ACT Math Exam 3

1. Solve the system of equations by graphing.

C. The correct graph has the two lines intersect at (-9, -1). See Lesson: Equations with Two Variables.

Explanation

C. The correct graph has the two lines intersect at (-9, -1). See Lesson: Equations with Two Variables.

2. Apply the polynomial identity to rewrite x^²+ 20x + 100.

X2 + 100

(x + 10)2

(x2 + 10)2

(10x)2

B. The correct solution is (x + 10)^{^²}. The expression x^{^²}+ 20x + 100 is rewritten as (x + 10)^{^²} 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)^{^²}. The expression x^{^²}+ 20x + 100 is rewritten as (x + 10)^{^²} because the value of a is x and the value of b is 10. See Lesson: Polynomials.

3. 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.

4. Multiply. (4x + 5)(3x - 2)

12x2 - 7x + 10

12x2 + 7x + 10

12x2 + 7x - 10

12x2 - 7x - 10

C. The correct solution is 12x²+7x-10.

(4x + 5)(3x - 2) = 4x(3x - 2) + 5(3x-2) = 12x² - 8x + 15x - 10 = 12x² + 7x - 10

See Lesson: Polynomials.

Explanation

C. The correct solution is 12x²+7x-10.

(4x + 5)(3x - 2) = 4x(3x - 2) + 5(3x-2) = 12x² - 8x + 15x - 10 = 12x² + 7x - 10

See Lesson: Polynomials.

5.

9

18

36

72

Explanation

6.

Explanation

7. How many millimeters are in a measurement that is 4 centimeters, 3 meters, and 7 millimeters long? (Note that a centimeter is 10 millimeters and a meter is 1,000 millimeters.)

347

437

3,047

3,407

C. The correct solution is 3,047. Place the digits in base-10 format, using the number of meters in the thousands place, the number of centimeters in the tens place, and the number of millimeters in the ones place. The measurement is 3,047 millimeters long. See Lesson: Basic Addition and Subtraction.

Explanation

C. The correct solution is 3,047. Place the digits in base-10 format, using the number of meters in the thousands place, the number of centimeters in the tens place, and the number of millimeters in the ones place. The measurement is 3,047 millimeters long. See Lesson: Basic Addition and Subtraction.

8.

Explanation

9. Solve. x³ = 64

2

3

4

5

C. The correct solution is 4 because the cube root of 64 is 4. See Lesson: Powers, Exponents, Roots, and Radicals.

Explanation

C. The correct solution is 4 because the cube root of 64 is 4. See Lesson: Powers, Exponents, Roots, and Radicals.

10. If 1 out of every 250 people will contract a certain disease, what percent of people will contract it?

0.004%

0.4%

2.5%

25%

B. If 1 out of every 250 contract a disease, the fraction of people is 1/250, which is equal to 0.004. Multiply by 100% to get 0.4%. See Lesson: Ratios, Proportions, and Percentages.

Explanation

B. If 1 out of every 250 contract a disease, the fraction of people is 1/250, which is equal to 0.004. Multiply by 100% to get 0.4%. See Lesson: Ratios, Proportions, and Percentages.

11. The table shows the speed in miles per hour of different roller coasters at an amusement park. Select the correct line graph for this data.

C. The correct solution is C. The line graph has the correct values for each roller coaster. See Lesson: Interpreting Graphics.

Explanation

C. The correct solution is C. The line graph has the correct values for each roller coaster. See Lesson: Interpreting Graphics.

12. 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.

13. 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.

14. 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.

15. 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.

16. Solve the system of equations. x + 3y = 34 -3x + y = -12

(-7, -9)

(-9, -7)

(7, 9)

(9, 7)

Explanation

17. Solve the equation for the unknown, 6x - 12 = -24.

-4

-2

2

4

B. The correct solution is –2.

6x = –12 Add 12 to both sides of the equation.

x= –2 Divide both sides of the equation by 6.

See Lesson: Equations with One Variable.

Explanation

B. The correct solution is –2.

6x = –12 Add 12 to both sides of the equation.

x= –2 Divide both sides of the equation by 6.

See Lesson: Equations with One Variable.

