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B) The mild temperature was lowered by a heavy rain in the morning, and the temperature dropped lower by evening. 8 page(D) 2 (E) 12
8. If 12v = 3w and v ≠ 0, then which of the following is equivalent to 2w − 8v?
(A) 0 (B) 4w (C) - 6w (D) 2v (E) – 2v
9. If x is a negative number and 2|x| + 1 > 5, then which of the following must be true?
(A) x < - 3 (B) x < - 2.5 (C) x < - 2 (D) x > - 2 (E) x > - 5
10. If x = −2, then − x2 − 8 x − 5 =
(A) 3 (B) 7 (C) 15 (D) 23 (E) 25
11. If
(A) 6 (B) 6.5 (C) 7 (D) 7.5 (E) 8
12. Theo wants to buy a sweater that is priced at $60.00 before tax. The store charges a 6% sales tax on all purchases. If he gives the cashier $70.00 for the sweater, how much should he receive in change?
(A) $3.60 (B) $6.40 (C) $7.40 (D) $9.40 (E) $66.40
13. When m is subtracted from n, the result is r. Which of the following expresses the result when 2m is added to s?
(A) s + 2n − 2r (B) s + 2n + 2r (C) 2s + 2n − 2r (D) 2s + 2n + 2r (E) s − 2n + 2r
14. In the figure below, the slope of line l is
(A) 13 (B) 14 (C) 19 (D) 22 (E) 96
15. Ellen takes a trip that is y miles long in total, where y > 20. She travels the first 15 miles at an average speed of 30 miles per hour and the rest of the trip at an average speed of 40 miles per hour. Which of the following represents the total time of the trip, in hours?
(A) (B) (C) (D) (E)
16. If y varies directly as m and inversely as the square of n, and if y = 8 when m = 16 and n = 1, then what is the value of y when m = 8 and n = 4?
(A) 0.125 (B) 0.25 (C) 0.5 (D) 1 (E) 2
17. If a + b = s and a − b = t, then which of the following expresses the value of ab in terms of s and t?
(A) st (B) (C) (D) (E)
18. If y = m4 = n3 and y is greater than 1, then mn =
(A) (B) (C) (D) y7 (E) y12
19. In the figure below, if AB = 6 and BC = 12, what is the area of the shaded region?
(A) 20 (B) 22 (C) 24 (D) 26 (E) 28
20. Every car at a certain dealership is either a convertible, a sedan, or both. If one-fifth of the convertibles are also sedans and one-third of the sedans are also convertibles, which of the following could be the total number of cars at the dealership?
(A) 28 (B) 29 (C) 30 (D) 31 (E) 32
21. A square has a perimeter of 36 centimeters. What is its area in square centimeters?
(A) 24 (B) 36 (C) 49 (D) 64 (E) 81
22. If b is a positive integer less than 100, then how many integer pairs (a, b) satisfy the equation
(A) 7 (B) 8 (C) 9 (D) 10 (E) 11
23. According to the table below, how much will it cost, in dollars, to clean each bathroom twice and each office once in the McKenzie Office Building?
(A) 200 (B) 400 (C) 450 (D) 600 (E) 850
24. If a2 − b2 = 10 and a − b = 2, what is the value of a + b?
(A) 5 (B) 6 (C) 7 (D) 8 (E) 9
25. For all integers n greater than 1, let f (n) = k, where k is the sum of all the prime factors of n. What is the value of f(14) − f(6)?
(A) 4 (B) 5 (C) 6 (D) 9 (E) 14
26. The average (arithmetic mean) of four different positive integers is 20. What is the greatest possible value of any of these integers?
(A) 68 (B) 70 (C) 70 (D) 74 (E) 77
27. The radius of circle A is twice the radius of circle B. If the sum of their circumferences is 36π, then what is the radius of circle A?
(A) 9 (B) 12 (C) 14 (D) 16 (E) 18
28. The figure below shows a cube. How many different planes can be drawn such that each contains exactly two edges of the cube?
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8
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 18
1. If (x + 4) + 7 = 14, what is the value of x?
(A) 3 (B) 7 (C) 11 (D) 17 (E) 25
2. Erica spends $0.95 each day for her newspaper subscriptions. She would like to determine the approximate amount she spends during the month of July, which has 31 days. Which of the following would provide her with the best estimate?
