1. Mia recorded the following quiz scores for the week: 84, 91, 76, 88, and 71. What is the mean of her quiz scores?
2. A store sells notebooks for $3.50 each and pens for $1.25 each. Derek buys 4 notebooks and 6 pens. How much does Derek spend in total?
3. A bag contains 5 red marbles, 8 blue marbles, and 7 green marbles. If one marble is chosen at random, what is the probability it is blue?
4. On a number line, point R is located at −9 and point T is located at 15. What is the distance between R and T?
5. Which of the following lists all the factors of 36?
6. A recipe calls for 2¾ cups of flour. If Tomas wants to make 3 times the recipe, how many cups of flour does he need?
7. At a movie theater, 40% of the audience bought popcorn. If 70 people bought popcorn, how many people were in the audience?
8. If 3x + 7 = 28, what is the value of x?
9. Which of the following expressions is equivalent to 2x² + 11x + 15?
10. If y = 4x − 3, what is the value of y when x = −2?
11. A car rental company charges a flat fee of $25 plus $0.15 per mile driven. If Jordan paid $55 total, how many miles did Jordan drive?
12. Which of the following is equivalent to (3x − 4)²?
13. What are the solutions to the equation x² − 5x − 14 = 0?
14. For the function f(x) = x² − 4x + 3, what is the minimum value of f(x)?
15. If log₂(x) = 5, what is the value of x?
16. Which of the following gives all real values of x satisfying |2x − 3| < 7?
17. A rectangle has a length of 14 cm and a width of 9 cm. What is the area of the rectangle?
18. In triangle PQR, the measure of angle P is 48° and the measure of angle Q is 67°. What is the measure of angle R?
19. A circle has a diameter of 10 inches. What is the area of the circle? (Use π ≈ 3.14)
20. 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?
21. A right triangle has legs of length 9 and 40. What is the length of the hypotenuse?
22. A trapezoid has parallel sides of length 8 cm and 14 cm, and a height of 6 cm. What is the area of the trapezoid?
23. A regular hexagon has a perimeter of 48 cm. What is the length of one side?
24. What is the distance between the points (−3, 4) and (5, −2) in the standard (x, y) coordinate plane?
25. What is the slope of the line passing through the points (2, 7) and (6, 15)?
26. A line has the equation 3x − 6y = 12. What is the y-intercept of this line?
27. What is the midpoint of the segment with endpoints (−4, 9) and (10, −3)?
28. Which of the following equations represents a line parallel to y = −3x + 7?
29. In a right triangle, the side opposite angle θ has length 7 and the hypotenuse has length 25. What is cos θ?
30. For an angle β where 0° < β < 90°, if sin β = 3/5, what is the value of tan β?
31. A hardware store sells bolts in packages of 18 and nuts in packages of 24. A contractor wants to buy the same number of bolts and nuts with no leftovers. What is the minimum number of bolt packages the contractor must buy?
32. In the figure below, two parallel lines are cut by a transversal. One of the angles formed measures (3x + 15)° and its co-interior (same-side interior) angle measures (5x − 7)°. What is the value of x?
[Figure description: Two horizontal parallel lines crossed by a diagonal transversal, with (3x+15)° marked on the upper-left interior and (5x−7)° marked on the lower-left interior, making them co-interior angles.]
33. If 3(2m − 4) = 5m + 2, what is the value of m?
34. What are the solutions to the quadratic equation 2x² − 7x − 15 = 0?
35. Mei earns a weekly base salary of $480 plus a commission of 6% on all sales she makes. Last week her total earnings were $732. What were her total sales last week, in dollars?
36. Line segment PQ has endpoints P(−3, 7) and Q(9, −1). What are the coordinates of the midpoint of PQ?
37. A rectangle has a length of (2x + 5) inches and a width of (x − 1) inches. If the perimeter of the rectangle is 52 inches, what is the area of the rectangle, in square inches?
38. The table below shows the number of books read by students in a class during one month.
Books read | Number of students
0 | 3
1 | 7
2 | 10
3 | 6
4 | 4
What is the median number of books read per student?
39. The function f(x) = 3x² − 12x + 7 has a minimum value. What is that minimum value?
40. In a right triangle, the side adjacent to angle θ has length 8 and the hypotenuse has length 17. What is tan θ?
41. Which of the following is equivalent to (4x³y²)(−3x²y⁵)?
42. What is the slope of a line perpendicular to the line passing through the points (2, −3) and (8, 9)?
43. A recipe requires 2¾ cups of flour to make one batch of bread. If Darnell wants to make 3½ batches, how many cups of flour does he need?
44. In the figure below, triangle ABC is isosceles with AB = BC. The measure of angle B is 48°. What is the measure of angle ACB?
[Figure description: Triangle ABC with vertex B at the top and base AC at the bottom. AB and BC are the equal sides. Angle B is labeled 48°.]
45. If f(x) = x² + 3x − 4 and g(x) = 2x + 1, what is f(g(−2))?
46. A mixture of nuts contains cashews, almonds, and peanuts in the ratio 2:3:5. If the total mixture weighs 40 pounds, how many pounds of almonds are in the mixture?
47. A circular garden has a diameter of 14 meters. A gardener wants to place a fence around the entire garden. Approximately how many meters of fencing are needed? (Use π ≈ 3.14)
48. What is the distance between the points (−4, 3) and (2, −5) in the coordinate plane?
49. What is the value of |3x − 11| when x = −2?
50. In the figure below, a right triangle has legs of lengths 9 cm and 12 cm. A square is drawn on the hypotenuse of the triangle. What is the area, in square centimeters, of that square?
[Figure description: A right triangle with legs labeled 9 cm and 12 cm, with a square constructed outward on the hypotenuse.]
51. For what value(s) of x is the expression (x² − 9)/(x² − 5x + 6) undefined?
52. Tomás has $240 in his savings account. He withdraws 35% of his savings to pay for a concert ticket. How much money, in dollars, does he have left in his account after the withdrawal?
53. Two supplementary angles are in the ratio 4:5. What is the measure, in degrees, of the larger angle?
54. A 25-foot ladder leans against a vertical wall. The base of the ladder is 7 feet from the wall. What is the angle, to the nearest degree, that the ladder makes with the ground?
(Note: Use sin⁻¹, cos⁻¹, or tan⁻¹ as needed.)
55. Which of the following equations represents a line parallel to y = −(2/3)x + 5 and passing through the point (6, 1)?
56. In the figure below, a regular hexagon has a side length of 6 cm. What is the area of the hexagon, in square centimeters?
[Figure description: A regular hexagon with all sides labeled 6 cm.]
(Note: The area of a regular hexagon with side length s is (3√3/2)s²)
57. A store is having a sale. A jacket originally priced at $125 is discounted by 20%, and then an additional 10% is taken off the sale price at checkout. What is the final price of the jacket?
58. If the inequality 4 − 3x > 13 is satisfied, which of the following must be true?
59. In the figure below, circle O has a radius of 10 cm. Chord AB is 16 cm long. What is the distance, in centimeters, from the center O to chord AB?
[Figure description: A circle with center O and radius 10 cm. Chord AB is drawn, and a perpendicular line from center O meets chord AB at its midpoint M.]
60. Which of the following is equivalent to (2x − 3)²?