AI-GENERATED GEN-001 · Sonnet

Math

60 questions ~15 min recommended

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Score

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1. Mia recorded the following quiz scores for the week: 85, 92, 78, 90, and 75. What is the mean of her quiz scores?

A. 82

B. 84

C. 85

D. 86

E. 88

2. A jar contains 5 red marbles, 8 blue marbles, and 7 green marbles. If one marble is drawn at random, what is the probability that it is blue?

F. 2/5

G. 8/15

H. 4/9

J. 7/20

K. 1/3

3. A store is having a 30% off sale. If a jacket originally costs $140, what is the sale price of the jacket?

A. $42

B. $84

C. $98

D. $110

E. $112

4. In the Venn diagram below, circle A represents students who play basketball and circle B represents students who play soccer. Circle A contains the number 14 (only basketball), the overlap contains 6, circle B contains 9 (only soccer), and 5 students play neither sport. How many total students are represented?

F. 29

G. 30

H. 34

J. 35

K. 40

5. What is the least common multiple (LCM) of 12 and 18?

A. 6

B. 24

C. 36

D. 54

E. 216

6. Terrence earns $12.50 per hour and worked 32 hours last week. If he spends $185 on groceries, how much money does he have left from last week's earnings?

F. $195

G. $200

H. $210

J. $215

K. $220

7. A recipe calls for 2¾ cups of flour to make one batch of cookies. How many cups of flour are needed to make 4 batches?

A. 8

B. 9

C. 10

D. 11

E. 12

8. If 3x + 7 = 22, what is the value of x?

F. 3

G. 4

H. 5

J. 6

K. 7

9. Which of the following expressions is equivalent to x² + 7x + 12?

A. (x + 3)(x + 4)

B. (x + 2)(x + 6)

C. (x − 3)(x − 4)

D. (x + 1)(x + 12)

E. (x + 6)(x + 2)

10. If y = 3x − 5, what is the value of y when x = −2?

F. −11

G. −9

H. −7

J. 1

K. 11

11. A car rental company charges a flat fee of $25 plus $0.15 per mile driven. If Dana's total bill was $58, how many miles did she drive?

A. 180

B. 200

C. 220

D. 240

E. 260

12. Which of the following is equivalent to 4(2x − 3) − 2(x + 5)?

F. 6x − 22

G. 6x − 2

H. 10x − 22

J. 6x + 2

K. 8x − 22

13. What are the solutions to x² − 5x − 14 = 0?

A. x = 7 and x = −2

B. x = −7 and x = 2

C. x = 7 and x = 2

D. x = −7 and x = −2

E. x = 14 and x = −1

14. If f(x) = 2x² − 3x + 1, what is f(−2)?

F. 3

G. 9

H. 11

J. 15

K. 19

15. For what value(s) of x is the expression (x + 4)/(x² − 9) undefined?

A. x = −4 only

B. x = 3 only

C. x = −3 only

D. x = 3 and x = −3

E. x = 3, x = −3, and x = −4

16. The value of a car depreciates according to the formula V = 24000(0.85)^t, where t is the number of years since purchase. What is the value of the car, to the nearest dollar, after 3 years?

F. $12,480

G. $14,706

H. $17,340

J. $20,400

K. $22,440

17. Triangle PQR has angle P = 52° and angle Q = 79°. What is the measure of angle R?

A. 29°

B. 39°

C. 49°

D. 59°

E. 69°

18. A rectangle has a length of 14 cm and a width of 9 cm. What is the area of the rectangle in square centimeters?

F. 46

G. 92

H. 116

J. 126

K. 196

19. A circle has a diameter of 10 inches. What is the circumference of the circle, in inches? (Use π ≈ 3.14)

A. 15.70

B. 31.40

C. 62.80

D. 78.50

E. 314.00

20. In the figure described: Two parallel lines are cut by a transversal. One of the co-interior (same-side interior) angles measures 112°. What is the measure of the other co-interior angle?

F. 22°

G. 58°

H. 68°

J. 78°

K. 112°

21. A right triangle has legs of length 9 and 12. What is the length of the hypotenuse?

A. 13

B. 14

C. 15

D. 16

E. 17

22. A trapezoid has parallel bases of length 8 cm and 14 cm and a height of 5 cm. What is the area of the trapezoid in square centimeters?

