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B) The mild temperature was lowered by a heavy rain in the morning, and the temperature dropped lower by evening. 9 page
(A) 8 (B) 12 (C) 14 (D) 16 (E) 18
20. The price of a certain stock was d dollars on January 1, 2003. The price decreased by 20% in January, increased by 40% in February, decreased by 25% in March, and increased by 25% in April. In terms of d, what was the price of the stock at the end of April?
(A) 0.80d (B) 0.84d (C) 1.05d (D) 1.12d (E) 1.20d
21. Eric earns a 5% commission on each $200 stereo that he sells. How many stereos must he sell to earn $100?
(A) 5 (B) 10 (C) 15 (D) 20 (E) 25
22. Jane’s Discount Music Superstore sells both new and used CDs and DVDs. On the basis of the information listed below, how many used DVDs were sold during the holiday season?
(A) 2,500 (B) 3,000 (C) 4,000 (D) 6,500 (E) 7,000
23. One bag of potatoes of a certain brand weighs 40 ounces. Five pounds of these potatoes cost $4.00. If Larry has exactly $20.00 to spend on potatoes, what is the maximum number of bags he can buy? (1 pound = 16 ounces)
(A) 7 (B) 8 (C) 9 (D) 10 (E) 11
24. What is the area of the shaded region in the figure below?
(A) 15 (B) 20 (C) 25 (D) 30 (E) 35
25. The rectangular solid below is constructed of 12 cubes that each have a volume of 8 cubic inches. What is the surface area of the solid?
(A) 32 (B) 48 (C) 96 (D) 128 (E) 144
26. Set M consists of the consecutive integers from −15 to y, inclusive. If the sum of all of the integers in set M is 70, how many numbers are in the set?
(A) 33 (B) 34 (C) 35 (D) 36 (E) 37
27. In a round robin tennis tournament involving seven players, each player will play every other player twice. How many total matches will be played in the tournament?
(A) 21 (B) 28 (C) 42 (D) 48 (E) 56
28. The figure below shows a right prism, the base of which is a quarter of a circle with center C. If the area of each base of the prism is 12.5π and the volume of the solid is 300π, what is the distance from point A to point B?
(A) 24 (B) 26 (C) 28 (D) 30 (E) 32
29. Find the second order derivatives of the function
(A) (B) (C) (D) (E)
30. Find the integral of the function in the below.
(A) (B) (C) (D) (E)
TEST 20
1. In the figure below, if the coordinates of points J and K are added together, this sum will be the coordinate of a point between
(A) -3 and -2 (B) -2 and -1 (C) 0 and 1 (D) 1 and 2 (E) 2 and 3
2. If 6x + 9y = 8, then 2x +3y =
(A) (B) (C) 2 (D) (E) 3
3. Glenna had three boxes of pencils, each of which contained y pencils. She distributed these pencils by giving one to each student in her class, and had 9 pencils left over. If there are 21 students in Glenna’s class, what is y?
(A) 3 (B) 4 (C) 6 (D) 8 (E) 10
4. If an integer n is divisible by both 12 and 20, then it must also be divisible by
(A) 15 (B) 24 (C) 32 (D) 80 (E) 240
5. A container in the shape of a right circular cylinder contains 12 liters of liquid when it is filled to
(A) 18 (B) 16 (C) 15 (D) 10 (E) 9
6. The profit that a company earns is equal to its revenue minus its expenses. If the revenue, in dollars, that a company makes for selling x items is given by the function R(x) = 12x and the expenses it must pay for selling those x items is given by the function E(x) = 3x + 12, then which of the following expresses the profit, in dollars, that the company earns for selling those x items?
(A) P(x) = 15x + 12 (B) P(x) = 15x –12 (C) P(x) = 9x + 12 (D) P(x) = 9x –12 (E) P(x) = 12 – 9x
7. The average (arithmetic mean) of x and y is m, where m
(A) m (B) (C) (D) (E) 2m
8. In the figure below, what is the value of x?
(A) 30 (B) 40 (C) 50 (D) 60 (E) 70
9. For all real values of x and y, let x ♦ y be defined by the equation x ♦ y = 2 – xy. If –1 < a < 0 and 0 < b < 1, then which of the following must be true?
(A) –2 < a ♦ b < –1 (B) –1 < a ♦ b < 0 (C) 0 < a ♦ b < 1 (D) 1 < a ♦ b < 2 (E) 2 < a ♦ b < 3
10. The figure below shows a circle with an area of 25π square units. If each vertex of the rectangle is on the circle as shown, what is the area of the rectangle, in square units?
