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B) The mild temperature was lowered by a heavy rain in the morning, and the temperature dropped lower by evening. 11 page
(A) 30 (B) 60 (C) 90 (D) 120 (E) 150
7. Three integers have a sum of 7 and a product of 0. If the difference of the greatest number and the least number is 11, then the least of these numbers is
(A) −18 (B) −11 (C) −9 (D) −2 (E) 0
8. Four points lie on a circle. How many different triangles can be drawn with three of these points as vertices?
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8
9. If a, b, and c are consecutive positive integers such that a < b < c and abc is not a multiple of 4, then which of the following must be true?
(A) a is even (B) b is even (C) c is even (D) a + b + c is odd (E) abc is odd
10. For which class was the change in percent participation the greatest from 2002 to 2003?
(A) A (B) B (C) C (D) D (E) E
11. If class B and class E each had 100 students in 2002 and 2003, then, in total, how many more students participated in the fund-raiser from class E than from class B over the 2 years?
(A) 10 (B) 20 (C) 30 (D) 40 (E) 60
12. In 2002, the same number of students participated in the fund-raiser from class C as from class D. If class D contained 120 students in 2002, how many students were there in class C in 2002?
(A) 90 (B) 100 (C) 120 (D) 140 (E) 160
13. If x = −1 is a solution of the equation x2 = 4x + c where c is a constant, what is another value of x that satisfies the equation?
(A) -5 (B) -2 (C) 1 (D) 2 (E) 5
14. A three-digit integer is to be formed from the digits listed below. If the first digit must be odd, either the second or the third digit must be 2, and no digit may be repeated, how many such integers are possible? 1, 2, 6, 7, 9
(A) 6 (B) 9 (C) 18 (D) 24 (E) 30
15. If one pound of grain can feed five chickens or two pigs, then ten pounds of grain can feed 20 chickens and how many pigs?
(A) 8 (B) 10 (C) 12 (D) 24 (E) 40
16. Point C is the center of the circle on the figure below. The shaded region has an area of 3π square centimeters. What is the perimeter of the shaded region in centimeters?
(A) 2π + 6 (B) 2π + 9 (C) 2π + 12 (D) 3π + 6 (E) 3π + 12
17. If four apples cost 20 cents, then, at this rate, how much would ten apples cost?
(A) $.40 (B) $.50 (C) $.60 (D) $.70 (E) $.80
18. If 2b = 8, then 3b =
(A) 6 (B) 9 (C) 27 (D) 64 (E) 81
19. How much greater is the average (arithmetic mean) of a, b, and 18 than the average of a, b, and 12?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
20. The first day of a particular month is a Tuesday. What day of the week will it be on the 31st day of the month?
(A) Wednesday (B) Thursday (C) Friday (D) Saturday (E) Sunday
21. How many integer pairs (m, n) satisfy the statements 0 < m + n < 50 and
(A) 5 (B) 6 (C) 7 (D) 8 (E) more than 8
22. If y% of 50 is 32, then what is 200% of y?
(A) 16 (B) 32 (C) 64 (D) 128 (E) 256
23. For x > 0, the function g(x) is defined by the equation g(x) = x + x1/2. What is the value of g(16)?
(A) 16 (B) 20 (C) 24 (D) 64 (E) 272
24. In the figure below, if the slope of
(A) 54 (B) 72 (C) 96 (D) 108 (E) 192
25. The sequence below continues according to the pattern shown. What is the sum of the first 25 terms of this sequence? –1, 1, 2, −1, 1, 2, −1, 1, 2 . . .
(A) 15 (B) 16 (C) 18 (D) 19 (E) 21
26. A jar contains only white and blue marbles of identical size and weight. The ratio of the number of white marbles to the number of blue marbles is 4 to b. If the probability of choosing a white marble from the jar at random is 1⁄4, then what is the value of b?
(A) 1 (B) 2 (C) 6 (D) 12 (E) 16
27. The area of a right triangle is 10 square centimeters. If the length of each leg, in centimeters, is a positive integer, then what is the least possible length, in centimeters, of the hypotenuse?