18. What is 96 ÷ 12?

8

84

960

1,512

A. Use the division algorithm. Knowing the multiplication table well helps you recognize these numbers. See Lesson: Basic Multiplication and Division.

Explanation

A. Use the division algorithm. Knowing the multiplication table well helps you recognize these numbers. See Lesson: Basic Multiplication and Division.

19. ΔMNO has points M (2, 6), N (3, –1), and O (0, –2). After a transformation, the points are M' (–1, 2), N' (0, –5), and O' (–3, –6). What is the transformation between the points?

Translation right 3 units and up 4 units

Translation left 3 units and up 4 units

Translation right 3 units and down 4 units

Translation left 3 units and down 4 units

D. The correct solution is a translation left 3 units and down 4 units because the points (x, y) become (x – 3, y – 4). See Lesson: Congruence.

Explanation

D. The correct solution is a translation left 3 units and down 4 units because the points (x, y) become (x – 3, y – 4). See Lesson: Congruence.

20. Change the following to a decimal and simplify completely.

5.275

5.325

5.375

5.425

C. The correct answer is 5.375 because 3.000 ÷ 8 = 0.375. See Lesson: Decimals and Fractions.

Explanation

C. The correct answer is 5.375 because 3.000 ÷ 8 = 0.375. See Lesson: Decimals and Fractions.

21. Write 12.5% as a fraction.

Explanation

22. Write 0.21 as a percent.

2.1%

20%

20.1%

21%

D. The correct answer is 21% because 0.21 as a percent is 0.21 × 100 = 21%. See Lesson: Decimals and Fractions.

Explanation

D. The correct answer is 21% because 0.21 as a percent is 0.21 × 100 = 21%. See Lesson: Decimals and Fractions.

23. Solve the equation for the unknown.

-20

-10

10

20

Explanation

24. Solve the system of equations. x = -3y + 10 x = 3y - 8

(-1, 3)

(-3, 1)

(1, 3)

(3, 1)

Explanation

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

-6, -9

-6, 9

6, -9

6, 9

Explanation

26. Three vertices of a parallelogram are (8, 5), (-2, 5), and (-1, 1). What is the fourth coordinate?

(9, 1)

(8, 1)

(9, -1)

(8, -1)

A. The correct solution is (9, 1) because this point shows a parallelogram with a base length of 10 units. See Lesson: Similarity, Right Triangles, and Trigonometry.

Explanation

A. The correct solution is (9, 1) because this point shows a parallelogram with a base length of 10 units. See Lesson: Similarity, Right Triangles, and Trigonometry.

27. A right triangular prism has a triangular base with legs of 5 centimeters and 12 centimeters and a hypotenuse of 13 centimeters. What is the surface area in square centimeters if the height is 2 centimeters?

60

120

180

240

B. The correct solution is 120. Substitute the values into the formula and simplify using the order of operations, SA = (2)(½)(5)(12) + (2)(5) + 2(12) + 2(13) = 60 + 10 + 26 + 24 = 120 square centimeters. See Lesson: Similarity, Right Triangles, and Trigonometry.

Explanation

B. The correct solution is 120. Substitute the values into the formula and simplify using the order of operations, SA = (2)(½)(5)(12) + (2)(5) + 2(12) + 2(13) = 60 + 10 + 26 + 24 = 120 square centimeters. See Lesson: Similarity, Right Triangles, and Trigonometry.

28. A stop sign is a regular octagon with an area of 27,000 square centimeters and an apothem of 90 centimeters. What is the length in centimeters of one side?

38

75

300

600

B. The correct solution is 75. Substitute the values into the formula, 27,000 = ½(90)p and simplify using the order of operations, 27,000 = 45p. Divide both sides of the equation by 45 to find the perimeter, p = 600 centimeters. Divide the perimeter by 8 to find the length of 75 centimeters for each side. See Lesson: Similarity, Right Triangles, and Trigonometry.

Explanation

B. The correct solution is 75. Substitute the values into the formula, 27,000 = ½(90)p and simplify using the order of operations, 27,000 = 45p. Divide both sides of the equation by 45 to find the perimeter, p = 600 centimeters. Divide the perimeter by 8 to find the length of 75 centimeters for each side. See Lesson: Similarity, Right Triangles, and Trigonometry.

