.67 to 87.6 and increases the median from 85 to 85.5. See Lesson: Interpreting Categorical and Quantitative Data.

Explanation

A. The correct solution is the mean and median increase. The test score of 105 increases the mean from 85.67 to 87.6 and increases the median from 85 to 85.5. See Lesson: Interpreting Categorical and Quantitative Data.

11. The table shows the weight of 100 laptops. Find the mean weight to the nearest hundredth of a pound.

3.79

4.09

4.39

4.69

C. The correct solution is 4.39 pounds. The sum of the weights is 3 × 35 + 4 × 24 + 5 × 19 + 6 × 11 + 7 × 11 = 105 + 96 + 95 + 66 + 77 = 439. The average weight is 439 divided by 100, or 4.39 pounds. See Lesson: Interpreting Graphics.

Explanation

C. The correct solution is 4.39 pounds. The sum of the weights is 3 × 35 + 4 × 24 + 5 × 19 + 6 × 11 + 7 × 11 = 105 + 96 + 95 + 66 + 77 = 439. The average weight is 439 divided by 100, or 4.39 pounds. See Lesson: Interpreting Graphics.

12. A cone has a diameter of 12 feet and a height of 5 feet. What is the volume in cubic feet? State the answer in terms of π.

60π

120π

180π

240π

Explanation

13. If the ratio of women to men in a certain industry is 5:4, how many people are in that industry?

9

20

900

Not enough information

D. The ratio 5:4 is the industry’s relative number of women to men. But the industry could have 10 women and 8 men, 100 women and 80 men, or any other breakdown whose ratio is 5:4. Therefore, the question provides too little information to answer. Had it provided the total number of people in the industry, it would have been possible to determine how many women and how many men are in the industry. See Lesson: Ratios, Proportions, and Percentages.

Explanation

D. The ratio 5:4 is the industry’s relative number of women to men. But the industry could have 10 women and 8 men, 100 women and 80 men, or any other breakdown whose ratio is 5:4. Therefore, the question provides too little information to answer. Had it provided the total number of people in the industry, it would have been possible to determine how many women and how many men are in the industry. See Lesson: Ratios, Proportions, and Percentages.

14. Draw a square with the coordinates (-3, 4), (-3, -2), (3, -2), (3, 4).

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.

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.

15. A county contains 25 villages, 12 towns, and 3 cities. There is an average of 6 stoplights in a village, 27 in a town, and 148 in a city. Estimate the total number of stoplights.

800

900

1,200

1,300

B. The correct solution is 900 because the expression for estimation is 25(6) + 10(30) + 150(3). The expression simplifies to 150 + 300 + 450 = 900 stoplights. See Lesson: Solving Real World Mathematical Problems.

Explanation

B. The correct solution is 900 because the expression for estimation is 25(6) + 10(30) + 150(3). The expression simplifies to 150 + 300 + 450 = 900 stoplights. See Lesson: Solving Real World Mathematical Problems.

16. Karida has a part-time job. She works 4.25 hours on Thursday and Friday and 6.5 hours on Saturday and Sunday. What is her hourly rate if her check is $268.75?

$8.50

$12.50

$14.50

$21.50

B. The correct solution is $12.50 because she worked a total of 4.25(2) + 6.5(2) = 8.5 + 13 = 21.5 hours. The hourly rate is 268.75 ÷ 21.50 = $12.50. See Lesson: Solving Real World Mathematical Problems.

Explanation

B. The correct solution is $12.50 because she worked a total of 4.25(2) + 6.5(2) = 8.5 + 13 = 21.5 hours. The hourly rate is 268.75 ÷ 21.50 = $12.50. See Lesson: Solving Real World Mathematical Problems.

17.

