Читайте также:
|
(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 
, and ray AC bisects angle BAD. What is the value of x?
(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 
. If m is a positive integer, what is 
?
(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 
. How many black marbles must be added to the jar so that the probability of choosing a black marble 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 
150
(B) (16) · 5 + x ≥ 150
(C) (16) · 5 − x ≥ 150
(D) (16) · 5+ 5x 
150
(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 n 8 = 480 and n 7 = 12 m, what is the value of 3 mn?
(A) 30
(B) 60
(C) 90
(D) 120
(E) 480
13. In Δ PQR, the length of side 
is 24 and the length of side 
is 18. What is the least possible integer length of 
?
(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 = a n b p, which of the following must be true?
I. 2 m = 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 
of a number is 20, what is 
of the number?
(A) 0.5
(B) 4
(C) 8
(D) 16
(E) 32
18. In Δ XYZ 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 2 n?
(A) 18
(B) 36
(C) 64
(D) 72
(E) 144
21. If 
= 16, which of the following could be the value of x?
(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) 50 p + 400
(B) 400 - 
(C) 400 – 50 p
(D) 500 p - 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
(D) 2000
(E) 2001
24. When a positive integer, m, is divided by 7, the remainder is 4. Which of the following expressions will yield a remainder of 3 when it is divided by 7?
(A) m + 2
(B) m + 3
(C) m + 4
(D) m + 5
(E) m + 6
25. If a 2 − b 2 = 12, and (a − b) = 4, then what is the value of ab?
(A) -1 
(B) -0.5
(C) 0
(D) 3.5
(E) 
26. For all numbers x and y, let x♣y be defined as x♣y = x 2 − 2 xy + y 2. What is the value of (2♣4)♣8?
(A) 1
(B) 4
(C) 12
(D) 16
(E) 20
27. In one day, Mitchell spends 30% of the day sleeping, 35% of the day at work, 5% of the day at the gym, five additional hours at home, and the rest of the day in the car. How many minutes does he spend in the car each day? (1 hour = 60 minutes)
(A) 2.2
(B) 60
(C) 120
(D) 132
(E) 432
28. In the figure below, the circle with center O is inscribed in square WXYZ. What is the area of the shaded portion of the figure?
(A) 8 - 2π
(B) 8 - π
(C) 4 - 2π
(D) 2 - π
(E) 4 - π
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 22
1. If one of the angles in a triangle is 100°, what is the average (arithmetic mean) of the measures, in degrees, of the other two angles?
(A) 20°
(B) 30°
(C) 40°
(D) 60°
(E) 80°
2. If k is an integer that is 1 less than a multiple of 6, which of the following could be k + 1?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
3. Which of the following expresses the number that is 15 more than the product of 3 and m − 2?
(A) 3 m - 21
(B) 3 m - 13
(C) 3 m - 6
(D) 3 m + 9
(E) 3 m + 13
4. In the figure below, four line segments intersect at a single point. What is the value of m + n?
(A) 45
(B) 50
(C) 60
(D) 65
(E) 85
5. If x % of 30 is 12, what is 4 x % of 15?
(A) 6
(B) 12
(C) 18
(D) 24
(E) 48
6. If 0 < x < 1 then which of the following must be true?
I. 
< x
II. x 2 > x
III. − x < −1
(A) None
(B) I only
(C) II only
(D) III only
(E) I and III only
7. If every gadget costs p dollars to make, and each one sells for m dollars, then which of the following expressions represents the profit made if 10 gadgets are made but only 9 are sold?
(A) 10 m – 9 p
(B) 9 m – 10 p
(C) 10(m - p) – 9 m
(D) 9 p + 10 m
(E) 10(m – p) + 9 m
8. If y = f (x) such that y varies inversely as x, and the points (4, 6) and (2, m) lie on the graph of y = f (x), what is the value of m?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
9. A machine can fill 200 boxes of cereal in 5 minutes. At this rate, how many hours will it takes this machine to fill 24,000 boxes of cereal? (60 minutes = 1 hour)
(A) 10
(B) 24
(C) 100
(D) 210
(E) 600
10. In the figure below, what is the value of x in terms of n?
(A) 
(B) 
(C) 
(D) 
(E) 
11. Which of the following represents all possible solutions to the equation below?
(r – 5)2 = (r + 2)2
(A) -5 and 2 only
(B) 5 and -2 only
(C) 3.5 only
(D) 1.5 only
(E) 0 only
12. A certain class has 8 boys and 10 girls. How many different sets of four class officers-president, vice president, treasurer and secretary-can be formed from students in this class if the president and treasurer must be girls and the vice president and secretary must be boys?
(A) 25,600
(B) 6,400
(C) 5,040
(D) 3,200
(E) 2,520
13. In the figure below, if the shaded region has an area of 15, what is the slope of AB?
(A) 
(B) 
(C) 
(D) 1
(E) 
14. If m > 1, then 
=
(A) m + 1
(B) m
(C) m - 1
(D) -1
(E) 
15. If a circle on the coordinate plane has a center at (6, −6), which of the following could not be the number of points on the circle that also lie on a coordinate axis?
