1. Mia recorded the following temperatures (in °F) over 6 days: 52, 67, 71, 48, 63, and 75. What is the mean temperature, in °F, for these 6 days?
2. A store sells notebooks for $3 each and pens for $1.50 each. Jordan buys 4 notebooks and 6 pens. How much does Jordan spend in total?
3. A bag contains 5 red marbles, 3 blue marbles, and 7 green marbles. If one marble is selected at random, what is the probability that it is NOT green?
4. The Venn diagram below shows students enrolled in Art (A) and Music (M) classes. Circle A contains 14 students only in Art, circle M contains 9 students only in Music, and the overlapping region contains 6 students in both. How many total students are represented in the diagram?
[Figure: Two overlapping circles labeled A and M. The left region of A shows 14, the overlap shows 6, and the right region of M shows 9.]
5. What is the least common multiple (LCM) of 12 and 18?
6. A recipe calls for 2¾ cups of flour. If Darnell wants to make 3 batches of the recipe, how many cups of flour does he need in total?
7. On a number line, point P is located at −4 and point Q is located at 9. What is the distance between P and Q?
8. If 3x + 7 = 22, what is the value of x?
9. Which of the following expressions is equivalent to 2(x + 4) − 3(x − 1)?
10. If y = 4x − 3, what is the value of y when x = −2?
11. Which of the following is equivalent to x² − 9x + 20?
12. A gym charges a one-time membership fee of $40 plus $25 per month. Which equation represents the total cost C, in dollars, for m months of membership?
13. What are the solutions to the equation x² − 5x − 14 = 0?
14. For f(x) = 2x² − 3x + 1, what is f(−1)?
15. Which of the following is equivalent to (3x²y³)²?
16. The system of equations below is given. What is the value of y in the solution to this system?
3x + y = 11
x − y = 1
17. A rectangle has a length of 12 cm and a width of 7 cm. What is the perimeter of the rectangle, in centimeters?
18. In triangle DEF, the measure of ∠D is 48° and the measure of ∠E is 75°. What is the measure of ∠F?
19. A circle has a diameter of 10 inches. What is the area of the circle, in square inches? (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. The figure below shows a trapezoid with 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?
[Figure: A trapezoid with top base labeled 8 cm, bottom base labeled 14 cm, and height labeled 5 cm.]
23. A square has a perimeter of 52 feet. What is the area of the square, in square feet?
24. What is the slope of the line passing through the points (2, 5) and (6, 13)?
25. Which of the following is the equation of a line with slope −3 and y-intercept 7?
26. What is the midpoint of the segment with endpoints (−4, 6) and (10, −2)?
27. A line has the equation 4x − 2y = 12. What is the y-intercept of this line?
28. What is the distance between points (1, 2) and (4, 6)?
29. In a right triangle, the side adjacent to angle θ has length 8 and the hypotenuse has length 17. What is cos θ?
30. In a right triangle, the side opposite to angle β has length 5 and the hypotenuse has length 13. What is the value of tan β?
31. A store sells a jacket originally priced at $120. The jacket is first discounted by 20%, and then the discounted price is reduced by an additional 15%. What is the final price of the jacket after both discounts?
32. A recipe requires 2¾ cups of flour for every 1½ dozen cookies. How many cups of flour are needed to make exactly 5 dozen cookies?
33. The ratio of red marbles to blue marbles in a bag is 3:7. If there are 84 blue marbles, how many total marbles are in the bag?
34. Devlin earns a weekly base salary of $480 plus a 6% commission on all sales above $2,000. In a week where his total sales were $5,500, what were his total earnings for that week?
35. A number N is 40% greater than 70. A second number M is 30% less than N. What is M?
36. The table below shows the scores of 6 students on a quiz:
Student: A, B, C, D, E, F
Score: 72, 85, 91, 68, 85, 79
What is the positive difference between the median and the mode of these scores?
37. If 3 printers can print 1,800 pages in 4 hours, how many hours would it take 5 printers to print 3,000 pages, assuming all printers work at the same constant rate?
38. If 4(2x − 3) − 2(x + 5) = 3x + 7, what is the value of x?
39. What are the solutions to x² − 7x − 18 = 0?
40. If f(x) = 3x² − 2x + 5, what is the value of f(−3)?
41. A line passes through the points (2, 5) and (−1, −4). What is the equation of this line?
42. Which of the following is equivalent to (3x − 2)² − (x + 4)(x − 4)?
43. The function g(x) = 2x² + bx − 15 has a zero at x = 3. What is the other zero of g(x)?
44. If log₄(x) + log₄(x − 6) = 2, what is the positive value of x?
45. For what value(s) of k does the equation kx² − 8x + 4 = 0 have exactly one real solution?
46. Which of the following is the inverse function of f(x) = (3x + 1)/5 ?
47. An arithmetic sequence has first term a₁ = 7 and common difference d = −3. What is the sum of the first 12 terms of this sequence?
48. In the figure described below, two parallel lines m and n are cut by a transversal. One of the angles formed at line m measures (5x + 12)° and its co-interior (same-side interior) angle at line n measures (3x + 28)°. What is the value of x?
[Figure: Two horizontal parallel lines m and n cut by a diagonal transversal, with the described angles on the same side between the lines.]
49. A right triangle has legs of length 9 cm and 12 cm. What is the area of the semicircle whose diameter equals the hypotenuse of this triangle?
50. In the figure below, triangle PQR is isosceles with PQ = PR. The measure of angle QPR is 48°. Point S lies on QR such that PS bisects angle QPR. What is the measure of angle PSQ?
[Figure: Isosceles triangle PQR with vertex angle at P = 48°. PS is the angle bisector from P to QR.]
51. A trapezoid has parallel sides of length 8 inches and 14 inches. The height of the trapezoid is 6 inches. What is the area of the trapezoid, in square inches?
52. A circle with center O has a chord AB of length 16 cm. The perpendicular distance from O to chord AB is 6 cm. What is the radius of the circle, in centimeters?
53. Two circles are externally tangent to each other. The radius of the larger circle is 9 cm and the radius of the smaller circle is 4 cm. A common external tangent touches both circles. What is the length of the segment of this tangent between the two points of tangency?
[Figure: Two externally tangent circles with a common external tangent line touching each circle at one point.]
54. In the figure described, a regular hexagon has a side length of 6 cm. What is the area of the hexagon in square centimeters?
[Figure: A regular hexagon with one side labeled 6 cm.]
55. What is the distance between the points (−3, 7) and (5, −2) in the standard coordinate plane?
56. A circle in the standard coordinate plane has center (−2, 5) and passes through the point (3, −7). What is the equation of this circle?
57. Line ℓ has equation 4x − 3y = 12. Which of the following is the equation of a line perpendicular to ℓ that passes through the point (8, 1)?
58. In the standard (x,y) coordinate plane, what is the midpoint of the segment with endpoints (2a, b−3) and (4a, 3b+1)?
59. In right triangle DEF, angle F is the right angle, DE = 26, and EF = 10. What is the value of sin(D) + cos(D)?
60. For 0° ≤ θ < 360°, which of the following gives ALL values of θ where sin θ = −(√3)/2?