(A) 30 (B) 36 (C) 42 (D) 48 (E) 54
11. Line l passes through the origin and is perpendicular to the line given by the equation 2x + y = 8. Which of the following points is not on line l?
(A) (-4, -2) (B) (-1, 1) (C) (2, 1) (D) (4, 2) (E) (7, 3.5)
12. If a and b are positive numbers, which of the following is equivalent to a% of 5b?
(A) (B) (C) (D) (E)
13. If the triangle in the figure below is reflected over line l, what will be the coordinates of the reflection of point A?
(A) (4, 1) (B) (6, 1) (C) (10, 1) (D) (11, 1) (E) (12, 1)
14. How many positive 3-digit integers contain only odd digits?
(A) 15 (B) 75 (C) 125 (D) 225 (E) 500
15. If k is a positive odd integer greater than 4, which of the following always represents the product of two even integers?
(A) k2 = – 4 (B) k2 + 4k –5 (C) k2 + 5k + 6 (D) k2 + 3k – 10 (E) k2 + k –20
16. The figure below shows the graph of the function f(x) = x2 – k. Points A and B lie on the graph of the function and are the vertices of rectangle ABCD. If AB = 6 and the area of rectangle ABCD is 20, what is the value of k?
(A) (B) (C) (D) (E)
17. In the figure below, if the coordinates of points P and Q are multiplied together, the result will be closest to which of the following points?
(A) A (B) B (C) C (D) D (E) E
18. If
(A) 3 (B) 4 (C) 12 (D) 24 (E) 36
19. When a positive integer p is divided by 7, the remainder is 2. Which of the following expressions will yield a remainder of 4 when divided by 7?
(A) p + 2 (B) p + 3 (C) p + 4 (D) p + 5 (E) p + 6
20. Which of the following graphs best represents the information in the table below?
(A)
(B)
(C)
(D)
(E)
21. Four hundred dollars was invested at a yearly simple interest rate of x percent. If at the end of one year the investment had grown to 500 dollars, what is the value of x?
(A) 20 (B) 25 (C) 30 (D) 45 (E) 40
22. In the figure below, which of the following line segments (not shown) has a slope of − 3?
(A) (B) (C) (D) (E)
23. In a parking lot, 3/4 of the vehicles are cars and 1/3 of the cars are more than 3 years old. If 20 cars in the lot are more than 3 years old, how many vehicles are there in total?
(A) 30 (B) 40 (C) 60 (D) 80 (E) 90
24. What is the average (arithmetic mean) of 8 consecutive odd integers if the smallest of those integers is n?
(A) n + 5 (B) n + 6 (C) n + 7 (D) n + 8 (E) n + 9
25. If w is an integer and w
(A) w4 (B) (w – 2)3 (C) 4w2 (D) 4w (E) 3(w2)
26. In the circle below, W is the center of the circle and the length of ZY is 8. If the area of the circle is 64π, what is the value of x?
(A) 40 (B) 50 (C) 60 (D) 70 (E) 80
27. Which of the following expressions is equivalent to 16x4? I. (64x6)2/3 II. III.
(A) I only (B) II only (C) II and III only (D) I and II only (E) I, II, and III
28. In April of 2004, d dogs and c cats lived in an animal shelter. If 4 cats arrived at the shelter in May of 2004 and the ratio of dogs to cats remained unchanged, in terms of c and d, how many dogs arrived at the shelter in May of 2004?
(A) 4 (B) (C) (D) (E)
29. Find the second order derivatives of the function
(A) (B) (C) (D) (E)
30. Find the integral of the function in the below.
(A) (B) (C) (D) (E)
TEST 21
1. A cookie recipe requires 2.5 cups of flour and makes 36 cookies. At this rate, how many cups of flour are required to make 54 cookies?
(A) 3 (B) 3 (C) 3 (D) 4 (E) 4
2. What is the product of 1.1 and 1.9 rounded to the nearest tenth?
(A) 1.5 (B) 1.7 (C) 2.0 (D) 2.1 (E) 3.0
3. In the figure below, points A and B lie on line
(A) 25 (B) 30 (C) 35 (D) 40 (E) 45
4. Which of the following ratios is equivalent to the ratio of 2.4 to 5?
(A) 6:15 (B) 12:25 (C) 1:2 (D) 4:7 (E) 24:25
5. In the figure below, line l is parallel to line m. If b = 36, what is the value of a?
(A) 32 (B) 33 (C) 34 (D) 35 (E) 36
6. For all positive integers a and b, let
(A) -0.5 (B) (C) (D) 0.5 (E) 2
7. Which of the following graphs in the xy-plane has the property that no two points on the graph have equal y-coordinates?
