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B) The mild temperature was lowered by a heavy rain in the morning, and the temperature dropped lower by evening. 12 page(A) –6 (B) –4 (C) (D) 15 (E) The equation has no solution.
25. If circle O has its center at (1, 1), and line
(A) (B) (C) (D) 1 (E)
26. If 25 – 2
(A) -81 (B) 9 (C) 36 (D) 81 (E) 256
27. What is the value of n if 310
(A) 6 (B) 10 (C) 12 (D) 15 (E) 30
28. In the figure below, what is the area of the shaded triangle?
(A) 30 (B) 32 (C) 34 (D) 35 (E) 36
29. Differentiate the function in the below.
(A) (B) (C) (D) (E)
30. Find the integral of the function in the below.
(A) (B) (C) (D) (E)
TEST 27
1. If 5c + 3 = 3c + 5, what is the value of c?
(A) -1 (B) 0 (C) 1 (D) 3 (E) 5
2. In the figure below, C is the only point that right triangle ABC and square CDEF have in common. What is the value of a + b?
(A) 135 (B) 180 (C) 210 (D) 225 (E) 270
3. A lacrosse team raised some money. The members used 74% of the money to buy uniforms, 18% for equipment, and the remaining $216 for a team party. How much money did they raise?
(A) $2400 (B) $2450 (C) $2500 (D) $2600 (E) $2700
4. For all positive numbers a and b, let ab =
(A) (B) (C) (D) (E) 1
5. In the figure below, what is the value of b?
(A) 30 (B) 36 (C) 45 (D) 60 (E) 72
6. In the figure below, if x is 150 more than y, what is the value of y?
(A) 10 (B) 15 (C) 20 (D) 25 (E) 30
7. Heidi wrote the number 1 on 1 slip of paper, the number 2 on 2 slips of paper, the number 3 on 3 slips of paper, the number 4 on 4 slips of paper, the number 5 on 5 slips of paper, and the number 6 on 6 slips of paper. All the slips of paper were placed in a bag, and Sally drew 1 slip at random. What is the probability that the number on the slip Sally drew was odd?
(A) (B) (C) (D) (E)
8. For how many positive numbers a is it true that
(A) 0 (B) 1 (C) 2 (D) 3 (E) more than 3
9. Last year Jose sold a painting for $2000. If he made a 25% profit on the sale, how much had he paid for the painting?
(A) $1200 (B) $1500 (C) $1600 (D) $2400 (E) $2500
10. For any positive integer n > 1, n! represents the product of the first n positive integers. For example, 3! = I. 5! – 4! – 3! II. III. 15(3!)
(A) I only (B) II only (C) III only (D) I and III only (E) I, II, and III
11. A rectangle is twice as long as it is wide. If the width is a, what is the length of a diagonal?
(A) (B) (C) (D) 3a (E) 5a
12. If abc = 1, which of the following could be the number of integers among a, b, and c? I. 1 II. 2 III. 3
(A) None (B) I only (C) I and II only (D) I and III only (E) I, II, and III
13. At Essex High School 100 students are taking chemistry and 80 students are taking biology. If 20 students are taking both chemistry and biology, what is the ratio of the number of students taking only chemistry to the number taking only biology?
(A) (B) (C) (D) (E) It cannot be determined from the information given
14. In the figure below, a small square is drawn inside a large square. If the shaded area and the white area are equal, what is the ratio of the side of the large square to the side of the small square?
(A) (B) (C) (D) (E) It cannot be determined from the information given.
15. In rectangle ABCD below, diagonal
(A) 25 (B) 25 (C) 48 (D) 50 (E) 100
16. The value of 10 pounds of gold is d dollars, and a pound of gold has the same value as p pounds of silver. What is the value, in dollars, of one pound of silver?
(A) (B) (C) (D) (E)
17. If a and b are positive integers such that (a – 4)(b – 5) = 0, what is the least possible value of a + b?
(A) 5 (B) 6 (C) 8 (D) 10 (E) 11
18. The number of cells growing in a particular Petri dish doubles every 30 minutes. If at 8:00 A.M. there were 60 cells in the dish, how many were there at noon of the same day?
