ACT Math Exam 1 (In Book)

1. A school wants to know the daily attendance of all classes. What data would be good for a census?

Attendance on Fridays

Attendance every day

Attendance for math classes

Attendance after holiday breaks

B. The correct solution is attendance every day because data is collected from every class every day. See Lesson: Statistical Measures.

Explanation

B. The correct solution is attendance every day because data is collected from every class every day. See Lesson: Statistical Measures.

2. 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.

3. Change 0.375 to a fraction. Simplify completely.

Explanation

4. The data below shows the number of minutes available to eat breakfast for a group of employees. 10, 20, 40, 30, 50, 60, 50, 40, 30, 20, 40, 30, 10, 20, 30, 50, 40, 10, 10, 20, 30, 40, 20, 50, 40, 30 Select a dot plot for the data.

A. The correct solution is A. There are 4 employees who have 10 minutes and 50 minutes, 5 employees who have 20 minutes, 6 employees who have 30 minutes and 40 minutes, and 1 employee who has 60 minutes. See Lesson: Interpreting Categorical and Quantitative Data.

Explanation

A. The correct solution is A. There are 4 employees who have 10 minutes and 50 minutes, 5 employees who have 20 minutes, 6 employees who have 30 minutes and 40 minutes, and 1 employee who has 60 minutes. See Lesson: Interpreting Categorical and Quantitative Data.

5. 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.

6. Solve the equation for the unknown, $\frac {c} {-4}\, =\, -12.$

-16

-8

3

48

D. The correct solution is 48 because both sides of the equation are multiplied by –4. See Lesson: Equations with One Variable.

Explanation

D. The correct solution is 48 because both sides of the equation are multiplied by –4. See Lesson: Equations with One Variable.

7. Multiply. (5x - 3)(5x + 3)

25x2 - 9

25x2 + 9

25x2 + 30x - 9

25x2 + 30x + 9

Explanation

8. Change the following fraction to a decimal and simplify completely.

Explanation

9. 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.

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. Evaluate the expression. 15 x (-15)

-225

-30

-1

0

A. When multiplying signed numbers, remember that the product of a negative and a positive is negative. Other than the sign, the process is the same as multiplying whole numbers. See Lesson: Basic Multiplication and Division.

Explanation

A. When multiplying signed numbers, remember that the product of a negative and a positive is negative. Other than the sign, the process is the same as multiplying whole numbers. See Lesson: Basic Multiplication and Division.

12. Identify 3:00 p.m. in military time.

0300

0600

1200

1500

D. The correct solution is 1500. Add 1200 to the time, 1200 + 300 = 1500. See Lesson: Standards of Measure.

Explanation

D. The correct solution is 1500. Add 1200 to the time, 1200 + 300 = 1500. See Lesson: Standards of Measure.

13. Multiply.

1

2

3

4

Explanation

14. A circular dinner plate has a diameter of 13 inches. A ring is placed along the edge of the plate. Find the circumference of the ring in inches. Use 3.14 for π.

31.4

40.82

62.8

81.64

B. The correct solution is 40.82 because C = πd ≈ 3.14(13) ≈ 40.82 inches. See Lesson: Circles.

Explanation

B. The correct solution is 40.82 because C = πd ≈ 3.14(13) ≈ 40.82 inches. See Lesson: Circles.

15.

C. The two rays intersect at point D. See Lesson: Congruence.

Explanation

C. The two rays intersect at point D. See Lesson: Congruence.

16. The histogram below shows the amount a family spent on groceries during the year. Which statement is true for the histogram?

The lowest frequency is between $80 and $110.

The highest frequency is between $140 and $170.

More than half of the amount spent is greater than $140.

More than half of the amount spent is between $110 and $170.

D. The correct solution is more than half of the amount spent is between $110 and $170. There are 14 weeks where the amount spent is between $110 and $140 and 13 weeks where the amount spent is between $140 and $170. This is 27 weeks, which is more than half the data set. See Lesson: Interpreting Categorical and Quantitative Data.

Explanation

D. The correct solution is more than half of the amount spent is between $110 and $170. There are 14 weeks where the amount spent is between $110 and $140 and 13 weeks where the amount spent is between $140 and $170. This is 27 weeks, which is more than half the data set. See Lesson: Interpreting Categorical and Quantitative Data.