(A)
(B)
(C)
(D)
(E)
8. There are 72 marbles in a jar. If a marble is chosen at random, the probability that it will be black is
(A) 2 (B) 4 (C) 6 (D) 8 (E) 10
9. Gregory must inspect 12 working devices, labeled alphabetically from A to L, that are arranged in a linear array. He must start with device A and proceed alphabetically, returning to the beginning and repeating the process after inspecting device L, stopping when he encounters a defective device. If the first defective device he encounters is device D, which of the following could be the total number of devices that Gregory inspects, including the defective one?
(A) 64 (B) 68 (C) 72 (D) 74 (E) 78
10. Kiara’s goal is to sell at least $150 worth of cookies. If each box of cookies sells for $5, and she has already sold 16 boxes of cookies, which of the following inequalities could be used to determine x, where x is how many more boxes of cookies she must sell to make her goal?
(A) (16) · 5 − x (B) (16) · 5 + x ≥ 150 (C) (16) · 5 − x ≥ 150 (D) (16) · 5+ 5x (E) (16) · 5 + 5x ≥ 150
11. The figure below shows the graph of the function f in the xy-plane. If g(x) = f(x – 2), which of the following is a true statement describing the graph of g in comparison with the graph of f?
(A) Its vertex is 2 units lower than the vertex of the graph of f. (B) Its vertex is 2 units to the left of the vertex of the graph of f. (C) Its vertex is 2 units to the right of the vertex of the graph of f. (D) It is wider than the graph of f. (E) It is narrower than the graph of f.
12. If n8 = 480 and n7 = 12m, what is the value of 3mn?
(A) 30 (B) 60 (C) 90 (D) 120 (E) 480
13. In Δ PQR, the length of side
(A) 6 (B) 7 (C) 18 (D) 30 (E) 41
14. A beaker contains 15 grams of a water and salt solution that is 20% salt. If x more grams of water are added to the solution, which of the following expresses the percentage of salt in the new solution?
(A) (B) (C) (D) (E)
15. The figure below shows 5 cubbyholes in a day care center. Five different-colored jackets—one red, one blue, one green, one brown, and one white—are to be randomly placed in these cubby holes, one jacket per cubby hole. What is the probability that the red and brown jackets will each be assigned to one of the cubby-holes indicated by the shaded squares?
(A) (B) (C) (D) (E)
16. If a, b, m, n, and p are all positive integers greater than 1, and if (ab)m = anbp, which of the following must be true? I. 2m = n + p II. a = b III. If n = p then n = m.
(A) None (B) III only (C) I and II only (D) I and III only (E) II and III only
17. If
(A) 0.5 (B) 4 (C) 8 (D) 16 (E) 32
18. In ΔXYZ below, XY = ZY. Which of the following must be true?
(A) a = c (B) a = e (C) a = d (D) b = e (E) c = d
19. If the statement below is true, which of the following must also be true? All of Mark’s former students go to college.
(A) If Ethan was not Mark’s student, then he is not going to college. (B) If Joyelle goes to college, then she was not Mark’s student. (C) If Ginger goes to college, then she was Mark’s student. (D) If Stephanie was Mark’s student, then she is not going to college. (E) If Steve does not go to college, then he was not Mark’s student.
20. If 30 percent of n is 72, what is 15 percent of 2n?
(A) 18 (B) 36 (C) 64 (D) 72 (E) 144
21. If
(A) - 4 (B) - 2 (C) 2 (D) 3 (E) 5
22. While reading a 400-page book, Colin averages 50 pages per hour for the first p hours, where p < 8. In terms of p, how many pages remain to be read?
(A) 50p + 400 (B) 400 - (C) 400 – 50p (D) 500p - 400 (E)
23. The bar graph below shows the annual sales revenue for the Bartswell Corporation for the years 1995 through 2001. For which of the following years was the percent increase in revenue from the previous year the same as it was in 1996?
(A) 1997 (B) 1998 (C) 1999 Date: 2015-12-24; view: 1013 |
of its height. How many liters does it contain when it is completely filled?
0. What is the average (arithmetic mean) of x, y, and 2m?
= 5z and 
=5y then xy =
0, which of the following must be a positive even integer?
, and ray AC bisects angle BAD. What is the value of x?
. If m is a positive integer, what is 
?
. How many black marbles must be added to the jar so that the probability of choosing a black marble is 
?
150
150
is 24 and the length of side 
is 18. What is the least possible integer length of 
?
of a number is 20, what is 
of the number?
= 16, which of the following could be the value of x?