LM

PN

OJ

LP

A. The correct solution is LM because L and M are on the circle. See Lesson: Circles.

Explanation

A. The correct solution is LM because L and M are on the circle. See Lesson: Circles.

18. Write 1.5 as a percent.

0.15%

1.5%

15%

150%

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

Explanation

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

19. A tree has a circumference of 340 centimeters. Find the diameter to the nearest tenth of a centimeter. Use 3.14 for π.

27.1

54.1

81.4

108.3

D. The correct solution is 108.3 because C = πd; 340 = 3.14d; d ≈ 108.3 centimeters. See Lesson: Circles.

Explanation

D. The correct solution is 108.3 because C = πd; 340 = 3.14d; d ≈ 108.3 centimeters. See Lesson: Circles.

20. A tire has a circumference of 70 inches. Find the radius to the nearest tenth of an inch. Use 3.14 for π.

11.1

22.2

33.3

44.4

A. The correct solution is 11.1 because C = 2πr; 70 = 23.14r; 70 = 6.28r; r ≈ 11.1 inches. See Lesson: Circles.

Explanation

A. The correct solution is 11.1 because C = 2πr; 70 = 23.14r; 70 = 6.28r; r ≈ 11.1 inches. See Lesson: Circles.

21. ΔJKL has points J (5, -3), K (-2,4), and L (3, 0). After a transformation the points are J' (5, 3), K' (-2, -4), and L' (3, 0). What is the transformation between the points?

Reflection across the x-axis

Reflection across the y-axis

Reflection across the y = x

Reflection across the y = –x

A. The correct solution is a reflection across the x-axis because the points (x, y) become (x, –y). See Lesson: Congruence.

Explanation

A. The correct solution is a reflection across the x-axis because the points (x, y) become (x, –y). See Lesson: Congruence.

22. Multiply.

Explanation

23. Divide.

Explanation

24. A sphere has a volume of 972π cubic millimeters. Find the radius in millimeters.

3

9

27

81

B. The correct solution is 9 millimeters. Substitute the values into the formula, , then multiply by the reciprocal, 729 = r³, and apply the cube root, r = 9 millimeters. See Lesson: Measurement and Dimension.

Explanation

B. The correct solution is 9 millimeters. Substitute the values into the formula, , then multiply by the reciprocal, 729 = r³, and apply the cube root, r = 9 millimeters. See Lesson: Measurement and Dimension.

25.

Explanation

26. The original height of a plant is 1.75 inches. The plant grows an average of 1.08 inches each month for 6 months. What is the new height of the plant in inches?

7.13

7.23

8.13

8.23

D. The correct solution is 8.23 because 1.75 + 1.08(6) = 1.75 + 6.48 = 8.23 inches. See Lesson: Solving Real World Mathematical Problems.

Explanation

D. The correct solution is 8.23 because 1.75 + 1.08(6) = 1.75 + 6.48 = 8.23 inches. See Lesson: Solving Real World Mathematical Problems.

27. Convert 0.5 kiloliter to milliliters.

50,000 milliliters

500,000 milliliters

5,000,000 milliliters

50,000,000 milliliters

B. The correct solution is 500,000 milliliters.

See Lesson: Standards of Measure.

Explanation

B. The correct solution is 500,000 milliliters.

See Lesson: Standards of Measure.

28. A teacher wants to know if seat location affects test scores. What data needs to be collected for an experiment?

The teacher should collect data on one seat for every class.

The teacher should collect data on one student for every class.

The teacher should collect data on a random sample of students for the final exam.

The teacher should collect data on a random sample of students of test scores and seat location.

D. The correct solution is that the teacher should collect data on a random sample of students of test scores and seat location because there are specific groups based on seat location. See Lesson: Statistical Measures.

Explanation

D. The correct solution is that the teacher should collect data on a random sample of students of test scores and seat location because there are specific groups based on seat location. See Lesson: Statistical Measures.