(A) (B) (C) (D) (E)
28. If y is a number less than 0 but greater than −1, which of the following expressions has the greatest value?
(A) 100y (B) y2 (C) y3 (D) y4 (E) y5
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 25
1. If 4x + 5 = 20, what is the value of 4x + 8?
(A) 3 (B) 7 (C) 16 (D) 23 (E) 30
2. If one serving of cereal is
(A) 3 (B) 9 (C) 18 (D) 27 (E) 36
3. If the radius of the circle with center O below is 4, what is the length of arc RST?
(A) 2π (B) 4π (C) 8π (D) 12π (E) 16π
4. In the triangle below, what is the value of x?
(A) 7 (B) 7 (C) 7 (D) 14 (E) 28
5. For x > 0, let ∇x be defined by the equation ∇x = 3x − 3. Which of the following is equivalent to
(A) ∇2 (B) ∇3 (C) ∇6 (D) ∇8 (E) ∇9
6. Stephanie can clean a pool in 1 hour, and Mark can clean the same pool in 1.5 hours. If the rate at which they work together is the sum of their rates working separately, how many minutes should they need to clean the pool if they work together? (1 hour = 60 minutes)
(A) 24 minutes (B) 36 minutes (C) 60 minutes (D) 72 minutes (E) 100 minutes
7. Which of the following has the greatest value?
(A) (1003)4 (B) (1005)(1006) (C) (10,000)4 (D) (1002 × 1002)2 (E) (1,000,000)3
8. Line m (not shown) is the reflection of line l over the x-axis. What is the slope of line m?
(A) 3/2 (B) 2/3 (C) 0 (D) −2/3 (E) −3/2
9. If a2 + b2 = 4 and ab = 5, what is the value of (a + b)2?
(A) 10 (B) 12 (C) 14 (D) 16 (E) 18
10. The figure below shows the dimensions, in feet, of a stone slab. How many of these slabs are required to construct a rectangular patio 24 feet long and 12 feet wide?
(A) 18 (B) 20 (C) 24 (D) 36 (E) 48
11. $12,000 in winnings for a golf tournament were distributed in the ratio of 7:2:1 to the first, second, and third-place finishers, respectively. How much money did the first-place finisher receive?
(A) $1,200 (B) $1,700 (C) $2,400 (D) $8,400 (E) $10,000
12. If 2x + 3y = 7 and 4x − 5y = 12, what is the value of 6x − 2y?
(A) 5 (B) 8 (C) 15 (D) 17 (E) 19
13. If r and s are positive integers and s + 1 = 2r, which of the following must be true? I. s is odd II. r is even III.
(A) I only (B) III only (C) I and II only (D) I and III only (E) I, II, and III
14. A bag contains six chips, numbered 1 through 6. If two chips are chosen at random without replacement and the values on those two chips are multiplied, what is the probability that this product will be greater than 20?
(A) (B) (C) (D) (E)
15. In the sequence below, each term after the second is equal to the product of the two pre ceding terms. For example, the third term, −8, is the product of 2 and −4. How many of the first 100 terms of this sequence are negative? 2, -4, -8…
(A) 33 (B) 34 (C) 50 (D) 66 (E) 67
16. In the figure below, points C and D are midpoints of edges of a cube. A triangle is to be drawn with R and S as two of the vertices. Which of the following points should be the third vertex of the triangle if it is to have the largest possible perimeter?
(A) A (B) B (C) C (D) D (E) E
17. If 3x + 5x + 8x = 32, what is the value of x?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
18. If
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
19. If 5b −10 ≥ 15, which of the following expresses all of the possible values of b?
(A) b ≥ 5 (B) b ≥ 1 (C) b ≥ 9 (D) b ≤ 1 (E) b ≤ 5
20. If t% of 60 is equal to 30% of 50, what is the value of t?
(A) 12 (B) 15 (C) 25 (D) 30 (E) 35
21. If it takes 40 minutes to write h holiday cards, then in terms of h, how many holiday cards can be written at that rate in 8 hours?
(A) (B) 8h (C) 12h (D) (E)
22. Which of the labeled points on the number line below could represent the product −1.5 ×1.25?
(A) A (B) B (C) C (D) D (E) E
23. If four people share 100 baseball cards and each person must receive a different positive whole number of cards, what is the greatest possible number of cards any one person may have?
(A) 28 (B) 29 (C) 94 (D) 95 (E) 97
24. Which of the following graphs best represents the data presented in the table below?
(A)
(B)
(C)
(D)
(E)
25. If the sum of seven integers is even, at most how many of these integers could be odd?
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7
26. In a particular year, if January 22 is the fourth Wednesday of the month, what is the date of the fourth Monday in January?
(A) January 20 (B) January 21 (C) January 26 (D) January 27 (E) January 28
27. The graph below shows the number of teachers in Hamden who live in a house, the number of teachers who live in an apartment, and the number of each who use gas or oil heat. Of the teachers who use gas heat, what fraction live in a house?
(A) (B) (C) (D) (E)
28. If 5x + 7y = 18 and 2x − 4y = 6, what is the value of 7x + 3y?
(A) 7 (B) 12 (C) 19 (D) 24 (E) 31
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 26
1. In the figure below, what is the value of a?
(A) 10 (B) 20 (C) 28 (D) 36 (E) 45
2. The Rivertown Little League is divided into d divisions. Each division has t teams, and each team has p players. How many players are there in the entire league?