17. Multiply.

Explanation

18. Solve the inequality for the unknown, 3(x + 1) + 2(x+1) > 5 (3 -x) + 4(x +2).

X > 0

X > 1

X > 2

X > 3

D. The correct solution is x > 3.

3x + 3 + 2x +2 > 15 - 5x + 4x + 8 Apply the distributive property.

5x + 5 > -- x + 23 Combine like terms on both sides of the inequality.

6x + 5 > 23 Add x to both sides of the inequality.

6x > 18 Subtract 7 from both sides of the inequality.

x > 3 Divide both sides of the inequality by 6.

See Lesson: Equations with One Variable.

Explanation

D. The correct solution is x > 3.

3x + 3 + 2x +2 > 15 - 5x + 4x + 8 Apply the distributive property.

5x + 5 > -- x + 23 Combine like terms on both sides of the inequality.

6x + 5 > 23 Add x to both sides of the inequality.

6x > 18 Subtract 7 from both sides of the inequality.

x > 3 Divide both sides of the inequality by 6.

See Lesson: Equations with One Variable.

19. Identify 1435 in 12-hour clock time.

12:35 a.m.

2:35 a.m.

12:35 p.m.

2:35 p.m.

D. The correct solution is 2:35 p.m. Subtract 1200 from the time, 1435-1200 = 2: 35 p.m. See Lesson: Standards of Measure.

Explanation

D. The correct solution is 2:35 p.m. Subtract 1200 from the time, 1435-1200 = 2: 35 p.m. See Lesson: Standards of Measure.

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

(4, 8)

(4, -8)

(-4, 8)

(-4, -8)

Explanation

21. Solve the system of equations. -2x + 2y = 28 3x + y = -22

(9, 5)

(-9, -5)

(9, -5)

(-9, 5)

Explanation

22. A survey group wants to know the percentage of voters in a town who favor building a new shopping center. What is the survey group's population?

All eligible voters in the town

All people who live in the town

All interviewed people in the town

All voters 35 years and older in the town

A. The correct solution is all eligible voters in the town because this is the population for the entire survey. See Lesson: Statistical Measures.

Explanation

A. The correct solution is all eligible voters in the town because this is the population for the entire survey. See Lesson: Statistical Measures.

23. There is an election at a school where 4 candidates out of 10 will be elected. Which object and results are the most appropriate for a simulation?

Toss a coin

Ten-sided number cube and use multiples of 2

Eight-section spinner and use the odd numbers

Throw two six-sided number cubes and use the results of 1 and 6

B. The correct solution is ten-sided number cube and use multiples of 2 because there are 4 results out of 10 that would match the probability of the actual event. See Lesson: Statistical Measures.

Explanation

B. The correct solution is ten-sided number cube and use multiples of 2 because there are 4 results out of 10 that would match the probability of the actual event. See Lesson: Statistical Measures.

24. Write as a percent.

15%

20%

25%

30%

B. The correct answer is 20% because 1/5 as a percent is 0.2 × 100 = 20%. See Lesson: Decimals and Fractions.

Explanation

B. The correct answer is 20% because 1/5 as a percent is 0.2 × 100 = 20%. See Lesson: Decimals and Fractions.

25. Find the median for the data set 34, 31, 37, 35, 38, 33, 39, 32, 36, 35, 37, and 33.

34

35

36

37

B. The correct solution is 35. The data set in order is 31, 32, 33, 33, 34, 35, 35, 36, 37, 37, 38, 39, and the middle numbers are both 35. Therefore, the median is 35. See Lesson: Interpreting Graphics.

Explanation

B. The correct solution is 35. The data set in order is 31, 32, 33, 33, 34, 35, 35, 36, 37, 37, 38, 39, and the middle numbers are both 35. Therefore, the median is 35. See Lesson: Interpreting Graphics.

26. Solve. x³ = -216

-6

-4

4

6

A. The correct solution is -6 because the cube root of -216 is -6. See Lesson: Powers, Exponents, Roots and Radicals.

Explanation

A. The correct solution is -6 because the cube root of -216 is -6. See Lesson: Powers, Exponents, Roots and Radicals.

27. In a game, positive and negative points can be scored. For 10 turns, the point total is - 5, + 4, - 7, - 2, 0, +3, +5, - 6, - 4, +2. What is the average point total?