29.

See Lesson: Multiplication and Division of Fractions.

Explanation

See Lesson: Multiplication and Division of Fractions.

30. 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.

31. Eric buys pounds of apples each week for four weeks. How many total pounds does he buy?

Explanation

32. Convert 0.75 kilograms to grams.

0.0075 grams

0.075 grams

75 grams

750 grams

Explanation

33. 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.

34. 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

35. 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.

36. A club wants to meet once a week. The available times are Tuesday, Wednesday, and Thursday at 2:00 p.m., 3:00 p.m., and 4:00 p.m. How many outcomes are there for the sample space?

3

6

9

12

C. The correct solution is 9 possible outcomes. There are three days and three times available, or 3 times 3, which is 9 times. See Lesson: Statistics & Probability: The Rules of Probability.

Explanation

C. The correct solution is 9 possible outcomes. There are three days and three times available, or 3 times 3, which is 9 times. See Lesson: Statistics & Probability: The Rules of Probability.

37. 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.

38. Which statement is true?

The sum of a positive number and a negative number is always negative.

The sum of a positive number and a negative number is always positive.

The sum of a positive number and a negative number is always zero.

None of the above.

D. The correct solution is none of the above. Try some test cases. For example, –1 + 5 = 4, but –5 + 1 = –4. Also, –5 + 5 = 0. Counterexamples therefore show that statements A, B, and C are false. See Lesson: Basic Addition and Subtraction.

Explanation

D. The correct solution is none of the above. Try some test cases. For example, –1 + 5 = 4, but –5 + 1 = –4. Also, –5 + 5 = 0. Counterexamples therefore show that statements A, B, and C are false. See Lesson: Basic Addition and Subtraction.

39. Half of a circular garden with a radius of 11.5 feet needs weeding. Find the area in square feet that needs weeding. Round to the nearest hundredth. Use 3.14 for π.

207.64

415.27

519.08

726.73

A. The correct solution is 207.64 because A = ½πr²≈ ½(3.14)(11.5)² ≈ 12(3.14)(132.25) ≈ 207.64 square feet. See Lesson: Circles.

Explanation

A. The correct solution is 207.64 because A = ½πr²≈ ½(3.14)(11.5)² ≈ 12(3.14)(132.25) ≈ 207.64 square feet. See Lesson: Circles.

40. The circumference of a circle is 92 centimeters. Find the area of the circle to the nearest tenth of a square centimeter. Use 3.14 for π.

669.3

858.5

1,338.6

2,695.7

A. The correct solution is 669.3. C = 2πr; 92 = 2(3.14)r; 92 = 6.28r; r ≈ 14.6 centimeters. A = πr² ≈ 3.14 (14.6)² ≈ 3.14(213.16) ≈ 669.3 square centimeters. See Lesson: Circles.

Explanation

A. The correct solution is 669.3. C = 2πr; 92 = 2(3.14)r; 92 = 6.28r; r ≈ 14.6 centimeters. A = πr² ≈ 3.14 (14.6)² ≈ 3.14(213.16) ≈ 669.3 square centimeters. See Lesson: Circles.

41. 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.

42. 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.

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

> 2

X > 9

X > 10

X > 18

Explanation

44. What are the unique prime factors of 56?

2, 7

1, 2, 7

2, 5, 7

2, 4, 7, 8, 14, 16, 28

A. The prime factorization of 56—for example, using a factor tree—yields the numbers 2, 2, 2, and 7. Ignoring repeats of 2, the unique prime factors are 2 and 7. See Lesson: Factors and Multiples.

Explanation

A. The prime factorization of 56—for example, using a factor tree—yields the numbers 2, 2, 2, and 7. Ignoring repeats of 2, the unique prime factors are 2 and 7. See Lesson: Factors and Multiples.

45. 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.

46. 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.

47. Which number is composite?

2

11

73

91

D. A composite number has factors other than 1 and itself. Note that 2 is prime by definition: it only has itself and 1 as factors. Answer B is easy to confirm as prime. That leaves answers C and D. One approach is to start at 2 and test each successive whole number to determine whether it is a factor by dividing. If the quotient is a whole number, it is a factor. In this case, 91 has 7 as a factor. Therefore, it is composite. See Lesson: Factors and Multiples.

