1. A point at (−4,10) in the standard (x,y) coordinate plane is translated right 10 coordinate units and down 4 coordinate units. What are the coordinates of the point after the translation?
2. A function, f, is defined by f(x,y)=3x²−2y. What is the value of f(2,3)?
3. What is the value of x when 9 − 11x = 13 − 9x is true?
4. A company reimburses its employees for use of a personal vehicle for company travel at the rate of $10.00 per day plus $0.445 per mile. Jorge, an employee of the company, traveled exactly 120 miles on Monday and exactly 100 miles on Tuesday using his personal vehicle for company travel. For these 2 days, what was the amount of Jorge’s reimbursement?
5. Given that a n b = a² + b − _a_, what is the value of an b when a = 5 and b = _1_?
6. Before opening her lemonade stand, Haley purchased lemonade mix for $2.30 and a package of cups for $1.50. Haley sells each cup of lemonade for $0.50. Which of the following expressions gives Haley’s total profit, in dollars, from selling x cups of lemonade?
7. In triangle ABC, the measure of ∠B is 90°, and the measure of ∠A is 4 times the measure of ∠C. What is the measure of ∠C?
8. The Sheffield High School girls’ softball team currently has a record of 11 wins, 8 losses, and 0 ties. What is the least number of its remaining 14 games the team must win to finish the season winning more than 50% of all the team’s games?
9. A line in the standard (x,y) coordinate plane passes through the point (3,4). The slope of the line:
10. The probability that a certain basketball player will make any given free throw is 0.8. Based on this probability, how many free throws should this player expect to have to attempt in order to make 20 free throws?
11. Jerrica drives to and from school once per day in a car that travels 20 miles on 1 gallon of gas. A trip from Jerrica’s house to school and back is 6 miles. Gas costs $5 per gallon. Suppose Jerrica rides her bike to and from school for 10 school days. How much money will Jerrica save on gas by not driving to and from school those days?
12. If x > 0 and 2x² + 5x = 3, what is the value of x?
13. A 5-foot awning extends 2 feet horizontally over the entrance to the vertical building shown below. Which of the following expressions has a value equal to the measure of the angle θ between the building and the awning?
14. What is the mean, in seconds, of the times listed in the table for the 200-meter dash?
15. Each ticket for the track meet had a price of $8. Tickets were sold for exactly 85% of the stadium’s capacity. How many dollars did SHS collect through ticket sales for this meet?
16. The circular region containing the track and the infield (the grassy region enclosed by the track) is divided into sectors that each have a central angle of 60°. Each sector is a different color. What is the area, in square meters, of each sector?
17. The solution set of the system of inequalities below includes which of the following (x,y) pairs? x > y, x + y > 3
18. The area of the trapezoid shown below is 20 square feet, the height is 5 feet, and the length of one base is 2 feet. What is b, the length of the other base, in feet?
19. A square and a rectangle have the same area. The length of the rectangle is 196 centimeters, and the width of the rectangle is 4 centimeters. What is the length, in centimeters, of a side of the square?
20. Let (3x − 1)(2x − 5) = ax² + bx + c. What is the value of a + b + c?
21. For a ≠ 0 and any real number n, the expression a²/n + 1 is equivalent to which of the following?
22. A basket contains 3 red apples, 4 green apples, and 2 yellow apples. An apple is drawn at random, eaten, and then another apple is randomly drawn. If the first apple is red, what is the probability the second apple is yellow?
23. Which of the following numbers is irrational?
24. The expression 7[3 −2(x−4)] is equivalent to:
25. Rate of change is defined to be the vertical change between any 2 points divided by the horizontal change between the same 2 points. A function containing the point (0,1) has a constant rate of change equal to _3_. The function is shown in one of the standard (x,y) coordinate plane graphs below. Which one?
26. What rational number is exactly halfway between _3_8 and _7__ on the real number line?
27. One neon sign flashes every 4 seconds, and another neon sign flashes every 6 seconds. At a certain instant, the 2 signs flash at the same time. How many seconds elapse until the 2 signs next flash at the same time?
28. Jerry will purchase 42 cubic feet of gravel for his patio. The local rock quarry will sell gravel in the exact volume needed by the customer. What is the cost, in dollars, to purchase the gravel from the local rock quarry?
29. What is the area, in square feet, of the top surface of Jerry’s patio?
30. Jerry will use bags of concrete mix to make the step. Each bag makes 0.4 cubic feet of concrete. To the nearest 0.1 bag, how many bags of concrete mix will he need for the step?
31. A carpenter needs a board 35_5_ inches long and another board 27_1_ inches long. Both pieces are to be cut from a single board 72 inches long. Together, the 2 cuts subtract a total of _1_ inch. What length of board is left over, in inches?
32. Given matrices A and B such that A = 3−7 2 44 and B−A=36 7 44 , what is matrix B?
33. A Chinese language proficiency test was given to 60 university students. The students’ scores were recorded as integers. The table below shows the frequency and cumulative frequency of test scores in certain ranges. To be classified as proficient, a student must score 70 or higher on the test. What is the ratio of the number of students who were classified as proficient to the number who were NOT classified as proficient?
34. A group of 4 friends decide to go to a movie. After buying their tickets, they find 5 empty chairs in the theater. How many different seating arrangements are possible if the 4 friends sit, at most 1 person per chair, in these 5 chairs?
35. Carina rolls 2 cubes. Each has the whole numbers from 1 through 6 on its faces, 1 per face. The faces of each cube are equally likely to land up. What is the probability that the sum of the numbers on the faces landing up is 3 or more?
36. In the figure _s_h_own _b_e_low, AB i DE, C is the intersection of AE and BD, ∠D is a right angle, and the given side lengths are in inches. What is the length of AC, in inches?
37. The domain of the real-valued function f(x)= ___2____ √•x •−•3• is the set of all x-values that satisfy:
38. For f(x) = 2x + 3 and g(x) = x2 − 4, which of the following expressions represents f_g(x)+?
39. For all y > 0, which of the following is a simplified form of _y_ − __1_ − _2_(_y_ − __1_)?
40. A wheel with a radius of 1 centimeter rolls without slipping along the ground. After exactly 2 revolutions, how many centimeters has the wheel traveled along the ground?
41. When x, y, and z are positive integers, which of the following relationships will assure that the product x0y1z−1 will have a value greater than 1?
42. From her statistical analysis, Sumiko can correctly conclude that every $1 increase in the total amount of the check will result in approximately:
43. What would be the cost of carpet of this type to cover a rectangular floor 12 feet by 18 feet?
44. Which of the following expressions represents f−1(x)?
45. What fraction of a mile has the car traveled in these 30 seconds?
46. If a−b=5 and c=7a−9 −7b, then c=?
47. If sin,θ= 1/2 and tan,θ=−√3/3, then cos,θ=?
48. Which of the following is an equation of the reflection?
49. For i2=−1, _2_ +__3__i =?
50. After correcting the scoring error on Mandy’s test, the average test score for the class increased by how many points?
51. What is the value of z in the solution to the system of equations below?
52. What is the maximum possible value of x for x in the set {1, 2, 3, 4, 5}?
53. How many of the triangles numbered 1−5 have the same area as triangle AGH?
54. What is the area, in square meters, of the shaded portion?
55. What is the area, in square meters, of the triangle shown below?
56. Which of the equations below is a hyperbola with the same asymptotes as the graph of − =1?
57. Which of the following statements about the mean, median, and mode of the data set is true?
58. Which of the following expressions gives the weight, in pounds, of a larger solid rectangular block that is made of the same kind of steel and has length, width, and height 4 times those of the smaller block?