F. 55

G. 70

H. 80

J. 95

K. 110

23. A rectangular prism has length 6 ft, width 4 ft, and height 3 ft. What is the volume of the prism in cubic feet?

A. 52

B. 60

C. 72

D. 84

E. 96

24. What is the midpoint of the line segment with endpoints (−3, 7) and (5, −1)?

F. (1, 3)

G. (2, 3)

H. (1, 4)

J. (4, 3)

K. (2, 4)

25. What is the slope of the line passing through the points (2, −3) and (8, 9)?

A. −2

B. 1/2

C. 2

D. 3

E. 4

26. Which of the following is the equation of a line with slope −3 and y-intercept 4?

F. y = 4x − 3

G. y = 3x + 4

H. y = −3x − 4

J. y = −3x + 4

K. y = 4x + 3

27. What is the distance between the points (1, 2) and (4, 6)?

A. 3

B. 4

C. 5

D. 6

E. 7

28. A line passes through (0, −2) and has a slope of 3/4. Which of the following points also lies on this line?

F. (4, 1)

G. (4, 3)

H. (8, 4)

J. (8, 5)

K. (8, 6)

29. In a right triangle, the side adjacent to angle θ has length 5 and the hypotenuse has length 13. What is sin θ?

A. 5/13

B. 12/13

C. 5/12

D. 13/12

E. 13/5

30. For angle β in a right triangle, cos β = 3/5. What is tan β?

F. 3/4

G. 4/3

H. 4/5

J. 5/4

K. 5/3

31. A hardware store is having a sale where every item is marked down 35%. After the markdown, a power drill costs $84.50. What was the original price of the power drill, to the nearest cent? DO YOUR FIGURING HERE.

A. $55.93

B. $113.93

C. $130.00

D. $140.83

E. $241.43

32. A recipe calls for ingredients in the following ratio: 3 parts flour to 2 parts sugar to 1 part butter. If a baker wants to make a batch using exactly 4.5 cups of sugar, how many total cups of all three ingredients combined will be needed? DO YOUR FIGURING HERE.

F. 9

G. 13.5

H. 18

J. 22.5

K. 27

A. 0

B. 0.5

C. 1

D. 2

E. 3

34. A store sells trail mix in two sizes: a 12-ounce bag for $3.96 and a 20-ounce bag for $6.20. What is the positive difference in the cost per ounce between the two sizes, to the nearest cent? DO YOUR FIGURING HERE.

F. $0.02

G. $0.05

H. $0.08

J. $0.11

K. $0.24

35. A city's population grew from 124,000 to 155,000 over a 5-year period. To the nearest tenth of a percent, what was the percent increase in population over this period? DO YOUR FIGURING HERE.

A. 20.0%

B. 22.7%

C. 24.8%

D. 25.0%

E. 31.0%

36. The Venn diagram below shows students enrolled in Drama (D) and Orchestra (O) out of 80 total students. The number in D only is 22, the number in both D and O is 9, the number in O only is 14, and the remaining students are in neither. How many students are enrolled in neither Drama nor Orchestra? DO YOUR FIGURING HERE.

F. 25

G. 33

H. 35

J. 45

K. 57

37. A large water tank holds 6,000 gallons when full. Water drains out at a constant rate of 45 gallons per minute. At the same time, a pump adds water at a constant rate of 18 gallons per minute. The tank starts completely full. After how many minutes will the tank contain exactly 4,365 gallons? DO YOUR FIGURING HERE.

A. 36

B. 55

C. 60

D. 72

E. 97

38. If 3(2w − 5) + 4w = 2(w + 3) − 1, what is the value of w? DO YOUR FIGURING HERE.

F. 0.5

G. 1

H. 2

J. 2.5

K. 3

39. Which of the following expressions is equivalent to 2x² + 7x − 15? DO YOUR FIGURING HERE.

A. (2x − 3)(x + 5)

B. (2x + 3)(x − 5)

C. (2x − 5)(x + 3)

D. (x + 5)(2x − 3)

E. (2x + 5)(x − 3)

40. A phone plan charges a flat monthly fee of $25.00 plus $0.08 per text message sent. Another plan charges a flat monthly fee of $15.00 plus $0.12 per text message sent. For what number of text messages sent per month will the two plans cost the same amount? DO YOUR FIGURING HERE.

F. 125

G. 200

H. 250

J. 300

K. 375

41. If the inequality 4 − 3x > 2x + 19 is satisfied, which of the following must be true? DO YOUR FIGURING HERE.

A. x < −5

B. x > −3

C. x < 3

D. x > 5

E. x < −3

42. The sum of three consecutive even integers is 78. What is the largest of the three integers? DO YOUR FIGURING HERE.

F. 24

G. 26

H. 28

J. 30

K. 32

43. The function f(x) = 2x² − 12x + 14. What is the minimum value of f(x)? DO YOUR FIGURING HERE.

A. −18

B. −4

C. 3

D. 4

E. 14

44. Which of the following is a solution to the equation x² − 5x − 24 = 0? DO YOUR FIGURING HERE.

F. x = −3 only

G. x = 8 only

H. x = −3 or x = 8

J. x = 3 or x = −8

K. x = 6 or x = −4

45. For all x ≠ 0, which of the following is equivalent to (3x³ − 6x² + 9x) / (3x)? DO YOUR FIGURING HERE.

A. x² − 2x + 3

B. x³ − 2x² + 3x

C. 3x² − 6x + 9

D. x² − 6x + 9

E. 3x² − 2x + 3

46. If log₄(x) = 3, what is the value of log₄(x²)? DO YOUR FIGURING HERE.

F. 6

G. 9

H. 12

J. 16

K. 64

47. A ball is thrown upward from the ground. Its height in feet after t seconds is given by h(t) = −16t² + 48t. How many seconds after being thrown will the ball first reach a height of 32 feet? DO YOUR FIGURING HERE.

