 Math Section

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This chapter is from the book

Practice Questions

Time—25 minutes

18 Questions

Directions: Solve each problem and determine which is the best of the answer choices given. Fill in the corresponding circle on your answer sheet. Use any available space to solve the problems.

Set P = {14, 15, 16, 17, 18, 19, 20}

Set Q = {16, 17, 18, 19, 20, 21, 22}

1. Sets P and Q are shown above. How many numbers in Set P are also in Set Q?

1. Three

2. Four

3. Five

4. Six

5. Seven

2. If John traveled 30 miles in 6 hours and Seth traveled three times as far in half the time, what was Seth's average speed, in miles per hour?

1. 5

2. 15

3. (C) 30

4. (D) 45

5. 90

3. If r = -2 and p < 0, which of the following has the least value?

1. 4pr2

2. 2pr3

3. -2pr4

4. -4pr5

5. -6pr6 4. The figure above shows the graph of the line y = ax + b, where a and b are constants. Which of the following best represents the graph of the line y = ax + b?

1. 2. 3. 4. 5.  5. In the figure above, the perimeter of the triangle is . What is the value of x?

1. 2

2. 4

3. 6

4. 8

5. 12 6. At a recent coin collection exhibit, 18 coin collectors brought their collections for viewing. The number of coins each collector brought is shown in the table above. Mike, who was the only collector not able to attend the exhibit, would have brought 75 coins. Had he been able to attend, what would have been the median number of coins?

1. 90

2. 87.5

3. 85

4. 82.5

5. 80

7. If 4 more than twice n is a negative number and 6 more than n is a positive number, which of the following could be the value of n?

1. -8

2. -6

3. -4

4. -2

5. 4

8. Rectangle PQRS lies in the xy-coordinate plane so that its sides are not parallel to the axes. What is the product of the slopes of all four sides of rectangle PQRS?

1. -2

2. -1

3. 0

4. 1

5. 2

9. A 2 hour-long television movie included 30 minutes of commercials. What fraction of the 2 hour-long movie was not commercials?

10. If the product of 0.75 and a number is equal to 2, what is the number?

11. If 8s = 96 and sp = 4, what is the value of p?

12. Note: Figure not drawn to scale.

13. In the figure above, ACFD is a rectangle and ABED is a square. BC = 8 and AB is a positive integer. If the area of ACFD must be more than 14 but less than 35, what is one possible value of AB?

14. A company sells boxes of napkins in which the napkins are red, white, and blue. Betty purchased a box of napkins in which were blue. If there were twice as many white napkins as blue ones and 25 napkins were red, how many napkins were in the box?

15. The four distinct points T, U, V, and W lie on a line l; the five distinct points J, K, L, M, and N lie on a different line that is parallel to l. What is the total number of different lines that can be drawn so that each line contains exactly two of the nine points?

16. If 42x + 42x + 42x + 42x = 49, what is the value of x?

17. Each of 9 people had a blank card on which they wrote a positive integer. If the average (arithmetic mean) of these integers is 56, what is the greatest possible integer that could be on one of the cards?

18. Jeff and Scott stand back to back. They each take 12 steps in opposite directions away from each other and stop. Jeff then turns around, walks toward Scott, and reaches him in 16 steps. The length of one of Jeff's steps is how many times the length of one of Scott's steps? (All of Jeff's steps are the same length as each other, and all of Scott's steps are the same length as each other.)

19. If rs = 13 and 3r + 2s = 10, then 3r2s + 2rs2 = ?