29. Solve the inequality for the unknown. 2(3x - 1 ) +5 ≥ 3x - 4 - 4x

X ≥ -7

X ≥ -4

X ≥ -1

X ≥ 0

Explanation

30. If a truck's initial speed is 60 mph and its final speed is 100 mph, what is its percent change in speed

17%

33%

40%

67%

Explanation

31. 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 union of the first 10 cards.

Green cards

Cards 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Green cards and Red cards; 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Green cards 1, 2, 3, 4, 5; Red cards 6, 7, 8, 9, 10

D. The correct solution is Green cards 1, 2, 3, 4, 5; Red cards 6, 7, 8, 9, 10. The union is listing out all options of the sample space. See Lesson: Statistics & Probability: The Rules of Probability.

Explanation

D. The correct solution is Green cards 1, 2, 3, 4, 5; Red cards 6, 7, 8, 9, 10. The union is listing out all options of the sample space. See Lesson: Statistics & Probability: The Rules of Probability.

32. Select the statement that is true for the angles.

Points X and Y are vertices of angles.

Points X and U are vertices of angles.

Points W and Y are vertices of angles.

Points W and U are vertices of angles.

B. The correct solution is points X and U are vertices of angles because these points are the intersection of two rays. See Lesson: Congruence.

Explanation

B. The correct solution is points X and U are vertices of angles because these points are the intersection of two rays. See Lesson: Congruence.

33. Solve the system of equations by graphing. 6x + 5y = -7 2x - 4y = -8

A. The correct graph has the two lines intersect at (-2, 1). See Lesson: Equations with Two Variables.

Explanation

A. The correct graph has the two lines intersect at (-2, 1). See Lesson: Equations with Two Variables.

34. If x is divisible by y, which statement best relates x and y?

Y is a factor of x.

X is a multiple of y.

X and y are whole numbers.

All of the above.

D. Each statement about x and y is true. By definition, if one number is a factor of another, both are whole numbers. See Lesson: Factors and Multiples.

Explanation

D. Each statement about x and y is true. By definition, if one number is a factor of another, both are whole numbers. See Lesson: Factors and Multiples.

35. The dot plot shows the number of hours a group of students volunteered. How are the mean and median affected when removing the outliers?

The mean and median decrease.

The mean decreases, but the median increases.

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 by removal of the outlier values, but the median is still 20 hours. 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 by removal of the outlier values, but the median is still 20 hours. See Lesson: Interpreting Categorical and Quantitative Data.

36. Select the figure that is translated (x – 4, y + 4).

D. The correct solution is D. The translation for the points is (x – 4, y + 4). The points of the original square, (–1, 5), (–1, –1), (5, –1) and (5, 5), become (–5, 9), (–5, 3), (1, 3) and (1, 9). See Lesson: Congruence.

Explanation

D. The correct solution is D. The translation for the points is (x – 4, y + 4). The points of the original square, (–1, 5), (–1, –1), (5, –1) and (5, 5), become (–5, 9), (–5, 3), (1, 3) and (1, 9). See Lesson: Congruence.

37. A college class had one group use a traditional textbook and another group use an online textbook. The attendance for the class was compared. Determine the independent variable.

Class attendance

Type of textbook

Grade for the class

Online version of the textbook

B. The correct solution is the type of textbook because the other variables do not change the type of textbook. See Lesson: Interpreting Graphics.

Explanation

B. The correct solution is the type of textbook because the other variables do not change the type of textbook. See Lesson: Interpreting Graphics.

38. Perform the operation. (-2x² + 8x) + (3x³ - 4x² + 1)

3x3 - 6x2 + 8x + 1

3x3 - 2x2 + 8x + 1

3x3 + 6x2 + 8x + 1

3x3 + 2x2 + 8x + 1

Explanation

39.

Explanation

40. Identify the sampling technique that is a convenience sample.

A group of students selected by a principal

A group of students selected by their grade point average

A group of students selected by their after-school availability

A group of students selected by a random number generator

C. The correct solution is a group of students selected by their after-school availability because the students are only available after school. See Lesson: Statistical Measures.