A. 0.5

B. 0.75

C. 1

D. 2

E. 3

48. In the figure below, two parallel lines are cut by a transversal. One of the angles formed measures (5x + 12)° and the co-interior (same-side interior) angle measures (3x + 28)°. What is the value of x? (Note: Co-interior angles are supplementary.) DO YOUR FIGURING HERE.

F. 7

G. 10

H. 17.5

J. 20

K. 35

49. A rectangular garden measures 24 feet by 10 feet. A walkway of uniform width w feet is to be built around the outside of the garden. The total area of the garden plus walkway is 630 square feet. What is the width of the walkway in feet? DO YOUR FIGURING HERE.

A. 2.5

B. 3

C. 3.5

D. 4

E. 5

50. A rectangular garden measures 22 feet by 8 feet. A walkway of uniform width w feet is to be built around the outside of the garden. The total area of the garden plus walkway is 480 square feet. What is the width of the walkway in feet? DO YOUR FIGURING HERE.

F. 2

G. 2.5

H. 3

J. 4

K. 5

51. In triangle PQR, PQ = 13, QR = 5, and angle Q = 90°. What is the length of PR, and what is tan(∠R)? DO YOUR FIGURING HERE.

A. PR = 12, tan(∠R) = 5/13

B. PR = 14, tan(∠R) = 13/5

C. PR = √194, tan(∠R) = 13/5

D. PR = √194, tan(∠R) = 5/13

E. PR = 12, tan(∠R) = 13/5

52. A circle has a central angle of 135° that intercepts an arc. The radius of the circle is 8 inches. What is the length of the intercepted arc, in inches? (Note: Arc length = (θ/360°) × 2πr) DO YOUR FIGURING HERE.

F. 3π

G. 5π

H. 6π

J. 9π

K. 12π

53. In the figure described below, quadrilateral ABCD is a trapezoid with AB ∥ CD. AB = 18, CD = 10, and the height of the trapezoid is 7. What is the area of the trapezoid? DO YOUR FIGURING HERE.

A. 56

B. 98

C. 112

D. 126

E. 196

54. In the figure below, lines m and n are parallel. A transversal crosses both lines, creating an angle of (7x − 4)° with line m and an alternate interior angle of (5x + 16)° with line n. What is the measure, in degrees, of the angle that measures (7x − 4)°? DO YOUR FIGURING HERE.

F. 56°

G. 66°

H. 71°

J. 76°

K. 80°

55. What is the distance between the points (−3, 7) and (5, −8) in the standard (x, y) coordinate plane? DO YOUR FIGURING HERE.

A. √161

B. √289 = 17

C. √353

D. √(64+225)

E. 23

56. What is the distance between the points (2, −3) and (−4, 5) in the standard (x, y) coordinate plane? DO YOUR FIGURING HERE.

F. √28

G. √52

H. √73

J. 10

K. √116

57. Line ℓ passes through (2, 5) and (8, −1). What is the equation of the line perpendicular to ℓ that passes through the point (3, 4)? DO YOUR FIGURING HERE.

A. y = x + 1

B. y = −x + 7

C. y = x + 2

D. y = −x + 1

E. y = 2x − 2

58. A circle in the standard (x, y) coordinate plane has its center at (3, −2) and passes through the point (7, 1). Which of the following is the equation of this circle? DO YOUR FIGURING HERE.

F. (x−3)² + (y+2)² = 5

G. (x+3)² + (y−2)² = 25

H. (x−3)² + (y+2)² = 25

J. (x−3)² + (y+2)² = √5

K. (x+3)² + (y−2)² = 5

59. In right triangle ABC with the right angle at C, the hypotenuse AB = 20 and angle A = 32°. What is the length of BC, to the nearest tenth? (Note: sin 32° ≈ 0.5299, cos 32° ≈ 0.8480, tan 32° ≈ 0.6249) DO YOUR FIGURING HERE.

A. 6.5

B. 10.6

C. 12.5

D. 16.0

E. 21.2

60. Which of the following is equivalent to sin²(θ) − sin²(θ)cos²(θ) for all values of θ? DO YOUR FIGURING HERE.

F. cos⁴(θ)

G. sin⁴(θ)

H. 1 − cos²(θ)

J. sin²(θ)cos²(θ)

K. 1 − sin²(θ)

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