5. 100 400 500 400 500 400 500 300 200 100 Essential Skills Systems Functions & Inequalities Quadratics Potpourri

6. 100 400 500 400 500 400 500 300 200 100 Essential Skills Systems Functions & Inequalities Quadratics Potpourri

7. Essential Skills - $100 There is the same number of boys and girls on a school bus when it departs from school. At the first stop, 4 boys get off the bus and nobody gets on. After the first stop, there are twice as many girls as boys on the bus. How many girls are on the bus?

8. Essential Skills - $100 Answer

9. Essential Skills - $200 In the figure below, three line segments meet at a point to form three angles. What is the value of x? (Not drawn to scale.)

10. Essential Skills - $200 Answer

11. Essential Skills - $300 If p is an integer and 3 is the remainder when 2p + 7 is divided by 5, then p could be (A) 2 (B) 3 (C) 4 (D) 5 (E) 6

12. Essential Skills - $300 Answer (B) 3

13. Essential Skills - $400

14. Essential Skills - $400 Answer

15. Essential Skills - $500 How old was a person exactly 1 year ago if exactly x years ago the person was y years old?

16. Essential Skills - $500 Answer

17. Systems - $100

18. Systems - $100 Answer 3t3t

19. Systems - $200 For how many ordered pairs of positive integers (x, y) is

20. Systems - $200 Answer one

21. Systems - $300 What is the value of k that satisfies both equations below?

22. Systems - $300 Answer 13

23. Systems - $400 Edna and Nancy leave the house of a common friend at the same time and walk for 4 hours. Edna walks due east at the average rate of 4 kilometers per hour and Nancy walks due north at the average rate of 3 kilometers per hour. What is the straight-line distance between them, in kilometers, at the end of the 4 hours?

24. Systems - $400 Answer 20

25. Systems - $500 In the xy-plane, line l passes through the origin and is perpendicular to the line 4x + y = k, where k is a constant. If the two lines intersect at the point (t, t + 1), what is the value of t?

26. Systems - $500 Answer

27. Functions & Inequalities - $100 The figure below shows the graph of the function h. Which of the following is closest to h(5)? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5

28. Functions & Inequalities - $100 Answer (B) 2

29. Functions & Inequalities - $200 In the xy-coordinate plane, line l is perpendicular to the y-axis and passes through the point (5, −3). What is an equation of line l?

30. Functions & Inequalities - $200 Answer y = –3

31. Functions & Inequalities - $300 The total daily profit p, in dollars, from producing and selling x units of a certain product is given by the function p(x) as defined below, where b is a constant. If 300 units were produced and sold yesterday for a total profit of $1,900, what is the value of b?

32. Functions & Inequalities - $300 Answer 200

33. Functions & Inequalities - $400 A regulation for riding a certain amusement park ride requires that a child be between 30 inches and 50 inches tall. Write an absolute value inequality that can be used to determine whether 0r not a child’s height h satisfies the regulation for this ride.

34. Functions & Inequalities - $400 Answer

35. Functions & Inequalities - $500

36. Functions & Inequalities - $500 Answer (E) −8 ≤ xy ≤ 24

37. Quadratics - $100 For what value of x is the statement above FALSE? (A) −3 (B) 0 (C) 1/3 (D) 1 (E) For no value of x

38. Quadratics - $100 Answer (B) 0

39. Quadratics - $200 The figure above shows the graph of a quadratic function f that has a minimum at the point (1, 1). If f(b) = f(3), what is the value of b?

40. Quadratics - $200 Answer

41. Quadratics - $300 In the figure above, PQRS is a rectangle, and points Q and R lie on the graph of y = ax 2, where a is a constant. If the perimeter of PQRS is 10, what is the value of a? P QR S

42. Quadratics - $300 Answer 3

43. Quadratics - $400 *Daily Double!* The table above gives values of the quadratic function f for selected values of x. Write the quadratic function that defines f. x0123 f(x)f(x)12510

44. Quadratics - $400 Answer

45. Quadratics - $500 At time t = 0, a ball was thrown upward from an initial height of 6 feet. Until the ball hit the ground, its height, in feet, after t seconds was given by the function h below, in which c and d are positive constants. If the ball reached its maximum height of 106 feet at time t = 2.5, what was the height, in feet, of the ball at time t = 1?

46. Quadratics - $500 Answer

47. Potpourri - $100 According to a certain recipe, 25 pounds of flour are needed to make 300 rolls. At this rate, how many pounds of flour are needed to make 12 rolls?

48. Potpourri - $100 Answer 1 pound

49. Potpourri - $200

50. Potpourri - $200 Answer 20

51. Potpourri - $300 A “simple square” is any integer greater than 1 that has only three positive integer factors – itself, its square root, and 1. Which of the following is a simple square? (A)121 (B) 100 (C) 81 (D) 64 (E) 33

52. Potpourri - $300 Answer

53. Potpourri - $400 The perimeter of a rectangular plot of land is 250 meters. If the length of one side of the plot is 40 meter, what is the area of the plot, in square meters?

54. Potpourri - $400 Answer 3400

55. Potpourri - $500 If p, r, and s are three different prime numbers greater than 2, and n = p × r × s, how many positive Factors, including 1 and n, does n have?

56. Potpourri - $500 Answer

58. Final Jeopardy Category: Systems

59. Final Jeopardy Question A school ordered $600 worth of lightbulbs. Some of the lightbulbs cost $1 each and the others cost $2 each. If twice as many $1 bulbs as $2 bulbs were ordered, how many lightbulbs were ordered altogether?

60. Final Jeopardy Answer