1. Mia recorded her daily steps for 4 days: 8,200, 6,500, 9,100, and 7,400. On the fifth day she walked x steps. The mean number of steps over all 5 days is 7,800. What is the value of x?
2. In the Venn diagram below, circles T, B, and S represent students who play tennis, basketball, and soccer, respectively. The diagram shows the following values in each region: T only = 9, B only = 14, S only = 7, T and B only = 3, T and S only = 5, B and S only = 6, all three = 2, and none = 4. How many of the students represented in the diagram play basketball?
(Figure description: Three overlapping circles labeled T, B, and S with the values listed above in their respective regions.)
3. A bag contains 4 red marbles, 7 blue marbles, and 9 green marbles. One marble is drawn at random. What is the probability that the marble drawn is NOT green?
4. A store is offering a 35% discount on all jackets. If a jacket originally costs $140, what is the sale price after the discount?
5. The whole numbers 1 through 20 were each written on separate cards and placed in a box. One card is drawn at random. What is the probability that the number on the card is a multiple of 4?
6. Marcus earns $14.50 per hour and works 32 hours per week. His employer deducts 18% of his weekly earnings for taxes and benefits. How much does Marcus take home each week after deductions?
7. Three friends split a restaurant bill equally. The bill was $87.60, and they each left a $6.00 tip. What was the total amount each person paid?
8. Which of the following expressions is equivalent to x² + 3x − 28?
9. If 8y = 3x + 4, then x = ?
10. A car rental company charges a flat fee of $25 plus $0.18 per mile driven. Daria paid a total of $61.00 for her rental. How many miles did she drive?
11. Which of the following is equivalent to 3(2x − 5) − 4(x + 1)?
12. If a + b = 12 and a − b = 4, what is the value of a² − b²?
13. Solve for x: 5(x − 3) = 2x + 9
14. What are the solutions to the equation x² − 7x + 10 = 0?
15. Which of the following values of x is a solution to the system of equations below?
3x + y = 11
x − 2y = 2
16. For which value(s) of x is the expression (x² − 9)/(x² − x − 6) undefined?
17. A ball is dropped from a height and its height h(t) in meters after t seconds is given by h(t) = −5t² + 20. At what time t (in seconds) does the ball hit the ground?
18. In triangle PQR, the measure of angle P is 47° and the measure of angle Q is 68°. What is the measure of angle R?
19. A rectangle has a length of 15 cm and a width of 8 cm. What is the length of its diagonal?
20. A circle has a diameter of 14 inches. What is the area of the circle, in square inches? (Use π ≈ 3.14)
21. 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?
22. A trapezoid has parallel sides of length 10 cm and 16 cm, and a height of 7 cm. What is the area of the trapezoid, in square centimeters?
23. Triangle ABC is similar to triangle DEF. In triangle ABC, the sides have lengths 6, 9, and 12. In triangle DEF, the shortest side has length 8. What is the length of the longest side of triangle DEF?
24. A right triangle has legs of length 5 and 12. What is the perimeter of the triangle?
25. A regular hexagon has a side length of 6 cm. What is its perimeter, in centimeters?
26. What is the distance between the points (1, 3) and (7, 11) in the standard (x, y) coordinate plane?
27. What is the slope of the line passing through the points (−2, 5) and (4, −7)?
28. A line in the standard (x, y) coordinate plane has equation 4x − 2y = 8. What is the y-intercept of this line?
29. What is the midpoint of the segment with endpoints (−6, 2) and (4, 10) in the standard (x, y) coordinate plane?
30. Which of the following is the equation of a circle centered at (3, −2) with a radius of 5?
31. A store is having a sale where every item is marked down 35%. If a jacket originally costs $124.00, what is the sale price of the jacket?
DO YOUR FIGURING HERE.
32. The ratio of red marbles to blue marbles in a bag is 5:8. If there are 104 blue marbles in the bag, how many red marbles are in the bag?
DO YOUR FIGURING HERE.
33. Renata earns $18.50 per hour for regular time and 1.5 times that rate for overtime. Last week she worked 40 regular hours and 6 overtime hours. What were her total earnings for the week?
DO YOUR FIGURING HERE.
34. A number is chosen at random from the integers 1 through 20. What is the probability that the number chosen is a perfect square?
DO YOUR FIGURING HERE.