-2

-1

1

2

B. The correct solution is -1 because the sum of the scores is -10. The average is -10 divided by 10, or -1 point. See Lesson: Solving Real World Mathematical Problems.

Explanation

B. The correct solution is -1 because the sum of the scores is -10. The average is -10 divided by 10, or -1 point. See Lesson: Solving Real World Mathematical Problems.

28. In a game, positive and negative points can be scored. For 10 turns, the point total is - 5, + 4, - 7, - 2, 0, +3, +5, - 6, - 4, +2. What is the average point total?

-2

-1

1

2

B. The correct solution is -1 because the sum of the scores is -10. The average is -10 divided by 10, or -1 point. See Lesson: Solving Real World Mathematical Problems.

Explanation

B. The correct solution is -1 because the sum of the scores is -10. The average is -10 divided by 10, or -1 point. See Lesson: Solving Real World Mathematical Problems.

29. Perform the operation. (-3x² - 2xy + 4y²) + (5x² + 3xy -3y²)

2x2 - xy + y2

-2x2 - xy +y2

-2x2 + xy + y2

2x2 + xy + y2

D. The correct solution is 2x² + xy + y².

(-3x² - 2xy + 4y²) + (5x² + 3xy - 3y²)

= (-3x² + 5x²) + (-2xy + 3xy) + (4y² - 3y²)

= 2x² + xy +y²

See Lesson: Polynomials

Explanation

D. The correct solution is 2x² + xy + y².

(-3x² - 2xy + 4y²) + (5x² + 3xy - 3y²)

= (-3x² + 5x²) + (-2xy + 3xy) + (4y² - 3y²)

= 2x² + xy +y²

See Lesson: Polynomials

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

Explanation

31. 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.

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 rectangular pyramid has a length of 10 centimeters, a width of 11 inches, and a height of 12 inches. Find the volume in cubic inches.

220

440

660

880

Explanation

34. Find the range for the data set 34, 45, 27, 29, 36, 60, 52, 48, 41, 65, 44, 50, 64, 58, 47, and 31.

3

5

36

38

D. The correct solution is 38. The difference between the highest value of 65 and the lowest value of 27 is 38. See Lesson: Interpreting Graphics.

Explanation

D. The correct solution is 38. The difference between the highest value of 65 and the lowest value of 27 is 38. See Lesson: Interpreting Graphics.

35. Divide.

Explanation

36. If a letter is chosen at random from the word SUBSTITUTE, what is the probability that the letter chosen is "S" or "T"?

Explanation

37. Solve the equation for P. A= P + Prt

Explanation

38. A wedge of cheese is in the shape of a right triangular prism. The area of the base is 30 square inches. What is the height in inches of the cheese if the volume is 150 cubic inches?

2.5

5

7.5

10

B. The correct solution is 5. Substitute the values into the formula, 150 = 30h. Divide both sides of the equation by 30, h = 5 inches. See Lesson: Similarity, Right Triangles, and Trigonometry.

Explanation

B. The correct solution is 5. Substitute the values into the formula, 150 = 30h. Divide both sides of the equation by 30, h = 5 inches. See Lesson: Similarity, Right Triangles, and Trigonometry.

39. How many prime numbers are less than 20 but greater than 0?

8

9

10

11

A. Start by eliminating 1, which is not a prime number. The number 2 is the only even prime; the other even numbers are composite. Therefore, consider only odd numbers greater than 2. The prime numbers less than 20 but greater than 2 are 3, 5, 7, 11, 13, 17, and 19. The total is eight. See Lesson: Factors and Multiples.

Explanation

A. Start by eliminating 1, which is not a prime number. The number 2 is the only even prime; the other even numbers are composite. Therefore, consider only odd numbers greater than 2. The prime numbers less than 20 but greater than 2 are 3, 5, 7, 11, 13, 17, and 19. The total is eight. See Lesson: Factors and Multiples.

40. Find the height in centimeters of a cylinder with a volume of 800π cubic centimeters and a radius of 10 centimeters.

8

10

40

80

A. The correct solution is 8. Substitute the values into the formula, 800π = π10²h, and apply the exponent, 800π = π(100)h. Then, divide both sides of the equation by 100π, h = 8 centimeters. See Lesson: Measurement and Dimension.