Explanation

C. The correct solution is a group of students selected by their after-school availability because the students are only available after school. See Lesson: Statistical Measures.

41. There are 12 boys' and 14 girls' names in a hat. What is the probability of selecting a boy's name twice in a row without replacement?

See Lesson: Statistics & Probability: The Rules of Probability.

Explanation

See Lesson: Statistics & Probability: The Rules of Probability.

42. The volume of a hemi-sphere is

cubic feet. What is the diameter in feet?

1

2

3

4

Explanation

43. Apply the polynomial identity to rewrite 27x³ - 8.

(3x - 2)(9x2 - 6x + 4)

(3x - 2)(9x2 + 6x + 4)

(3x - 2)(9x2 + 6x - 4)

(3x - 2)(9x2 - 6x - 4)

Explanation

44. An outdoor game board is 20 feet by 30 feet. One corner of the game board on the coordinate plane is (-10, -20). What could be a second coordinate of the game board?

(-20, -10)

(-10, 10)

(10, -10)

(-20, 10)

B. The correct solution is (-10, 10) because 30 can be added to the y-coordinate, -20+30=10. See Lesson: Similarity, Right Triangles, and Trigonometry.

Explanation

B. The correct solution is (-10, 10) because 30 can be added to the y-coordinate, -20+30=10. See Lesson: Similarity, Right Triangles, and Trigonometry.

45. Solve the equation by factoring. 6x² - 11x - 35 = 0

Explanation

46. Which statement is true?

A numeral is a symbol that represents a number.

A number is a symbol that represents a numeral.

Numerals and numbers are the same.

None of the above.

A. The correct solution is a numeral is a symbol that represents a number. Recall that numbers are abstract quantities, but a numeral is a symbol that represents a number.

Explanation

A. The correct solution is a numeral is a symbol that represents a number. Recall that numbers are abstract quantities, but a numeral is a symbol that represents a number.

47. Which number is a multiple of 123?

-123

1

247

359

A. Any product of a number and an integer is a multiple of that number. Since 123 x -1 is -123, one multiple of 123 is -123. See Lesson: Factors and Multiples.

Explanation

A. Any product of a number and an integer is a multiple of that number. Since 123 x -1 is -123, one multiple of 123 is -123. See Lesson: Factors and Multiples.

48. The mean of eight numbers is 71. The numbers in the data set are 72, 75, 64, 80, 79, and 68. What is the other number in the data set if the number is the mode of the set?

65

68

70

71

A. The correct solution is 65. The sum of the entire data set is 568, and the sum of the given items is 438. The difference between the sums is 130. Divide the result by 2 to get the missing value of 65. See Lesson: Interpreting Graphics.

Explanation

A. The correct solution is 65. The sum of the entire data set is 568, and the sum of the given items is 438. The difference between the sums is 130. Divide the result by 2 to get the missing value of 65. See Lesson: Interpreting Graphics.

49. At a school, the probability a student has a study hall is two-thirds. What object and results could be used for a simulation of 1,000 times?

A. Flipping a coin

Playing rock, paper, scissors and looking for rock

Using a four-sided spinner and spinning 1, 2, or 3

Throwing a six-sided number cube and looking for 1, 2, 3, or 4

D. The correct solution is throwing a six-sided number cube and looking for 1, 2, 3, or 4 because the dice has 4 out of 6, or two-thirds, options to match the probability of the event. See Lesson: Statistical Measures.

Explanation

D. The correct solution is throwing a six-sided number cube and looking for 1, 2, 3, or 4 because the dice has 4 out of 6, or two-thirds, options to match the probability of the event. See Lesson: Statistical Measures.

50. Solve the equation by the quadratic formula. 6x² - 4x - 3 = 0

-1.12 and -0.45

1.12 and -0.45

-1.12 and 0.45

1.12 and 0.45

Explanation

Tasc Math Exam 4