(A) $0.50 (B) $1.00 (C) $1.50 (D) $0.50 (E) $1.00
3. In the figure below, lines l, m, and n intersect in a single point. What is the value of w + x?
(A) 40 (B) 70 (C) 90 (D) 130 (E) 140
4. Let the function g be defined by the equation g(x) = 3x + 4. What is the value of g(5)?
(A) 8 (B) 11 (C) 15 (D) 19 (E) 23
5. If x > y, which of the following equations expresses the fact that when the difference between x and y is multiplied by their sum, the product is 18?
(A) (x – y)2 = 18 (B) (x + y)2 = 18 (C) (x – y) (D) x2 – y2 = 18 (E) x2 + y2 = 18
6. If 3
(A) 3 (B) 9 (C) 27 (D) 36 (E) 81
7. Chris buys a chocolate bar and a pack of gum for $1.75. If the chocolate bar costs $.25 more than the pack of gum, how much does the pack of gum cost?
(A) $0.25 (B) $0.50 (C) $0.75 (D) $1.00 (E) $1.50
8. 40% of 80 is what percent of 96?
(A) 20% (B) 30% (C) 331/3 (D) 50% (E) 662/3%
9. If l, m, and n are positive integers greater than 1, lm = 21, and mn = 39, then which of the following must be true?
(A) n > l > m (B) m > n > l (C) m > l > n (D) l > n > m (E) n > m > l
10. According to the graph below, ABC Company showed the greatest change in profits between which 2 years?
(A) 1996 and 1997 (B) 1997 and 1998 (C) 1998 and 1999 (D) 1999 and 2000 (E) 2000 and 2001
11. In a 9th-grade class, 12 students play soccer, 7 students play tennis, and 9 students play lacrosse. If 4 students play exactly two of the three sports and all other students play only one, how many students are in the class?
(A) 28 (B) 24 (C) 20 (D) 18 (E) 16
12. The point (14, 14) is the center of a circle, and (2, 9) is a point on the circle. What is the length of the diameter of the circle?
(A) 24 (B) 26 (C) 50 (D) 144 (E) 169
13. The population of Boomtown doubles every 18 months. In January of 2000, its population was exactly 12,000. At this rate, approximately when should the population reach 96,000?
(A) January 2003 (B) July 2004 (C) January 2006 (D) July 2007 (E) January 2012
14. In how many different ways can five students of different heights be arranged in a line if the tallest student cannot be on either end?
(A) 24 (B) 25 (C) 72 (D) 96 (E) 120
15. In the figure below, a > 90 and b = c + 3. If a, b, and c are all integers, what is the greatest possible value of b?
(A) 43 (B) 46 (C) 60 (D) 86 (E) 89
16. In the figure below, Δ ACF is equilateral, with sides of length 4. If B, D, and E are the midpoints of their respective sides, what is the sum of the areas of the shaded regions?
(A) 3 (B) 3 (C) 4 (D) 4 (E) 6
17. Given the graph of y = f(x) below, which of the following sets represents all values of x for which f(x) ≥ 1?
(A) all real numbers (B) x ≥ 1 (C) −5 ≤ x ≤−1; 1 ≤ x ≤ 5 (D) −4 ≤ x ≤ −2; 2 ≤ x ≤ 4 (E) x ≤ −4; x ≥ 4
18. If a is a number chosen randomly from set X and b is a number chosen randomly from set Y, what is the probability that ab is greater than 20 but less than 50?
(A) (B) (C) (D) (E)
19. If wa × w5 = w15 and (w4)b = w12, what is the value of a + b?
(A) 6 (B) 7 (C) 11 (D) 12 (E) 13
20. Given the graph of y = f(x) below, which of the following represents the graph of y = f(x − 2)?
(A)
(B)
(C)
(D)
(E)
21. In the figure below, what is the value of 2x?
(A) 36 (B) 72 (C) 90 (D) 108 (E) 132
22. If (x − 4)2 = 36, then x could be
(A) - 6 (B) - 2 (C) 0 (D) 4 (E) 6
23. In the figure below, what is the value of a + b + c + d?
(A) 56 (B) 128 (C) 256 (D) 264 (E) 322
24. If f(x) = x2 − 4, for what positive value of x does f(x) = 32?
(A) 5 (B) 6 (C) 7 (D) 8 (E) 9
25. A can of mixed nuts contains cashews, almonds, peanuts, and walnuts in the ratio of 2 to 4 to 5 to 7, respectively, by weight. What fraction of the mixture by weight is almonds?
(A) (B) (C) (D) (E)
26. Twenty students in a chemistry class took a test on which the overall average score was 75. If the average score for 12 of those students was 83, what was the average score for the remaining members of the class?
