1. Destiny recorded her daily steps for 5 days: 8,200, 6,500, 9,100, 7,400, and 10,300. What is the mean number of steps she walked per day?
2. In the figure below, two parallel lines are cut by a transversal. One of the angles formed measures 112°. What is the measure of its co-interior (same-side interior) angle?
[Figure description: Two horizontal parallel lines cut by a diagonal transversal. The angle marked 112° is above the upper parallel line on the left side of the transversal.]
3. A store sells notebooks for $3.75 each. If Terrell buys 8 notebooks and pays with a $40 bill, how much change will he receive?
4. If 3(2x − 4) = 18, what is the value of x?
5. In a bag of 60 marbles, 15 are red, 20 are blue, and the rest are green. What percent of the marbles are green?
6. What is the distance between the points (1, 3) and (5, 6) in the standard coordinate plane?
7. A rectangle has a length of 14 cm and a width of 9 cm. What is the area of the rectangle in square centimeters?
8. Which of the following is equivalent to the expression x² + 5x − 24?
9. A recipe calls for 2¾ cups of flour. If Marcus wants to make 3 batches of the recipe, how many cups of flour does he need in total?
10. What is the slope of the line that passes through the points (−2, 5) and (4, −1)?
11. The length of a rectangular garden is 5 more than twice its width. If the perimeter of the garden is 58 meters, what is the width of the garden in meters?
12. Triangle PQR has angles measuring 47°, 68°, and x°. What is the value of x?
13. What are the solutions to 2x² − 8 = 0?
14. In the Venn diagram below, circle A represents students who play basketball, and circle B represents students who play soccer. The overlap shows students who play both. If 18 students play basketball only, 11 play both, and 14 play soccer only, how many students play neither sport if the total number of students surveyed is 55?
[Figure description: Two overlapping circles labeled A and B. The left region of A shows 18, the overlap shows 11, and the right region of B shows 14.]
15. In a right triangle, the side adjacent to angle θ measures 7 units and the hypotenuse measures 25 units. What is cos θ?
16. Which of the following is the equation of a line with slope −3 and y-intercept 7?
17. A circle has a radius of 6 inches. What is the circumference of the circle? (Use π ≈ 3.14)
18. If f(x) = 4x² − 3x + 1, what is the value of f(−2)?
19. What is the value of y in the system of equations below?
3x + y = 10
x − 2y = −3
20. A right triangle has legs measuring 9 cm and 12 cm. What is the length of the hypotenuse?
21. A worker earns $14.50 per hour. If she works 32 hours in a week, how much does she earn that week before taxes?
22. What is the midpoint of the segment with endpoints (−4, 7) and (10, −3)?
23. The area of a triangle with base 16 cm and height h is 72 cm². What is the height h?
24. Which of the following expressions is equivalent to (3x − 2)²?
25. For all nonzero values of a and b, which of the following is equivalent to (6a³b²) ÷ (2ab⁴)?
26. In the figure below, line m is parallel to line n, and a transversal crosses both lines. If angle 1 measures 74°, what is the measure of the alternate interior angle?
[Figure description: Two parallel horizontal lines m and n cut by a diagonal transversal. Angle 1 is formed above line m on the right side of the transversal.]
27. In a right triangle, angle B measures 30°. The hypotenuse is 20 units long. What is the length of the side opposite angle B?
28. Which of the following points lies on the graph of y = 2x − 5?
29. A circular pizza has a diameter of 16 inches. What is the area of the pizza to the nearest square inch? (Use π ≈ 3.14)
30. If 5 − 3|x| = −7, what are the possible values of x?
31. A hardware store is having a sale. A box of nails originally priced at $8.40 is marked down 15%. What is the sale price of the box of nails?
32. A recipe calls for 2¾ cups of flour for every 1½ cups of sugar. If Darnell wants to use 6 cups of sugar, how many cups of flour does he need?