Explanation

D. A composite number has factors other than 1 and itself. Note that 2 is prime by definition: it only has itself and 1 as factors. Answer B is easy to confirm as prime. That leaves answers C and D. One approach is to start at 2 and test each successive whole number to determine whether it is a factor by dividing. If the quotient is a whole number, it is a factor. In this case, 91 has 7 as a factor. Therefore, it is composite. See Lesson: Factors and Multiples.

48. Solve the equation by any method. x² + 16x + 33 = 0

-8 ± √31

8 ± √31

-8 ± √33

8 ± √33

Explanation

49. 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.

50. What is 36% as a ratio?

9:25

36:100

18:40

25:9

Explanation

51.

242

276

484

552

D. The correct solution is 552 because the dimensions of the walls are approximately 13 feet by 12 feet and 12 feet by 10 feet. The area is 2(13)(12) + 2(12)(10) = 312 + 240 =552 square feet. See Lesson: Solving Real World Mathematical Problems.

Explanation

D. The correct solution is 552 because the dimensions of the walls are approximately 13 feet by 12 feet and 12 feet by 10 feet. The area is 2(13)(12) + 2(12)(10) = 312 + 240 =552 square feet. See Lesson: Solving Real World Mathematical Problems.

52. If a company's automobile fleet includes 132 cars of brand A and 48 cars of brand B, what is the fleet's ratio of brand B to brand A?

4: 11

11: 15

15: 11

11: 4

A. The ratio is 4:11. A ratio is like a fraction of two numbers, although in this case the answer uses colon notation. The ratio of brand B to brand A is the number of brand-B cars divided by the number of brand-A cars. Reduce to lowest terms:

See Lesson: Ratios, Proportions, and Percentages.

Explanation

A. The ratio is 4:11. A ratio is like a fraction of two numbers, although in this case the answer uses colon notation. The ratio of brand B to brand A is the number of brand-B cars divided by the number of brand-A cars. Reduce to lowest terms:

See Lesson: Ratios, Proportions, and Percentages.

53. Convert 9 meters to yards.

4.09 yards

8.23 yards

9.84 yards

12.28 yards

Explanation

54. Convert 16 gallons to liters.

12.21 liters

19.79 liters

58.28 liters

60.64 liters

Explanation

55. A doctor wants to study the effects of a low-fat diet in patients. What would be needed to create an observational study?

Ask how many fat calories were eaten and track weight.

Ask about the amount of weight patients have gained or lost.

Have one-half of the patients eat a high-fat diet and the other eat a low-fat diet.

Select a group of patients with a low-fat diet and ask how they feel being on the diet.

A. The correct solution is to ask how many fat calories patients eat and track patients’ weight because the researcher is observing the number of fat calories eaten and the weight. See Lesson: Statistical Measures.

Explanation

A. The correct solution is to ask how many fat calories patients eat and track patients’ weight because the researcher is observing the number of fat calories eaten and the weight. See Lesson: Statistical Measures.

56. Identify the study that is a census.

A restaurant asks all customers what they want to add to the menu.

A restaurant asks some of its customers what they want to add to the menu.

A restaurant asks all customers on a Friday what they want to add to the menu.

A restaurant asks random customers by email what they want to add to the menu.

A. The correct solution is a restaurant asking all customers what they want to add to the menu because all customers are being asked their opinion. See Lesson: Statistical Measures.

Explanation

A. The correct solution is a restaurant asking all customers what they want to add to the menu because all customers are being asked their opinion. See Lesson: Statistical Measures.

57. A paper cup in the shape of a cone has a diameter of 8 centimeters and a height of 11 centimeters. How much liquid does the cup hold if filled to the top? Use 3.14 for π.

92.11 cubic centimeters

184.21 cubic centimeters

368.42 cubic centimeters

736.84 cubic centimeters

Explanation

58. 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 = ½πr²; 45 = (½)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 = ½πr²; 45 = (½)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.

59. Evaluate the expression 462 ÷ 53.

1R3

8R0

8R38

8R53

C. Because 462 is not evenly divisible by 53, remainder division is necessary. Use the division algorithm to obtain 8R38. See Lesson: Basic Multiplication and Division.