(A) 60 (B) 61 (C) 62 (D) 63 (E) 64
27. If Anthony had 3 times as many marbles as he actually has, he would have
(A) 1:9 (B) 1:3 (C) 1:1 (D) 3:1 (E) 9:1
28. The first term of sequence I is 2, and each subsequent term is 2 more than the preceding term. The first term of sequence II is 2 and each subsequent term is 2 times the preceding term. What is the ratio of the 32nd term of sequence II to the 32nd term of sequence I?
(A) 1 (B) 2 (C) 226 (D) 227 (E) 232
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 19
1. A playground with an area of 3,600 square feet is to be divided into six different play stations. What is the average (arithmetic mean) area, in square feet, of the six stations?
(A) 400 (B) 500 (C) 600 (D) 700 (E) 800
2. If 3a = 15 and 4b = 10, what is the value of
(A) (B) (C) (D) 2 (E)
3. The graph below shows the salaries of five employees at UltraCorp over an eight-year period. Which employee’s salary has risen at the fastest rate over this period?
(A) Employee 1 (B) Employee 2 (C) Employee 3 (D) Employee 4 (E) Employee 5
4. One bucket of fried chicken serves either three adults or five children. If the Memorial Day fair committee wants to have enough chicken to serve 100 children and 60 adults, how many buckets of chicken are needed?
(A) 29 (B) 32 (C) 35 (D) 40 (E) 45
5. (5x − 3x + 4)(3x + 6x − 2) =
(A) 9x2 + 16x − 4 (B) 18x2 + 32x − 8 (C) 18x2 - 40x + 8 (D) 72x2 + 20x − 8 (E) 72x2 - 20x + 8
6. In the figure below, l || m and z = 55. What is the value of a + b + c?
(A) 235 (B) 265 (C) 275 (D) 305 (E) 315
7. If
(A) 3 (B) 6 (C) 9 (D) 27 (E) 81
8. Each term in a sequence of numbers, except for the first term, is 2 less than the square root of the previous term. If the third term of this sequence is 1, what is the first term?
(A) 1 (B) 9 (C) 11 (D) 121 (E) 123
9. In the figure below, rectangle ABCD has an area of 90 and is divided into 15 smaller squares. What is the sum of the areas of the shaded regions?
(A) 39 (B) 42 (C) 45 (D) 48 (E) 51
10. For all x greater than 2, let
(A) 27 (B) 29 (C) 42 (D) 45 (E) 54
11. In the correctly worked addition problem below, X and Y represent two different digits. What digit does X represent?
(A) 0 (B) 1 (C) 4 (D) 8 (E) 9
12. If the average (arithmetic mean) of the three numbers below is 3x and x ≠ 0, what is y in terms of x?
(A) (B) 2x (C) 3x (D) x + 7 (E) 3x - 3
13. In the figure below, what is the value of x in terms of w?
(A) w - 2 (B) w - 1 (C) w (D) w + 1 (E) w + 2
14. When r is divided by 10, the remainder is 9. What is the remainder when r + 2 is divided by 5?
(A) 0 (B) 1 (C) 3 (D) 4 (E) 14
15. If five distinct lines lie in a plane, then at most how many distinct points can lie on two or more of these lines?
(A) 6 (B) 7 (C) 8 (D) 9 (E) 10
16. A pile of playing cards consists of only kings, jacks, and queens. If the probability of randomly choosing a king is
(A) (B) (C) (D) (E)
17. In the figure below, ΔVXT is equilateral and WU = WY. If the measure of ∠VWU is twice the measure of ∠VUW, what is the measure of ∠TUY?
(A) 55 (B) 60 (C) 65 (D) 70 (E) 75
18. If m and n are positive numbers, what percent of m − 4 is n + 2? (A) (B) (C) (D) (E)
19. At time t = 0, a rocket was launched from a platform m meters below the ground. Until the rocket hit the ground, its height, in meters, after t seconds was given by the function h bellow. For which of the following values of t did the rocket have the same height as it did when t = 10? Date: 2015-12-24; view: 1002 |
, then what is the smallest possible positive value of m?
and the area of the triangle is 48 square units. What is the value of x + y?
?
30
30
(x + y) = 18
- 7 = 20, what is the value of x?
as many marbles as Billy has. What is the ratio of the number of marbles Anthony has to the number of marbles Billy has?
?
+ 16 = 79, what is the value of x?
be defined as the sum of the positive integers less than x. What is the value of 
?
and the probability of randomly choosing a queen is 
, what is the probability of randomly choosing a jack?