Explanation

A. The correct solution is 8. Substitute the values into the formula, 800π = π10²h, and apply the exponent, 800π = π(100)h. Then, divide both sides of the equation by 100π, h = 8 centimeters. See Lesson: Measurement and Dimension.

41. Find the area in square centimeters of a circle with a diameter of 16 centimeters. Use 3.14 for π.

25.12

50.24

100.48

200.96

D. The correct solution is 200.96. The radius is 8 centimeters and A = πr² ≈ 3.1482 ≈ 3.14(64) ≈ 200.96 square centimeters. See Lesson: Circles.

Explanation

D. The correct solution is 200.96. The radius is 8 centimeters and A = πr² ≈ 3.1482 ≈ 3.14(64) ≈ 200.96 square centimeters. See Lesson: Circles.

42. Convert 15,000 grams to metric tons.

0.00015 metric ton

0.0015 metric ton

0.015 metric ton

0.15 metric ton

Explanation

43. Simplify.

Explanation

44. Solve the system of equations by graphing. 2x + y = 4 4x + y = 14

B. The correct graph has the two lines intersect at (5, -6). See Lesson: Equations with Two Variables.

Explanation

B. The correct graph has the two lines intersect at (5, -6). See Lesson: Equations with Two Variables.

45. 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.

46. A soccer team has scored 1, 1, 2, 2, 3, 3, 4, 4, 5 goals in its first 9 games. During the next game, the team scores 8 goals. Compare the mean and the standard deviation before and after the next game.

The mean and standard deviation increase.

The mean and standard deviation decrease.

The mean increases, but the standard deviation does not change.

The mean decreases, but the standard deviation does not change.

A. The correct solution is the mean and standard deviation increase. The game with 8 goals increases the mean from 2.8 to 3.3 and increases the standard deviation from 1.315 to 2.002. See Lesson: Interpreting Categorical and Quantitative Data.

Explanation

A. The correct solution is the mean and standard deviation increase. The game with 8 goals increases the mean from 2.8 to 3.3 and increases the standard deviation from 1.315 to 2.002. See Lesson: Interpreting Categorical and Quantitative Data.

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. A spinner contains numbers 1–20. What is the probability of spinning a multiple of 3 or a multiple of 5?

Explanation

49. 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.

50. Which option results in the largest loss on a product?

30% of gaining $2 million and 70% of losing $1 million

60% of gaining $1 million and 40% of losing $2 million

30% of gaining $3 million and 70% of losing $1.5 million

60% of gaining $1.5 million and 40% of losing $2.5 million

B. The correct solution is 60% of gaining $1 million and 40% of losing $2 million. The expected value is 0.60(1) + 0.4(-2) = 0.6 + (-0.8) = -0.2. See Lesson: Statistics & Probability: The Rules of Probability.

Explanation

B. The correct solution is 60% of gaining $1 million and 40% of losing $2 million. The expected value is 0.60(1) + 0.4(-2) = 0.6 + (-0.8) = -0.2. See Lesson: Statistics & Probability: The Rules of Probability.

51. A service group collects trash from area roadways for four straight weeks. The amount of trash they pick up is about . Estimate the total number of pounds collected.

70

71

72

73

D. The correct solution is 73. The estimated weights are 20, 15, 21, and 17 pounds, and the total weight is about 73 pounds. See Lesson: Solving Real World Mathematical Problems.

Explanation

D. The correct solution is 73. The estimated weights are 20, 15, 21, and 17 pounds, and the total weight is about 73 pounds. See Lesson: Solving Real World Mathematical Problems.

52. One athlete had a salary of about 3m10⁷ dollars per year and another athlete had a salary of about 2m10⁶ dollars per year. How many times larger is the salary of the first athlete?

2

5

10

15

D. The correct solution is 15 because the first athlete’s salary is about $30,000,000 and the second athlete’s salary is about $2,000,000. So, the first athlete’s salary is about 15 times larger. See Lesson: Powers, Exponents, Roots, and Radicals.

