1. Destiny recorded the following quiz scores for the week: 84, 91, 76, 88, and 71. What is the mean of her quiz scores?
2. In the Venn diagram below, circle A represents students who play soccer, circle B represents students who play basketball, and circle B represents students who play baseball (circle C). The numbers in the diagram are: only A = 9, only B = 14, only C = 7, A and B only = 3, A and C only = 5, B and C only = 6, all three = 2. How many of the 46 total students play soccer?
(Figure description: Three overlapping circles A, B, C with values 9, 14, 7, 3, 5, 6, 2 in the respective regions.)
3. A bag 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?
4. What is the least common multiple (LCM) of 12 and 18?
5. A store sells notebooks for $3.25 each and pens for $1.50 each. Tomás buys 4 notebooks and 6 pens. How much does he spend in total?
6. A recipe calls for 2/3 cup of sugar. If Priya wants to make 4 and a half batches of the recipe, how many cups of sugar does she need?
7. Which of the following is equivalent to 3.6 × 10⁴?
8. If 3x + 7 = 28, what is the value of x?
9. Which of the following expressions is equivalent to x² + 7x + 12?
10. If 5y − 3 = 2y + 9, what is the value of y?
11. Marcus earns $12 per hour working at a bookstore. One week he worked h hours and earned a total of $156. Which equation can be used to find h?
12. What is the value of the expression 4a² − 3b when a = 2 and b = 5?
13. What are the solutions to x² − 5x − 14 = 0?
14. If f(x) = 2x² − 3x + 1, what is f(−2)?
15. For what value(s) of x is the expression (x+4)/(x²−9) undefined?
16. A company's profit P (in dollars) is modeled by P(x) = −2x² + 80x − 300, where x is the number of units sold. What is the maximum profit?
17. In triangle PQR, angle P measures 47° and angle Q measures 68°. What is the measure of angle R?
18. A rectangle has a length of 15 cm and a width of 8 cm. What is the length of the diagonal of the rectangle?
19. A circle has a radius of 6 inches. What is the area of the circle in square inches?
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 trapezoid has parallel bases of length 10 cm and 16 cm, and a height of 7 cm. What is the area of the trapezoid?
22. In the figure below, a regular hexagon has a perimeter of 54 cm. What is the length of one side?
(Figure description: A regular hexagon with all sides equal.)
23. A right triangle has legs of length 9 and 12. What is the perimeter of the triangle?
24. What is the distance between the points (1, 3) and (5, 6)?
25. What is the slope of the line passing through the points (−2, 4) and (4, −2)?
26. Which of the following is the equation of a line with slope 3 and y-intercept −5?
27. What is the midpoint of the segment with endpoints (−4, 6) and (8, −2)?
28. The graph of which equation is a vertical line passing through the point (−3, 7)?
29. In a right triangle, the side opposite to angle θ has length 8 and the hypotenuse has length 17. What is sin θ?
30. For an angle β in a right triangle, cos β = 5/13. What is tan β?
31. A store sells notebooks for $3.75 each and pens for $1.25 each. Deshawn buys a total of 12 items and spends exactly $30.00. How many notebooks did Deshawn buy?
32. A jar contains red, blue, and green marbles. The ratio of red to blue marbles is 3:5, and the ratio of blue to green marbles is 2:3. If there are 30 blue marbles in the jar, how many total marbles are in the jar?
(Note: The jar contains only red, blue, and green marbles.)
33. Valentina earns a base salary of $2,400 per month plus a 6% commission on all sales she makes that month. In March, her total earnings were $3,768. What were her total sales, in dollars, for March?
34. A sequence follows the rule: each term after the first is obtained by multiplying the previous term by −2 and then adding 3. If the first term is 5, what is the fifth term of the sequence?
35. On a map, 1 inch represents 45 miles. Two cities are 7.4 inches apart on the map. A third city is located exactly halfway between these two cities. What is the distance, in miles, from the third city to either of the other two cities?
36. In a school survey, students were asked about their preferred lunch option: pizza, salad, or sandwich. The results showed that 40% preferred pizza, 35% preferred salad, and the rest preferred sandwich. If 420 students preferred pizza, how many students total took the survey?
37. The product of two consecutive even integers is 3,248. What is the sum of these two integers?
38. If 3(2x − 4) + 5 = 4(x + 1) − 7, what is the value of x?
39. A rectangle has a length that is 5 more than twice its width. If the perimeter of the rectangle is 88 centimeters, what is the area of the rectangle, in square centimeters?
40. Which of the following is equivalent to (3x − 7)²?
41. If f(x) = 2x² − 3x + 1 and g(x) = x − 4, what is f(g(3))?
42. What are the solutions to the equation x² − 5x − 24 = 0?
43. What is the sum of all values of k for which the equation 2x² + kx + 8 = 0 has exactly one real solution?
44. If log₃(x) = 4 and log₃(y) = −1, what is the value of log₃(x²y³)?
45. The expression (x² − 9)/(x² − x − 6) simplifies to which of the following for all values of x where the expression is defined?
46. A function is defined as h(x) = (3x + 2)/(x − 5). For which value of x is h(x) undefined, and what is the value of h(0)?
47. If the function f(x) = ax² + bx + c has a vertex at (2, −3) and passes through the point (0, 5), what is the value of a?
48. In the figure below, two parallel lines are cut by a transversal. One of the angles formed measures (4x + 15)° and its co-interior (same-side interior) angle measures (2x + 45)°. What is the value of x?
(Figure description: Two horizontal parallel lines crossed by a diagonal transversal. The angle on the upper-left side of the upper intersection is labeled (4x + 15)° and the angle on the lower-left side of the lower intersection is labeled (2x + 45)°.)
49. A right triangle has legs of length 9 cm and 12 cm. A second triangle is similar to the first, and its hypotenuse is 25 cm. What is the perimeter of the second triangle, in centimeters?
50. In circle O, a chord AB has a length of 16 cm, and the chord is 6 cm from the center of the circle. What is the area of circle O, in square centimeters?
51. A regular hexagon has a perimeter of 72 inches. What is the area of the hexagon, in square inches?
52. Two rectangles share the same center point. The larger rectangle has dimensions 10 cm by 14 cm. The smaller rectangle has dimensions 6 cm by 8 cm and is entirely inside the larger rectangle. What is the area of the region inside the larger rectangle but outside the smaller rectangle, in square centimeters?
53. In triangle PQR, the measure of angle P is 52° and the measure of angle Q is 73°. Line segment RS is drawn from vertex R perpendicular to line PQ, where S is on PQ. What is the measure of angle QRS?
54. A trapezoid has parallel bases of length 11 meters and 17 meters, and a height of 8 meters. What is the area of the trapezoid, in square meters?
55. What is the distance between the points (−3, 7) and (5, −8) in the standard (x,y) coordinate plane?
56. A line passes through the points (−2, 5) and (4, −1). What is the equation of the line in slope-intercept form?
57. In the standard (x,y) coordinate plane, what is the center and radius of the circle with equation x² − 8x + y² + 6y = 0?
58. The midpoint of segment AB is M(3, −2). If point A has coordinates (−1, 4), what are the coordinates of point B?
59. From the top of a lighthouse that is 120 feet tall, the angle of depression to a boat on the water is 32°. To the nearest foot, how far is the boat from the base of the lighthouse?
(Note: tan 32° ≈ 0.6249)
60. In a right triangle, the hypotenuse has length 13 and one leg has length 5. If θ is the angle opposite the leg of length 5, which of the following gives the value of sin(2θ)?