33. The table below shows the number of students enrolled in four elective courses at Riverside High School.
Course | Enrollment
Art | 48
Music | 36
Drama | 24
Film | 12
What percent of the total enrollment is in Drama?
34. On a number line, point R is located at −7 and point T is located at 11. Point M is the midpoint of segment RT. What is the coordinate of point M?
35. A gym membership costs $45 per month plus a one-time registration fee of $60. Selena has already paid the registration fee and has budgeted $420 to spend on additional monthly fees. For how many months can she pay for the gym membership?
36. If 40% of a number is 34, what is 75% of that number?
37. The ratio of red marbles to blue marbles in a bag is 5:3. If there are 40 red marbles in the bag, what is the total number of marbles in the bag?
38. If 3(2x − 4) + 5 = 2(x + 7), what is the value of x?
39. Which of the following expressions is equivalent to 2x² + 7x − 15?
40. The cost C, in dollars, of producing n widgets is given by C = 0.35n + 120. For what value of n will the cost equal $260?
41. If |3x − 9| = 18, what are the possible values of x?
42. A line passes through the points (2, 5) and (6, 13). What is the equation of this line in slope-intercept form?
43. What are the solutions to x² − 4x − 21 = 0?
44. If f(x) = 3x² − 2x + 4 and g(x) = x − 3, what is f(g(2))?
45. For what value(s) of x is the expression (x² − 9)/(x² − x − 6) undefined?
46. The graph of f(x) = x² is shifted 3 units to the right and 5 units down. Which of the following represents the resulting function?
47. If log₂(x) = 5, what is the value of log₂(x³)?
48. In the figure below, two parallel lines are cut by a transversal. One of the angles formed measures (4k + 12)° and its co-interior (same-side interior) angle measures (2k + 48)°. What is the value of k?
(Figure description: Two horizontal parallel lines cut by a diagonal transversal, with the two labeled angles on the same side between the parallel lines.)
49. A circular garden has a diameter of 18 feet. A square patio is inscribed in the circle. What is the area of the square patio, in square feet?
50. Triangle PQR has vertices at P(0, 0), Q(8, 0), and R(4, 6). What is the perimeter of triangle PQR, to the nearest tenth?
(Figure description: Triangle with base PQ along the x-axis and apex R above the midpoint of PQ.)
51. Two similar triangles have corresponding sides in the ratio 3:5. If the area of the smaller triangle is 27 square centimeters, what is the area of the larger triangle, in square centimeters?
52. In a right triangle, the two legs have lengths 7 cm and 24 cm. What is the length of the hypotenuse?
53. A trapezoid has parallel bases of lengths 10 inches and 16 inches, and a height of 9 inches. What is the area of the trapezoid, in square inches?
54. A rectangle has a length of (3x + 2) units and a width of (x − 1) units. If the perimeter of the rectangle is 46 units, what is the area of the rectangle, in square units?
55. What is the distance between the points (−3, 4) and (5, −2) in the standard coordinate plane?
56. A circle in the standard coordinate plane has the equation (x − 4)² + (y + 3)² = 49. Which of the following gives the center and radius of the circle?
57. Which of the following is the equation of a line that is parallel to the line 6x − 2y = 10 and passes through the point (0, 4)?
58. In the standard (x, y) coordinate plane, the endpoints of a diameter of a circle are (−2, 6) and (8, −4). What are the coordinates of the center of the circle?
59. From the top of a lighthouse 120 feet tall, the angle of depression to a boat on the water is 28°. Which of the following expressions gives the horizontal distance, in feet, from the base of the lighthouse to the boat?
(Figure description: A right triangle with the lighthouse as the vertical leg, the horizontal distance as the horizontal leg, and the line of sight as the hypotenuse. The angle of depression from the top of the lighthouse to the boat is 28°.)
60. In triangle XYZ, angle X = 42°, angle Y = 73°, and side y (opposite angle Y) = 15 cm. Using the Law of Sines, what is the length of side x (opposite angle X), to the nearest tenth of a centimeter?