1. For all nonzero values of x and y, which of the following expressions is equivalent to -3/5 * x + 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. This is the only money deposited into the account. 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 nABC 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 2,500km, and between B and C is 1,200km. 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 is shown on a large computer screen. A blinking dot is 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 2seconds 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. By May 15, Ms. Chen had enrolled her 2 children for camp. One child was in Grade 3, and the other was in Grade 4.
20. For real numbers x and y such that 0≤x≤5 and y≥9, the expression can have which of the following values?
21. Given the functions f(x) = x² + 1 and g(x) = x − 3, which of the following expressions is f_g(x)+?
22. Given that the equation 4/x − y = 5 is true, what is the value of x?
23. Juro traveled to 3 locations during a workday. Juro remained at each location a whole number of hours. 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?
24. What is the amplitude of the function y=3 sin(x)?
25. For all nonzero values of w, which of the following expressions is equivalent to 4/w + 2/w²?
26. 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. Which of the following inequalities must be true?
27. Which of the following inequalities expresses an interval that must include the product ab?
28. Sani’s course grade in his chemistry class is based on 3 tests and 1 final exam. 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?
29. The triangle below has vertices A(−1,−2), B(2,2), and C(−1,4). What is the area of nABC, in square coordinate units?
30. For some real number x, √(x²) ≠ x. Therefore x is:
31. In the standard (x,y) coordinate plane, 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?
32. A wire binds 4 identical posts together as shown below. What is the length, to the nearest inch, of the shortest wire that will go around the 4 posts without overlap?
33. 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?
34. For positive integers x and y where x<8, log₈=y. What is the value of y?
35. The right triangle shown below is 8 squares high and 10 squares long. Which one is the ratio of the shaded area to the unshaded area?
36. For all positive integers x, which of the following expressions is equivalent to x⁴ · x⁶?
37. One day on the New York Currency Exchange, how much Canadian currency, rounded to the nearest Canadian cent, could be exchanged for £2?
38. 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?
39. Set A and Set B each consist of 5 distinct numbers. The value of which of the following measures must be greater for Set B than for Set A?
40. Thalia will rent 3 of these cars out of 16 cars on a rental-car lot. What is the probability that Thalia will rent 1 of each of the 3 types of cars?