Explanation

D. The correct solution is 15 because the first athlete’s salary is about $30,000,000 and the second athlete’s salary is about $2,000,000. So, the first athlete’s salary is about 15 times larger. See Lesson: Powers, Exponents, Roots, and Radicals.

53. If 35% of a cattle herd is Ayrshire and the rest is Jersey, and it has 195 Jerseys, how many cattle are in the herd?

230

263

300

557

C. There are 300 cattle in the herd. Because the herd is only Ayrshire or Jersey, it is 65% Jersey. The equivalent decimals are 0.35 Ayrshire and 0.65 Jersey. Set up a proportion that relates these decimals to the number of cattle of each type:

One approach is to divide 195 by 0.65 to get 300, then multiply by 0.35 to get the number of Ayrshires: 105. Add 195 and 105 to get the total number of cattle in the herd. See Lesson: Ratios, Proportions, and Percentages.

Explanation

C. There are 300 cattle in the herd. Because the herd is only Ayrshire or Jersey, it is 65% Jersey. The equivalent decimals are 0.35 Ayrshire and 0.65 Jersey. Set up a proportion that relates these decimals to the number of cattle of each type:

One approach is to divide 195 by 0.65 to get 300, then multiply by 0.35 to get the number of Ayrshires: 105. Add 195 and 105 to get the total number of cattle in the herd. See Lesson: Ratios, Proportions, and Percentages.

54. Solve the equation by factoring. x² - 5x - 50 = 0

-10, -5

-10, 5

10, -5

10, 5

Explanation

55. ⌂JKL 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.

56. Solve the equation by completing the square. x² - 2x - 37 = 0

-1 ± √37

1 ± √37

-1 ± √38

1 ± √38

Explanation

57. 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.

58. How many whole numbers are less than 3 but greater than –3?

2

3

4

5

B. The correct solution is 3. The whole numbers include 0, 1, 2, 3,…. All whole numbers are greater than –3, but only 0, 1, and 2 are less than 3. See Lesson: Basic Addition and Subtraction.

Explanation

B. The correct solution is 3. The whole numbers include 0, 1, 2, 3,…. All whole numbers are greater than –3, but only 0, 1, and 2 are less than 3. See Lesson: Basic Addition and Subtraction.

59. A circle has an area of 12 square feet. Find the diameter to the nearest tenth of a foot. Use 3.14 for π.

1.0

2.0

3.0

4.0

D. The correct solution is 4.0 because A = πr²; 12 = 3.14r²; 3.82 = r²; r ≈ 2.0. The diameter is twice the radius, or about 4.0 feet. See Lesson: Circles.

Explanation

D. The correct solution is 4.0 because A = πr²; 12 = 3.14r²; 3.82 = r²; r ≈ 2.0. The diameter is twice the radius, or about 4.0 feet. See Lesson: Circles.

60. A regular hexagon has a side length of 5 inches and an apothem of 2 inches. Find the area in square inches.

30

40

50

60

A. The correct solution is 30. Substitute the values into the formula and simplify using the order of operations, A = ½ap = ½(2)(6(5)) = 30 square inches. See Lesson: Similarity, Right Triangles, and Trigonometry.

Explanation

A. The correct solution is 30. Substitute the values into the formula and simplify using the order of operations, A = ½ap = ½(2)(6(5)) = 30 square inches. See Lesson: Similarity, Right Triangles, and Trigonometry.

ACT Math Exam 1 (In Book)

1. A school wants to know the daily attendance of all classes. What data would be good for a census?

2.

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

2. Evaluate the expression 26 ÷ 9.

3. Change 0.375 to a fraction. Simplify completely.

4. The data below shows the number of minutes available to eat breakfast for a group of employees. 10, 20, 40, 30, 50, 60, 50, 40, 30, 20, 40, 30, 10, 20, 30, 50, 40, 10, 10, 20, 30, 40, 20, 50, 40, 30 Select a dot plot for the data.

5. Which procedure is impossible?

6. Solve the equation for the unknown,

7. Multiply. (5x - 3)(5x + 3)

8. Change the following fraction to a decimal and simplify completely.

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

10. The number 22 is what percent of 54?

11. Evaluate the expression. 15 x (-15)

12. Identify 3:00 p.m. in military time.

13. Multiply.

14. A circular dinner plate has a diameter of 13 inches. A ring is placed along the edge of the plate. Find the circumference of the ring in inches. Use 3.14 for π.