(A) (B) (C) (D) (E)
19. The distance between Ali’s house and college is exactly 135 miles. If she drove
(A) 40 (B) 45 (C) 60 (D) 67.5 (E) It cannot be determined from the information given.
20. The average (arithmetic mean) weight of five students is 150.4 pounds. If no student weighs less than 130 pounds and if no two students’ weights are within 5 pounds of each other, what is the most, in pounds, that any one of the students can weigh?
(A) 172 (B) 192 (C) 202 (D) 232 (E) It cannot be determined from the information given.
21. What is the absolute value of the product of all the integers from –6 to 3, inclusive?
(A) -120 (B) -15 (C) 0 (D) 15 (E) 120
22. If
(A) 12 (B) 15 (C) 18 (D) 20 (E) 24
23. If A is the set of multiples of 5 less than 200 and B is the set of multiples of 7 less than 200, how many members are there in A∩B?
(A) 0 (B) 5 (C) 11 (D) 62 (E) 67
24. If
(A) -9 (B) 3 (C) 7 (D) 9 (E) 26
25. Let the lengths of the sides of a triangle be represented by x + 3, 2x – 3, and 3x – 5. If the perimeter of the triangle is 25, what is the length of the shortest side?
(A) 5 (B) 7 (C) 8 (D) 10 (E) It cannot be determined from the information given.
26. What is the maximum number of points of intersection between a square and a circle?
(A) less than 4 (B) 4 (C) 6 (D) 8 (E) more than 8
27. In square ABCD, vertex A is at (–1, –1) and vertex C is at (4, 2). What is the area of square ABCD?
(A) 9 (B) 15 (C) 17 (D) 25 (E) 34
28. If f(x) = x + 5, which of the following is a solution of f(3a) + 2 = f(2a) + 3?
(A) 1 (B) 2 (C) 5 (D) 6 (E) There are no solutions.
29. Differentiate the function in the below.
(A) (B) (C) 0 (D) 1 (E)
30. Find the integral of the function in the below.
(A) (B) (C) (D) (E)
TEST 28
1. If 3x = 12,5x =
(A) 2.4 (B) 14 (C) 15 (D) 20 (E) 60
2. In the figure below, x =
(A) 33 (B) 57 (C) 67 (D) 123 (E) 147
3. If 8 – (8 – m) = 8, then m =
(A) –16 (B) –8 (C) 0 (D) 8 (E) 16
4. If
(A) (B) (C) (D) (E) It cannot be determined from the information given.
5. In the figure below, what is the perimeter of pentagon ABCDE, formed by right triangle EAB and square BCDE?
(A) 20 (B) 8 + 12 (C) (D) (E) 32
6. If x4 = 10, what is x6?
(A) 10 (B) 100 (C) 100 (D) 1000 (E) 1000
7. The circumference of the circle with center O shown bellow is 2π. What is the area of the shaded region?
(A) (B) (C) 1 (D) 0.5 (E) 0.25
8. If
(A) 1 (B) 2 (C) 3 (D) 4 (E) It cannot be determined from the information given.
9. Brigitte’s average (arithmetic mean) on her six math tests this marking period is 75. Fortunately for Brigitte, her teacher drops each student’s lowest grade, thus raising Brigitte’s average to 85. What was her lowest grade?
(A) 20 (B) 25 (C) 30 (D) 40 (E) 50
10. If m is an integer, which of the following could be true? I. II. III. 17m is a prime.
(A) I only (B) II only (C) III only (D) I and II only (E) II and III only
11. Max purchased some shares of stock at $10 per share. Six months later the stock was worth $20 per share. What was the percent increase in the value of Max’s investment?
(A) 20% (B) 50% (C) 100% (D) 200% (E) The answer depends on the number of shares purchased.
12. Benjamin can type a full report in h hours. At this rate, how many reports can he type in m minutes?
(A) (B) (C) (D) (E)
13. The estate of a wealthy man was distributed as follows: 10% to his wife, 5% divided equally among his three children, 5% divided equally among his five grandchildren, and the balance to a charitable trust. If the trust received $1,000,000, how much did each grandchild inherit?
(A) $10,000 (B) $12,500 (C) $20,000 (D) $62,500 (E) $100,000
14. If A, B, C, and D lie on the same straight line, and if AC = 2CD = 3BD, what is the value of the ratio
(A) (B) (C) (D) (E) It cannot be determined from the information given.