35. The table below shows the number of books read by four students over the summer.
Student | Books Read
Alicia | 14
Brennan | 9
Carlos | 17
Denise | 12
What is the positive difference between the mean and the median number of books read?
DO YOUR FIGURING HERE.
36. A recipe calls for 2¾ cups of flour to make 24 cookies. How many cups of flour are needed to make 60 cookies?
DO YOUR FIGURING HERE.
37. If 15% of a number is 33, what is 40% of the same number?
DO YOUR FIGURING HERE.
38. What is the solution set for |3x − 7| = 14?
DO YOUR FIGURING HERE.
39. A rectangle has a length that is 3 more than twice its width. If the perimeter of the rectangle is 78 inches, what is the width of the rectangle, in inches?
DO YOUR FIGURING HERE.
40. Which of the following is equivalent to (3x² − 4x + 1) − (x² + 5x − 8)?
DO YOUR FIGURING HERE.
41. If f(x) = 3x² − 2x + 5, what is the value of f(−3)?
DO YOUR FIGURING HERE.
42. A number n satisfies the inequality −3(n + 4) > 2n − 2. Which of the following gives all possible values of n?
DO YOUR FIGURING HERE.
43. For all x ≠ 0, which of the following is equivalent to (6x³ − 9x² + 3x) ÷ 3x?
DO YOUR FIGURING HERE.
44. What are the solutions to the quadratic equation 2x² − 5x − 3 = 0?
DO YOUR FIGURING HERE.
45. A sequence is defined by aₙ = 3aₙ₋₁ − 4, where a₁ = 5. What is the value of a₄?
DO YOUR FIGURING HERE.
46. Which of the following is equivalent to log₂(32x³)?
DO YOUR FIGURING HERE.
47. The graph of a parabola has vertex (−2, 5) and passes through the point (0, 1). Which of the following equations represents this parabola?
DO YOUR FIGURING HERE.
48. In the figure below, two parallel lines are cut by a transversal. One angle formed measures (4x + 15)° and its co-interior (same-side interior) angle measures (5x − 6)°. What is the value of x?
DO YOUR FIGURING HERE.
49. A right circular cylinder has a radius of 6 cm and a height of 10 cm. A cone with the same base and the same height is removed from inside the cylinder. What is the remaining volume, in cubic centimeters?
DO YOUR FIGURING HERE.
50. In the figure below, triangle PQR is inscribed in a circle. If arc PQ = 110° and arc QR = 130°, what is the measure of angle QPR?
Note: The arc measures are the central angle measures of the respective arcs.
DO YOUR FIGURING HERE.
51. In right triangle ABC with the right angle at C, AC = 9 and BC = 12. Point D is on hypotenuse AB such that CD is perpendicular to AB. What is the length of CD?
DO YOUR FIGURING HERE.
52. A regular hexagon has a perimeter of 72 cm. What is the area of the hexagon, in square centimeters?
DO YOUR FIGURING HERE.
53. Two circles have the same center. The larger circle has a radius of 10 and the smaller circle has a radius of 6. What is the area of the region between the two circles (the annulus)?
DO YOUR FIGURING HERE.
54. In the figure below, a square is inscribed in a circle such that each vertex of the square touches the circle. If the side of the square is 8 cm, what is the area of the circle, in square centimeters?
DO YOUR FIGURING HERE.
55. What is the distance between the points (−3, 4) and (5, −2) in the standard (x, y) coordinate plane?
DO YOUR FIGURING HERE.
56. Line ℓ passes through the points (−4, 1) and (2, −5). Which of the following is the equation of line ℓ?
DO YOUR FIGURING HERE.
57. In the standard (x, y) coordinate plane, the midpoint of segment AB is (3, −1). If the coordinates of point A are (−1, 4), what are the coordinates of point B?
DO YOUR FIGURING HERE.
58. Which of the following is the equation of the circle with center (−2, 3) and radius 5 in the standard (x, y) coordinate plane?
DO YOUR FIGURING HERE.
59. In right triangle XYZ, angle Z = 90°, XZ = 7, and YZ = 24. What is the value of sin(∠X)?
DO YOUR FIGURING HERE.
60. For 0° ≤ θ < 360°, which of the following gives all values of θ such that cos θ = −√3/2?
DO YOUR FIGURING HERE.