Math

1. Daniela earned the following amounts babysitting over 5 weekends: $45, $60, $30, $75, and $40. What is the mean amount she earned per weekend?

2. In the Venn diagram below, circle A represents students who play guitar, circle B represents students who play piano, and circle B represents students who play drums (circle C). The numbers in the regions are: only A = 8, only B = 11, only C = 6, A and B only = 3, A and C only = 2, B and C only = 4, all three = 1. How many of the 35 total students play piano?

3. A bag contains 4 red marbles, 6 blue marbles, and 10 green marbles. If one marble is randomly selected from the bag, what is the probability that it is blue?

4. A store is having a 30% off sale. If a jacket originally costs $120, what is the sale price of the jacket?

5. Which of the following is equivalent to 3^4 × 3^2?

6. The ratio of boys to girls in a classroom is 3:5. If there are 24 boys in the classroom, how many girls are there?

7. What is the least common multiple (LCM) of 12 and 18?

8. If 3x + 7 = 28, what is the value of x?

9. Which of the following expressions is equivalent to x² + 5x + 6?

10. If 4y − 3 = 2y + 9, what is the value of y?

11. A car rental company charges a flat fee of $25 plus $0.15 per mile driven. If Terrence paid a total of $52.00, how many miles did he drive?

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

13. What are the solutions to the equation x² − 7x + 12 = 0?

14. If f(x) = 2x² − 3x + 1, what is f(−2)?

15. Which of the following is the solution set to the system of equations: 3x + y = 10 and x − y = 2?

16. The expression √(75) simplifies to which of the following?

17. In triangle PQR, angle P measures 48° and angle Q measures 67°. What is the measure of angle R?

18. A rectangle has a length of 14 cm and a width of 9 cm. What is the area of the rectangle in square centimeters?

19. A circle has a radius of 6 inches. What is the circumference of the circle, in 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 12. What is the length of the hypotenuse?

22. What is the area, in square feet, of a trapezoid with parallel bases of 8 feet and 14 feet, and a height of 5 feet?

23. A square has a perimeter of 52 meters. What is the area of the square in square meters?

24. What is the midpoint of the line segment with endpoints (−2, 6) and (8, −4)?

25. What is the slope of the line passing through the points (2, 5) and (6, 13)?

26. Which of the following is the equation of the line with slope −3 and y-intercept 7?

27. What is the distance between the points (1, 2) and (4, 6)?

28. The graph of the equation y = x² − 4 crosses the x-axis at which of the following pairs of x-values?

29. In a right triangle, the side adjacent to angle θ has length 5 and the hypotenuse has length 13. What is sin θ?

30. For an acute angle β, cos β = 3/5. What is the value of tan β?

31. A store is having a sale where all items are discounted 35%. If a jacket originally costs $124.00, what is the sale price of the jacket? DO YOUR FIGURING HERE.

32. The ratio of teachers to students at Westfield Academy is 2:27. If there are 486 students enrolled, how many teachers are there? DO YOUR FIGURING HERE.

33. A recipe requires 2¾ cups of flour to make 24 cookies. At this rate, how many cups of flour are needed to make 96 cookies? DO YOUR FIGURING HERE.

34. The table below shows the number of books read by 5 students over the summer. Student | Books Read Anika | 14 Bryce | 9 Carlos | 17 Diana | 6 Evan | 19 What is the positive difference between the median and the mean number of books read? DO YOUR FIGURING HERE.

35. A number is chosen at random from the integers 1 through 50, inclusive. What is the probability that the number chosen is a multiple of 6? DO YOUR FIGURING HERE.

36. A store buys an item for $45 and marks it up 60% to set the retail price. During a clearance sale, the item is then discounted 25% off the retail price. What is the clearance sale price? DO YOUR FIGURING HERE.

37. If 40% of a number equals 70, what is 15% of that number? DO YOUR FIGURING HERE.

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

39. Which of the following expressions is equivalent to (3x − 7)²? DO YOUR FIGURING HERE.

40. If f(x) = 2x² − 3x + 1, what is f(−2)? DO YOUR FIGURING HERE.

41. The sum of three consecutive even integers is 138. What is the largest of the three integers? DO YOUR FIGURING HERE.

42. A train travels d miles in h hours. Which of the following represents the number of miles the train travels in 3 hours at the same rate? DO YOUR FIGURING HERE.

43. What are the solutions to x² − 5x − 14 = 0? DO YOUR FIGURING HERE.

44. The expression (x² − 9)/(x² − x − 6) simplifies to which of the following for all values where the expression is defined? DO YOUR FIGURING HERE.

45. If log₃(x) = 4, what is the value of log₃(9x)? DO YOUR FIGURING HERE.

46. For the function g(x) = √(3x − 12), what is the domain of g? DO YOUR FIGURING HERE.

47. If the two roots of a quadratic equation are 5 and −3, which of the following could be the quadratic equation? DO YOUR FIGURING HERE.

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 cut by a diagonal transversal, with co-interior angles labeled on the same side between the parallel lines.) DO YOUR FIGURING HERE.

49. A right triangle has legs measuring 9 cm and 12 cm. What is the area of a square whose side length equals the hypotenuse of this triangle? DO YOUR FIGURING HERE.

50. A circle has a circumference of 20π inches. What is the area of the circle, in square inches? DO YOUR FIGURING HERE.

51. In the figure below, triangle PQR is isosceles with PQ = PR. The measure of angle QPR is 48°. A line segment QS is drawn perpendicular to PR, where S is on PR. What is the measure of angle SQR? (Figure description: Triangle PQR with PQ = PR. Angle QPR = 48°. QS is drawn from Q perpendicular to PR, meeting PR at point S.) DO YOUR FIGURING HERE.

52. A rectangular garden has a length that is 8 meters more than twice its width. If the perimeter of the garden is 88 meters, what is the area of the garden in square meters? DO YOUR FIGURING HERE.

53. A rectangular garden has a length that is 7 meters more than twice its width. If the perimeter of the garden is 86 meters, what is the area of the garden in square meters? DO YOUR FIGURING HERE.

54. What is the distance between the points (−3, 5) and (9, −4) in the standard (x, y) coordinate plane? DO YOUR FIGURING HERE.

55. Line m passes through the points (2, −1) and (6, 7). Line n is perpendicular to line m and passes through the point (4, 3). Which of the following is an equation of line n? DO YOUR FIGURING HERE.

56. A circle in the standard (x, y) coordinate plane has center (−2, 4) and passes through the point (4, 12). What is the equation of this circle? DO YOUR FIGURING HERE.

57. In the standard (x, y) coordinate plane, the midpoint of segment AB is (3, −2). If point A has coordinates (−1, 4), what are the coordinates of point B? DO YOUR FIGURING HERE.

58. In a right triangle, the side adjacent to angle θ has length 5, and the hypotenuse has length 13. What is the value of sin θ + tan θ? DO YOUR FIGURING HERE.

59. The function f(x) = 3sin(2x) has what amplitude and period, respectively? DO YOUR FIGURING HERE.

60. In the figure below, a regular hexagon has a perimeter of 72 cm. What is the area of the hexagon in square centimeters? (Figure description: A regular hexagon with all sides equal and all interior angles equal to 120°.) DO YOUR FIGURING HERE.