15.

16. The histogram below shows the amount a family spent on groceries during the year. Which statement is true for the histogram?

17. Multiply.

18. Solve the inequality for the unknown, 3(x + 1) + 2(x+1) > 5 (3 -x) + 4(x +2).

19. Identify 1435 in 12-hour clock time.

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

21. Solve the system of equations. -2x + 2y = 28 3x + y = -22

22. A survey group wants to know the percentage of voters in a town who favor building a new shopping center. What is the survey group's population?

23. There is an election at a school where 4 candidates out of 10 will be elected. Which object and results are the most appropriate for a simulation?

24. Write as a percent.

25. Find the median for the data set 34, 31, 37, 35, 38, 33, 39, 32, 36, 35, 37, and 33.

26. Solve. x3 = -216

27. In a game, positive and negative points can be scored. For 10 turns, the point total is - 5, + 4, - 7, - 2, 0, +3, +5, - 6, - 4, +2. What is the average point total?

28. In a game, positive and negative points can be scored. For 10 turns, the point total is - 5, + 4, - 7, - 2, 0, +3, +5, - 6, - 4, +2. What is the average point total?

29. Perform the operation. (-3x2 - 2xy + 4y2) + (5x2 + 3xy -3y2)

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

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

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

33. A rectangular pyramid has a length of 10 centimeters, a width of 11 inches, and a height of 12 inches. Find the volume in cubic inches.

34. Find the range for the data set 34, 45, 27, 29, 36, 60, 52, 48, 41, 65, 44, 50, 64, 58, 47, and 31.

35. Divide.

36. If a letter is chosen at random from the word SUBSTITUTE, what is the probability that the letter chosen is "S" or "T"?

37. Solve the equation for P. A= P + Prt

38. A wedge of cheese is in the shape of a right triangular prism. The area of the base is 30 square inches. What is the height in inches of the cheese if the volume is 150 cubic inches?

39. How many prime numbers are less than 20 but greater than 0?

40. Find the height in centimeters of a cylinder with a volume of 800π cubic centimeters and a radius of 10 centimeters.

41. Find the area in square centimeters of a circle with a diameter of 16 centimeters. Use 3.14 for π.

42. Convert 15,000 grams to metric tons.

43. Simplify.

44. Solve the system of equations by graphing. 2x + y = 4 4x + y = 14

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

46. A soccer team has scored 1, 1, 2, 2, 3, 3, 4, 4, 5 goals in its first 9 games. During the next game, the team scores 8 goals. Compare the mean and the standard deviation before and after the next game.

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

48. A spinner contains numbers 1–20. What is the probability of spinning a multiple of 3 or a multiple of 5?

49. Which number is a multiple of 123?

50. Which option results in the largest loss on a product?

51. A service group collects trash from area roadways for four straight weeks. The amount of trash they pick up is about . Estimate the total number of pounds collected.

52. One athlete had a salary of about 3m107 dollars per year and another athlete had a salary of about 2m106 dollars per year. How many times larger is the salary of the first athlete?

53. If 35% of a cattle herd is Ayrshire and the rest is Jersey, and it has 195 Jerseys, how many cattle are in the herd?

54. Solve the equation by factoring. x2 - 5x - 50 = 0

55. ⌂JKL 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?

56. Solve the equation by completing the square. x2 - 2x - 37 = 0

57. 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?

58. How many whole numbers are less than 3 but greater than –3?

59. A circle has an area of 12 square feet. Find the diameter to the nearest tenth of a foot. Use 3.14 for π.

60. A regular hexagon has a side length of 5 inches and an apothem of 2 inches. Find the area in square inches.

6. Solve the equation for the unknown, $\frac {c} {-4}\, =\, -12.$

26. Solve. x³ = -216

29. Perform the operation. (-3x² - 2xy + 4y²) + (5x² + 3xy -3y²)

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

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

52. One athlete had a salary of about 3m10⁷ dollars per year and another athlete had a salary of about 2m10⁶ dollars per year. How many times larger is the salary of the first athlete?

54. Solve the equation by factoring. x² - 5x - 50 = 0

56. Solve the equation by completing the square. x² - 2x - 37 = 0