Explanation

C. Because 462 is not evenly divisible by 53, remainder division is necessary. Use the division algorithm to obtain 8R38. See Lesson: Basic Multiplication and Division.

60. The base of an equilateral triangular pyramid has side lengths of 9 centimeters. The height of the triangular base is 3√3 centimeters, and the pyramid has a height of 10 centimeters. Find the volume of the pyramid in cubic centimeters.

45√3

90√3

135√3

180√3

Explanation

ACT Math Exam 3

1. Solve the system of equations by graphing.

2.

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

2. Apply the polynomial identity to rewrite x2+ 20x + 100.

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

4. Multiply. (4x + 5)(3x - 2)

5.

6.

7. How many millimeters are in a measurement that is 4 centimeters, 3 meters, and 7 millimeters long? (Note that a centimeter is 10 millimeters and a meter is 1,000 millimeters.)

8.

9. Solve. x3 = 64

10. If 1 out of every 250 people will contract a certain disease, what percent of people will contract it?

11. The table shows the speed in miles per hour of different roller coasters at an amusement park. Select the correct line graph for this data.

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

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

14. 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.

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

16. Solve the system of equations. x + 3y = 34 -3x + y = -12

17. Solve the equation for the unknown, 6x - 12 = -24.

18. What is 96 ÷ 12?

19. ΔMNO has points M (2, 6), N (3, –1), and O (0, –2). After a transformation, the points are M' (–1, 2), N' (0, –5), and O' (–3, –6). What is the transformation between the points?

20. Change the following to a decimal and simplify completely.

21. Write 12.5% as a fraction.

22. Write 0.21 as a percent.

23. Solve the equation for the unknown.

24. Solve the system of equations. x = -3y + 10 x = 3y - 8

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

26. Three vertices of a parallelogram are (8, 5), (-2, 5), and (-1, 1). What is the fourth coordinate?

27. A right triangular prism has a triangular base with legs of 5 centimeters and 12 centimeters and a hypotenuse of 13 centimeters. What is the surface area in square centimeters if the height is 2 centimeters?

28. A stop sign is a regular octagon with an area of 27,000 square centimeters and an apothem of 90 centimeters. What is the length in centimeters of one side?

29.

30. 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?

31. Eric buys pounds of apples each week for four weeks. How many total pounds does he buy?

32. Convert 0.75 kilograms to grams.

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

34. 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?

35. 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.

36. A club wants to meet once a week. The available times are Tuesday, Wednesday, and Thursday at 2:00 p.m., 3:00 p.m., and 4:00 p.m. How many outcomes are there for the sample space?

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

38. Which statement is true?

39. Half of a circular garden with a radius of 11.5 feet needs weeding. Find the area in square feet that needs weeding. Round to the nearest hundredth. Use 3.14 for π.

40. The circumference of a circle is 92 centimeters. Find the area of the circle to the nearest tenth of a square centimeter. Use 3.14 for π.

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

42. 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?

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

44. What are the unique prime factors of 56?

45. 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.

46. 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.

47. Which number is composite?

48. Solve the equation by any method. x2 + 16x + 33 = 0

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

50. What is 36% as a ratio?

51.

52. If a company's automobile fleet includes 132 cars of brand A and 48 cars of brand B, what is the fleet's ratio of brand B to brand A?

53. Convert 9 meters to yards.

54. Convert 16 gallons to liters.

55. A doctor wants to study the effects of a low-fat diet in patients. What would be needed to create an observational study?

56. Identify the study that is a census.

57. A paper cup in the shape of a cone has a diameter of 8 centimeters and a height of 11 centimeters. How much liquid does the cup hold if filled to the top? Use 3.14 for π.

58. 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.

59. Evaluate the expression 462 ÷ 53.

60. The base of an equilateral triangular pyramid has side lengths of 9 centimeters. The height of the triangular base is 3√3 centimeters, and the pyramid has a height of 10 centimeters. Find the volume of the pyramid in cubic centimeters.

2. Apply the polynomial identity to rewrite x^²+ 20x + 100.

9. Solve. x³ = 64

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

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

42. 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?

48. Solve the equation by any method. x² + 16x + 33 = 0