(A) d + t + p (B) dtp (C) (D) (E)
3. What is the value of n if 2n+1= 32?
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8
4. In the figure below, what is the value of a + b + c?
(A) 210 (B) 220 (C) 240 (D) 270 (E) 280
5. The chart below shows the number of tennis tournaments that Adam entered each year from 1990 through 1995. In what year did he enter 50% more tournaments than the year before?
(A) 1991 (B) 1992 (C) 1993 (D) 1994 (E) 1995
6. If, for any number b, b# = b + 1 and #b = b – 1, which of the following is not equal to (3#)(#5)?
(A) (1#)(#9) (B) 7# + #9 (C) (4#)(#4) (D) (7#)(#3) (E)
7. If a is a multiple of 5 and b = 5a, which of the following could be the value of a + b? I. 60 II. 100 III. 150
(A) I only (B) III only (C) I and III only (D) II and III only (E) I, II, and III
8. If 3a = b and 3c = d, then bd =
(A) 3ac (B) 3a+c (C) 6a+c (D) 9ac (E) 9a+c
9. If r and s are two nonzero numbers and if 78(r + s) = (78 + r)s, then which of the following must be true?
(A) r = 78 (B) s = 78 (C) r + s = rs (D) r < 1 (E) s < 1
10. If it is now June, what month will it be 100 months from now?
(A) January (B) April (C) June (D) October (E) December
11. If the average (arithmetic mean) of three consecutive integers is A, which of the following must be true? I. One of the numbers is equal to A. II. The average of two of the three numbers is A. III. A is an integer.
(A) I only (B) II only (C) III only (D) I and II only (E) I, II, and III
12. A bag contains 25 slips of paper, on each of which a different integer from 1 to 25 is written. Blindfolded, Scott draws one of the slips of paper. He wins if the number on the slip he draws is a multiple of 3 or 5. What is the probability that Scott wins?
(A) (B) (C) (D) (E)
13. If m2 = 17, then what is the value of (m + 1)(m – 1)?
(A) (B) (C) 16 (D) 18 (E) 288
14. Which of the following points lie on the interior of the circle whose radius is 10 and whose center is at the origin?
(A) (-9, 4) (B) (5, -9) (C) (0, -10) (D) (10, -1) (E) (-6, 8)
15. Several shoppers were surveyed at a supermarket and asked how many people were in their families and how much money they spend each week on food. The data were graphed in the following scatterplot diagram.
If the average weekly cost of food per person for each of the seven families, A–G, was calculated, which one would be the median?
(A) A (B) C (C) D (D) E (E) G
16. If p pencils cost c cents, how many pencils can be bought for d dollars?
(A) cdp (B) 100cdp (C) (D) (E)
17. If a is increased by 10% and b is decreased by 10%, the resulting numbers will be equal. What is the ratio of a to b?
(A) (B) (C) (D) (E)
18. In the figure below, line segments I. a + b II. b + c III. a+ b+ c + d
(A) II only (B) I and II only (C) II and III only (D) I and III only (E) I, II, and III
19. Which of the following cannot be expressed as the sum of two or more consecutive positive integers?
(A) 17 (B) 22 (C) 24 (D) 26 (E) 32
20. In the figure below, the legs of right triangle ACB are diameters of the two semicircles. If AB = 4 what is the sum of the areas of the semicircles?
(A) π (B) 2π (C) 4π (D) 8π (E) 16π
21. At the Fancy Furniture Factory, Brian bought two chairs for $299 each and a coffee table for $140. He paid
(A) $10.25 (B) $37.50 (C) $42.75 (D) $51.25 (E) $61.50
22. If f(x) = x2 – 2x, what is the value of f(4)?
(A) -16 (B) -8 (C) 0 (D) 8 (E) 16
23. The operation ** is defined as follows: For any positive numbers a and b, a**b=
(A) 11**5 (B) 4**9 (C) 4**16 (D) 7**4 (E) 9**9
24. Which of the following is a solution of the equation 3|x| + 5 = 23?
Date: 2015-12-24; view: 865 |
is −3⁄4, what is the area of ΔABO?
cup, how many servings are in 3 pints of cereal? (1 pint = 2 cups)
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is an integer
(6x) = 8, then x =
and 
partition pentagon ABCDE into a rectangle and two triangles. For which of the following can the value be determined?
of the total cost at the time of purchase and the balance in 12 equal monthly installments. What was the amount of each month’s payment?
.Which of the following is an integer?