I. 1
II. 2
III. 3
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) II and III only
16. A certain car race consists of three legs of equal distance. On the first two legs of the race, a car travels an average of 50 miles per hour. On the last leg of the race, the car travels at an average of 75 miles per hour. What is the average speed, in miles per hour, for this car over the entire race?
(A) 52.00
(B) 56.25
(C) 58.33
(D) 62.50
(E) 66.67
17. In the figure below, what is the length of line segment AE in terms of x?
(A) 3 x + 11
(B) 5 x + 14
(C) 7 x + 8
(D) 6 x + 11
(E) 6 x + 17
18. A video store charges an annual account fee of $3.00 per customer and has a total of 5,400 members. If everyone pays the fee, what is the total amount collected from the members?
(A) $16.20
(B) $162.00
(C) $1,620.00
(D) $16,200.00
(E) $162,000.00
19. A plastic container contains 2 pints of water. If 8 tablespoons of water are poured out, what fraction of the original amount remains? 1 pint = 2 cups, 1 cup = 16 tablespoons.
(A) 
(B) 
(C) 
(D) 
(E) 
20. Lines m and n intersect, as shown, in the figure below. What is the value of y?
(A) 52
(B) 58
(C) 62
(D) 68
(E) 72
21. Elysha uses air-conditioning year round and spends, on average, $125 per month to cool her apartment. A new energy-efficient air conditioning system would cost her $3,000 to install and only $25 per month thereafter to cool the apartment. If she installs the new system, how many months will it take for her total savings in cooling costs to equal the cost of the system?
(A) 30
(B) 35
(C) 40
(D) 45
(E) 50
22. In the correctly worked addition problem below, A, B, and C represent different digits. What is the value of B?
(A) 0
(B) 1
(C) 4
(D) 5
(E) 8
23. The radius of the base of the right circular cone below is 4 inches and the height of the cone is 14 inches. A cut is made parallel to the circular base such that it produces a smaller cone with a radius of 3 inches. What is the height, in inches, of the smaller cone?
(A) 3.5
(B) 6.0
(C) 7.0
(D) 10.5
(E) 11.0
24. A right triangle has side lengths of x − 1, x + 1, and x + 3. What is its perimeter?
(A) 7
(B) 24
(C) 28
(D) 32
(E) 36
25. In the repeating decimal below, what is the 3,000th digit to the right of the decimal?
0. 
= 0.245162451624516 …
(A) 2
(B) 4
(C) 5
(D) 1
(E) 6
26. The pie graph below shows the housing situation of families in Glenville. If there are 12,000 families in Glenville, then how many families own homes?
(A) 3,000
(B) 4,000
(C) 6,000
(D) 8,000
(E) 9,000
27. In the figure below, BD || CE. What is the length of DE?
(A) 6 
(B) 6 
(C) 2 
(D) 4 
(E) 3 
28. Given the graph of y = f (x) below, which of the following represents the graph of y = f (x + 3) + 3?
(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 23
1. If x 3y = x 9 and x > 1, then y =
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
2. The ratio of 1 to 1.4 is equal to the ratio of
(A) 1 to 4
(B) 3 to 4
(C) 5 to 7
(D) 7 to 5
(E) 4 to 3
3. A line and a ray intersect as shown below. What is the value of 2 x + 5?
(A) 20
(B) 25
(C) 40
(D) 45
(E) 50
4. When three times a number is divided by two, the result is 39. What is that number?
(A) 20
(B) 21
(C) 24
(D) 26
(E) 30
5. How much greater is x + 5 than x − 5?
(A) 2
(B) 5
(C) 7
(D) 10
(E) 12
6. Rectangle M has an area of A square feet. The length and width of another rectangle, N, are each triple the length and width of rectangle M. What is the area of rectangle N in terms of A?
(A) 2 A
(B) 3 A
(C) 6 A
(D) 9 A
(E) 12 A
7. If a circle has a circumference of 10, what is the ratio of the circumference of the circle to its diameter?
(A) 1:2π
(B) 1:π
(C) π:1
(D) 2π:1
(E) π:2
8. What is the distance from point A to point B in the figure below?
(A) 1
(B) 3
(C) 4
(D) 5
(E) 7
9. A theater purchases $500 worth of Sticky Bears and Chocolate Bombs. Each bag of Sticky Bears costs $1.50 and each bag of Chocolate Bombs costs $1.00. If a total of 400 bags of candy were purchased, how many bags of Chocolate Bombs did the theater buy?
(A) 100
(B) 150
(C) 200
(D) 250
(E) 300
10. The median of a set of seven consecutive even integers is 10. What is the average (arithmetic mean) of this set?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
11. The total revenue collected for movie tickets at the Bijou is what percent of the total revenue collected for movie tickets at the Community Cinema?
(A) 25%
(B) 50%
(C) 75%
(D) 100%
(E) 200%
Дата добавления: 2015-10-26; просмотров: 210 | Нарушение авторских прав
| <== предыдущая страница | | | следующая страница ==> |
| B) The mild temperature was lowered by a heavy rain in the morning, and the temperature dropped lower by evening. 8 страница | | | B) The mild temperature was lowered by a heavy rain in the morning, and the temperature dropped lower by evening. 10 страница |