Directions: For this section, solve each problem and decide which is the best of the
choices given. Fill in the corresponding circle on the answer sheet. You may use any
available space for scratchwork.
1. If 2 + a = 2 – a, what is the value of a ?
(A)
(B)
(C)
(D)
(E)
–1
0
1
2
4
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2. If AC = 4, what is the area of ABC above?
(A)
(B) 2
(C)
(D) 4
(E) 8
3. In the figure above, the perimeter of square A is
of square B is
the perimeter of square B, and the perimeter
the perimeter of square C. If the area of square A is 16, what is the area of
square C ?
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(A)
(B)
(C)
(D)
(E)
24
36
64
72
81
4. A bakery uses a special flour mixture that contains corn, wheat, and rye in the ratio of 3:5:2. If
a bag of the mixture contains 5 pounds of rye, how many pounds of wheat does it contain?
(A) 2
(B) 5
(C) 7.5
(D) 10
(E) 12.5
5. If
(A)
(B)
(C)
(D)
(E)
and
36
30
18
12
9
are diameters with lengths of 12, what is the area of the shaded region?
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6. If the product of x and y is 76, and x is twice the square of y, which of the following pairs of
equations could be used to determine the values of x and y ?
(A) xy = 76
x = 2y2
(B) xy = 76
x = (2y)2
(C) x + y = 76
x = 4y2
(D) x + y = 76
x = 4y
(E) xy = 76
x = 2y
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7. A coffee shop noticed that the outside temperature affected the number of customers who came
to the shop that day, as shown in the table above. Which of the following graphs best
represents the relationship between the outside temperature and the number of customers, as
indicated by the table?
(A)
(B)
(C)
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(D)
(E)
8. If c is positive, what percent of 3c is 9 ?
(A)
(B)
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(C)
(D) 3%
(E)
D (–6, 3)
E (–1, –1)
F (–1, 3)
9. The coordinates of points D, E, and F in the xy-plane are given above. What is the perimeter of
∆DEF ?
(A)
(B)
(C)
(D)
(E)
12
20
9+
9+
(approximately 13.12)
(approximately 15.40)
(approximately 12.25)
10. Fifteen percent of the coins in a piggy bank are nickels and five percent are dimes. If there are
220 coins in the bank, how many are not nickels or dimes?
(A)
(B)
(C)
(D)
(E)
80
176
180
187
200
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11. At the beginning of 1999, the population of Rockville was 204,000 and the population of
Springfield was 216,000. If the population of each city increased by exactly 20% in 1999, how
many more people lived in Springfield than in Rockville at the end of 1999 ?
(A)
(B)
(C)
(D)
(E)
2,400
10,000
12,000
14,400
43,200
12. If x + y = z and x = y, then all of the following are true EXCEPT
(A) 2x + 2y = 2z
(B) x − y = 0
(C) x − z = y − z
(D) x =
(E) z − y = 2x
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13. In a list of seven integers, 13 is the lowest member, 37 is the highest member, the mean is 23,
the median is 24, and the mode is 18. If the numbers 8 and 43 are then included in the list,
which of the following will change?
I. The mean
II. The median
III. The mode
(A)
(B)
(C)
(D)
(E)
I only
I and II only
I and III only
II and III only
I, II, and III
14. If |x| ≠ 0, which of the following statements must be true?
(A) x is positive.
(B) 2x is positive.
(C)
is positive.
(D) x2 is positive.
(E) x3 is positive.
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15. Rock climbing routes are rated on a numbered scale with the highest number representing the
most difficult route. Sally tried a range of shoe sizes on each of several routes of varying
difficulty and found that when she wore smaller shoes, she could climb routes of greater
difficulty. If D represents the difficulty rating of a route Sally successfully climbed
and s represents the size of the shoes she wore on such a route, then which of the following
could express D as a function of s ?
(A)
(B)
(C)
(D)
D(s) = s2
D(s) =
D(s) = 4s
D(s) = s − 3.5
(E) D(s) =
16. If a2b = 122, and b is an odd integer, then a could be divisible by all of the following EXCEPT
(A) 3
(B) 4
(C) 6
(D) 9
(E) 12
17. An equilateral triangle has sides of length x. If a second equillateral triangle has sides of length
2x, what is the ratio of the area of the first triangle to the area of the second?
(A) 1 : 16
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(B)
:2
(C) 1 : 2
(D) 1 : 4
(E) 1 :
Note: Figure not drawn to scale.
18. In the figure above,
(A)
(B)
(C)
(D)
(E)
||
. If the length of
is 3, what is the length of
?
3
4
5
3
It cannot be determined from the information given.
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19. If (a − 5)(b + 5) < 0, then which of the following must be true?
(A)
(B)
(C)
(D)
(E)
a<5
aπ − 5
bπ − 5
b > –5
a>5
20. The value of the nth term of a sequence is given by the expression a3n – 3. If the second term
of the sequence is 61, which of the following could be the value of a ?
I. –2
II. 2
III. 4
(A)
(B)
(C)
(D)
(E)
I only
II only
III only
I and II only
II and III only
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