15. A car going 40 miles per hour set out on an 80 mile trip at 9:00 A M . Exactly 10 minutes later, a second car left from the same place and followed the same route. How fast, in miles per hour, was the second car going if it caught up with the first car at 10:30 A M.?
(A) 45 (B) 50 (C) 53 (D) 55 (E) 60
16. In the figure below, what is the ratio of y to x?
(A) (B) (C) (D) (E) It cannot be determined from the information given.
17. Which of the following is equal to 10 – 9?
Questions 17 and 18 refer to the following definition. For any positive integer n, n represents the sum of the integers from 1 to n. For example, 5 = 1 + 2 + 3 + 4 + 5 = 15.
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
18. If 1000 = 50,500 and 10 = 55, what is the value of 1010?
(A) 50,555 (B) 55,555 (C) 60,500 (D) 60,555 (E) 65,555
19. A school’s honor society has 100 members: 40 boys and 60 girls, of whom 30 are juniors and 70 are seniors. What is the smallest possible number of senior boys in the society?
(A) 0 (B) 5 (C) 10 (D) 15 (E) 20
20. In the figure below, the small circle is inscribed in the square, which is inscribed in the large circle. What is the ratio of the area of the large circle to the area of the small circle?
(A) (B) (C) 2:1 (D) (E) It cannot be determined from the information given.
21. In a class, 20 children were sharing equally the cost of a present for their teacher. When 4 of the children decided not to contribute, each of the other children had to pay $1.50 more. How much, in dollars, did the present cost?
(A) 50 (B) 80 (C) 100 (D) 120 (E) 150
22. If Wally’s Widget Works is open exactly 20 days each month and produces 80 widgets each day it is open, how many years will it take to produce 96,000 widgets?
(A) less than 5 (B) 5 (C) more than 5 but less than 10 (D) 10 (E) more than 10
23. In the figure below, JL = KL = LM and m ∠JLK = 70. This information is sufficient to determine the value of which of the following?
(A) a only (B) b only (C) a and b only (D) b and c only (E) a, b, and c
24. The equation |1-
(A) 0 (B) 9 (C) 18 (D) 20 (E) 298
25. A(5, 1) lies on a circle whose center is O (1, 5). If
(A) (3, 3) (B) (6, 6) (C) (–1, 5) (D) (–1, 10) (E) (–3, 9)
26. What is the volume, in cubic inches, of a cube whose total surface area is 216 square inches?
(A) 6 (B) 18 (C) 36 (D) 216 (E) 1296
27. If f(x) =
(A) None (B) 3 (C) 4 (D) 7 (E) Infinitely many
28. If a point in the figure below is chosen at random, what is the probability that the point lies in the shaded outer ring?
(A) (B) (C) (D) (E)
29. Differentiate the function in the below.
(A) (B) (C) (D) (E)
30. Find the integral of the function in the below.
(A) (B) (C) (D) (E)
TEST 29
1. If 2x + 4x + 6x = –12, then x =
(A) -1 (B) -0.5 (C) 0 (D) 0.5 (E) 1
2. What is the average (arithmetic mean) number of students per class? Questions 2 and 3 refer to the information in the following table, which shows the number of students in each of the five fifth-grade classes at Taft Elementary School and, for each class, the number of students in the school band. Date: 2015-12-24; view: 972 |
is tangent to circle O at P(4, –4), what is the slope of 
?
= 7, then x =
272= 81 
?
. If n > 1, what does n 
equal?
= a + a + a?
= 6. Which of the following is (are) equal to 
?
makes a 30° angle with side 
. If AC = 10, what is the area of the rectangle?
of the distance in 135 minutes, what was her average speed, in miles per hour?
of a number is 7 more than 
of the number, what is 
of the number?
+ 3 = 5, then x =
of the members of the school chorus are boys, what is the ratio of girls to boys in the chorus?
is an integer, what is the remainder when a is divided by 5?
is an even integer.
is an even integer.
| = 7 has two solutions. What is the sum of these solutions?
is a diameter, what are the coordinates of B?
, how many integers are in the domain of f?
