Math

1. Mia recorded the high temperatures (in °F) for 5 days: 72, 68, 85, 91, and 74. What is the median high temperature for those 5 days?

2. A store marks up the wholesale price of an item by 40% to set the retail price. If the wholesale price of a jacket is $65, what is the retail price?

3. The ratio of cats to dogs at an animal shelter is 3:5. If there are 48 cats at the shelter, how many dogs are there?

4. In a survey of 120 students, 45 said they prefer science, 35 prefer math, and the rest prefer English. What percent of students prefer English?

5. A recipe calls for 2¾ cups of flour. If Derrick wants to make 3 times the recipe, how many cups of flour does he need?

6. What is the least common multiple (LCM) of 12, 18, and 24?

7. Theo has $240 in his savings account. He withdraws 15% of his balance each month for 2 months. How much money remains in his account after 2 months?

8. If 3(2x − 4) = 18, what is the value of x?

9. Which of the following expressions is equivalent to 2x² + 7x + 3?

10. If y = −3x + 7 and x = −2, what is the value of y?

11. For all values of n, which of the following is equivalent to (3n − 5)²?

12. If 5a + 3b = 29 and b = 3, what is the value of a?

13. What are the solutions to the equation x² − 5x − 14 = 0?

14. The function f(x) = −2x² + 8x − 3 has a maximum value. What is that maximum value?

15. If log₃(x) = 4, what is the value of x?

16. For which value(s) of x is the expression (x + 4)/(x² − x − 6) undefined?

17. A rectangle has a length of 14 cm and a width of 9 cm. What is the length of the diagonal of the rectangle, in centimeters?

18. 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?

19. A circle has a circumference of 20π inches. What is the area of the circle, in square inches?

20. 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?

21. A trapezoid has parallel bases of length 10 feet and 16 feet, and a height of 7 feet. What is the area of the trapezoid, in square feet?

22. A rectangular prism has a length of 8 cm, a width of 5 cm, and a height of 6 cm. What is the total surface area of the prism, in square centimeters?

23. In the figure below (described in text): Triangle ABC has a right angle at C. Side AC = 5 and side BC = 12. What is the perimeter of triangle ABC?

24. What is the slope of the line passing through the points (−3, 7) and (5, −1)?

25. What is the midpoint of the segment with endpoints (−4, 6) and (10, −2)?

26. Which of the following is the equation of a line with a slope of −2 and a y-intercept of 5?

27. What is the distance between the points (1, 4) and (7, 12)?

28. The graph of which of the following equations is a circle centered at (3, −2) with radius 6?

29. In a right triangle, the hypotenuse has length 17 and one leg has length 8. What is the sine of the angle opposite the leg of length 8?

30. For angle θ in a right triangle, cos θ = 5/13. What is the value of sin θ?

31. A store sells notebooks in packs of 4 and pens in packs of 7. Marta wants to buy the same number of notebooks and pens with no leftovers. What is the minimum total number of notebooks and pens she must buy?

32. A recipe calls for 2.5 cups of flour to make 24 cookies. At this rate, how many cups of flour are needed to make 60 cookies?

33. The ratio of boys to girls in a club is 3:5. If there are 40 students total in the club, how many more girls than boys are in the club?

34. A savings account earns simple interest at an annual rate of 4.5%. If an initial deposit of $2,400 is made, what is the total amount in the account after 3 years?

35. Which of the following is equivalent to |3 − 8| − |−2 + 7|?

36. A number is increased by 30%, then the result is decreased by 20%. What percent of the original number is the final result?

37. A bag contains marbles that are red, blue, or green. The probability of drawing a red marble is 1/4 and the probability of drawing a blue marble is 5/12. If there are 48 marbles in the bag, how many green marbles are there?

38. If 3(2x − 4) + 5 = 2(x + 3) − 1, what is the value of x?

39. Which of the following is equivalent to (3x − 2)² − (x + 4)²?

40. A line passes through the points (−3, 7) and (1, −1). What is the equation of the line in slope-intercept form?

41. If x² − 6x + k = 0 has exactly one real solution, what is the value of k?

42. The sum of three consecutive even integers is 78. What is the largest of the three integers?

43. If f(x) = 2x² − 3x + 1 and g(x) = x + 4, what is f(g(−2))?

44. What are the solutions to 2x² + 5x − 3 = 0?

45. For all nonzero values of a and b, which of the following is equivalent to (a³b⁻²)/(a⁻¹b³)?

46. The graph of y = f(x) is translated 3 units to the left and 5 units down. If f(x) = x², which of the following represents the translated function?

47. For which value(s) of x is the expression (x² − 9)/(x² − x − 6) undefined?

48. In the figure below (described here), 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 cut by a diagonal transversal, with the two described angles on the same side between the parallel lines.]

49. A right triangle has legs of length 7 cm and 24 cm. What is the length, in centimeters, of the altitude drawn from the right angle to the hypotenuse?

50. A circle has a diameter whose endpoints are (−4, 1) and (6, 1). What is the area of the circle, in square units?

51. In triangle RST, the measure of angle R is 48° and the measure of angle S is 67°. The side opposite angle T is 14 units long. Which expression gives the length of the side opposite angle R?

52. A rectangular garden has a perimeter of 56 meters. If the length is 6 meters more than twice the width, what is the area of the garden in square meters?

53. In the figure below, a regular hexagon is inscribed in a circle of radius 10 cm. What is the perimeter of the hexagon? [Figure description: A circle with a regular hexagon inscribed inside it, with all six vertices touching the circle. The radius of the circle is labeled 10 cm.]

54. Two similar triangles have corresponding sides in the ratio 3:7. If the area of the smaller triangle is 27 square inches, what is the area of the larger triangle, in square inches?

55. What is the distance between the points (−5, 2) and (3, −4)?

56. Line m passes through (2, −3) and is perpendicular to the line 4x − 2y = 8. What is the equation of line m?

57. Which of the following is the equation of a circle with center (−3, 5) and radius 6?

58. A line segment has endpoints P(1, 4) and Q(9, −2). What are the coordinates of the point that divides PQ in the ratio 3:1 from P to Q?

59. In right triangle ABC with the right angle at C, if angle A = 34° and BC = 11, what is the length of AB to the nearest tenth? [Figure description: Right triangle ABC with the right angle at vertex C. Angle A is at the left vertex, angle B is at the top right, and the right angle is at C. BC is the side opposite angle A.]

60. In triangle XYZ (not necessarily a right triangle), XY = 8, YZ = 11, and the measure of angle Y = 50°. What is the area of triangle XYZ to the nearest tenth of a square unit?