1. For all nonzero values of x and y, which of the following expressions is equivalent to −3/5x + 5y − 4?
2. The degree measures of the 3 angles of the triangle below are expressed in terms of x. What is the value of x?
3. A 48.5-ounce batch of cologne will be used to fill empty bottles. Each full bottle will contain 0.35 ounces of cologne. This batch of cologne will fill at most how many bottles full of cologne?
4. Of the 200 parking spaces in a parking lot, 6% of the spaces are reserved for handicapped parking. Of those parking spaces NOT reserved for handicapped parking, 20 are suitable for compact cars only. How many spaces that are NOT reserved for handicapped parking are suitable for noncompact cars?
5. What is the value of 2|2 − 9| − 3(5 + 2)?
6. Ricardo started a savings account for his daughter Ruth by depositing $500 into the account for her 1st birthday. For each successive birthday, Ricardo deposits $200 more than the amount deposited for the previous birthday. What is the total amount of money Ricardo will have deposited into the account for Ruth up to and including her 6th birthday?
7. Tawanna bought a used car. She made an initial payment of $700.00. She then made 36 equal monthly payments. The total amount Tawanna paid for the car was $7,000.00. What was the amount of each of her monthly payments?
8. Which of the following matrices is equal to 3 9 24 + 3 − 6 84?
9. Lyle and Ming are painting an art room. They started with 4 gallons of paint. On the first day, Lyle used 1/2 gallon of paint and Ming used 1 1/4 gallons of paint. How many gallons of paint were left when they completed their first day of painting?
10. In the standard (x,y) coordinate plane, what is the slope of the line through (−3,1) and (5,6)?
11. The lengths of corresponding sides of 2 similar right triangles are in the ratio 4:5. The hypotenuse of the smaller triangle is 24 inches long. How many inches long is the hypotenuse of the larger triangle?
12. The lengths of the 3 sides of right triangle ABC shown below are given in meters. What is sin A?
13. In the figure shown below, C is on the segment with endpoints A and D. The distance between A and B is 2,000 km, between A and C is 1,600 km, between A and D is 2,500 km, and between B and C is 1,200 km. What is the distance, in kilometers, between B and D?
14. What is the sum of the 2 solutions of the equation x^2 − 4x − 45 = 0?
15. In the figure shown below, all angles are right angles, and the side lengths given are in inches. What is the area, in square inches, of the figure?
16. Quadrant I of the standard (x,y) coordinate plane shows a blinking dot positioned at (2,3). The dot makes exactly 2 moves: first, horizontally in the positive x direction for 4 seconds at a speed of 0.5 coordinate units per second; then, vertically in the positive y direction for 2 seconds at the same speed. At what point is the dot located after these 2 moves?
17. By May 15, Mr. Ramirez had enrolled his 2 children for camp. One child was in Grade 4, and the other was in Grade 6. What was the total amount Mr. Ramirez paid to enroll his 2 children?
18. Which of the following equations gives a true relationship between the regular enrollment fee, f, and the grade, g, of any child enrolled in the camp?
19. What is the probability that the names of both of Ms. Chen’s children will be drawn?
20. Among the following, which is the lowest that the speed limit could have been?
21. What value of x makes the equation −1/81 = −3x true?
22. Which of the following expressions gives I in terms of P and R?
23. How many seconds elapse until the 2 signs next flash at the same time?
24. What is the perimeter of this square, in inches?
25. What is the DNR estimate of the deer population in the county?
26. What is the 1st term (a1)?
27. How much distance did the person cover, to the nearest 0.1 mile?
28. How many of the 20 students are NOT members of either club?
29. By how much would the sum of the 7 numbers have to increase?
30. Which of the following is an equation of the circle whose center is at (4,−3) and radius is 5?
31. How many students earned a score greater than 80 points?
32. What is the maximum number of apples she can purchase today?
33. What time did Fletcher leave his home?
34. What was the price of the bag of balloons?
35. How much greater was the price of the doll than the mean of the 4 prices?
36. Which line segment contains points for all possible combinations of x and y?
37. What is EG, in centimeters?
38. What is h(2)?
39. The interior angles of triangle ABC. Which of the following is closest to the degree measure of ∠C?
40. For real numbers x and y such that 0≤x≤5 and y≥9, the expression can have which of the following values?
41. Given the functions f(x) = x² + 1 and g(x) = x − 3, which of the following expressions is f(g(x))?
42. Given that the equation 4/x - y = 5 is true, what is the value of x/y?
43. Juro traveled to 3 locations during a workday. Juro remained at each location a whole number of hours. The graph below shows the relationship between time, in hours, into his workday and total distance, in kilometers, traveled. Which of the following values is closest to Juro’s average speed, in kilometers per hour, for the parts of the workday when he was traveling?
44. What is the amplitude of the function y=3 sin(x)?
45. For all nonzero values of w, which of the following expressions is equivalent to 4/w + 2/w²?
46. Let A, B, and C represent the digits in the hundreds, tens, and ones places, respectively, of a certain 3-digit whole number. Let D, E, and F represent the digits in the hundreds, tens, and ones places, respectively, of a different 3-digit whole number. The positive difference between the 2 numbers is greater than 100. Which of the following inequalities must be true?
47. A number line graph includes the points at real numbers a and b, as shown below. Which of the following inequalities expresses an interval that must include the product ab?
48. Sani’s course grade in his chemistry class is based on 3 tests and 1 final exam. Each of the 3 test scores is weighted as 20% of the course grade, and the final exam score is weighted as 40% of the course grade. Sani’s 3 test scores are 78, 86, and 82, respectively. What is the minimum score that Sani will have to earn on the final exam in order to receive a course grade of at least 86?
49. The triangle below has vertices A(−1,−2), B(2,2), and C(−1,4). What is the area of triangle ABC, in square coordinate units?
50. For some real number x, √(x²) ≠ x. Therefore x is:
51. In the standard (x,y) coordinate plane below, point A has coordinates (2,−4), and point B(8,−1) divides AC so that the ratio AB:BC is 1:3. What are the coordinates of point C?
52. A wire binds 4 identical posts together as shown below. Each post has a 3-inch radius. What is the length, to the nearest inch, of the shortest wire that will go around the 4 posts without overlap?
53. Given that b is rational and i = √(−1), the product of the expression (3 + bi) and which of the following expressions must be a rational number?
54. For positive integers x and y where x<8, log₈(y) = x. What is the value of y?
55. The right triangle shown below is 8 squares high and 10 squares long. One of the following values is the ratio of the shaded area to the unshaded area. Which one?
56. For all positive integers x, which of the following expressions is equivalent to x⁴ · x⁶?
57. One day on the New York Currency Exchange, 1 British pound (£1) could be exchanged for $2.75 in U.S. currency, and 1 Canadian dollar ($1) could be exchanged for $0.92 in U.S. currency. On that day, how much Canadian currency, rounded to the nearest Canadian cent, could be exchanged for £2?
58. The sides of an acute triangle measure 17 cm, 16 cm, and 15 cm, respectively. The measure of the smallest angle of the triangle is a solution for A to which of the following equations?
59. Set A and Set B each consist of 5 distinct numbers. The 2 sets contain identical numbers with the exception of the number with the least value in each set. The number with the least value in Set B is greater than the number with the least value in Set A. The value of which of the following measures must be greater for Set B than for Set A?
60. Of the 16 cars on a rental-car lot, 6 are minivans, 7 are sedans, and 3 are hatchbacks. Thalia will rent 3 of these cars, chosen at random, for business associates. What is the probability that Thalia will rent 1 of each of the 3 types of cars?