PAGE I
1. If x − y = 9 and x + 2 y = 3 , then x + y =
a) 5
b) 6
c) 7
d) 8
e) none of these
2.
If x = −2 , y = 3 and z = 5, then
a) 4
3.
b) 1
c) ½
x− y − x+ y
( x − y) + z − 6
d) -1
is
e) none of these
The line through the points (1,4) and (3,-3) has slope
a) 7/2
b) -7/2
c) 1/2
d) -1/2
e) none of these
4. A small circle passes through the center of a large circle and is tangent to
the large circle. The area of the large circle is 4 square inches. The area, in
square inches, outside the small circle and also inside the large circle is
a)
2
b) 8/3
5.
1/ 2 + 1/ 3
=
1/ 4 −1/ 5
a)
1/60
b) 60
c) 3π / 4
c) 50/3
d)
2π / 3
d) 3/50
e) none of these
e) none of these
PAGE II
6.
Let A and B be sets with A = {1,2,4,5,7} and B = {2,3,4,6,8} then ( A ∩ B) ∪ B =
a) {1,2,3,4,5,6,7,8}
b) {1,6,8}
c) empty set
d) {2,3,4,6,8}
e) none of these
7. Joe spent $900 for a car and spent an additional $200 for repairs. He then sold it for 10%
more than his total spending. What was his net profit in dollars?
a) 90
b) 100
c) 110
d) 120
e) none of these
8. A sequence of Figures is formed by starting with one square and adding
4 additional squares to obtain successive figures. Figures 1, 2 and 3 are
shown. How many squares will be in Figure 2012?
a) 4021
b) 6042
c) 8042
d) 10042
e) none of these
9.
If x and y are two numbers whose sum is a and whose product is b, then x 2 + y 2 is
a)
a − b2
10.
b)
a 2 − 2b
c)
a2 + b
d
a2 + b2
e) none of these
If f ( x) = 1 + x 3 and g ( x) = 3 x − 1 , then g ( f (2 )) is
a) -2
b) 8
c) 2
d) 4
e) none of these
PAGE III
11.
If 10 is the median of the list, [n,n+3,n+4,n-5,n+6,n+1,n-2], then the average of the list is
a) 6
b) 8
c) 10
d) 11
e) none of these
12.
Sally walks on a level path from A to B at 4 mph, up a hill from B to C
at 3 mph, back down to B at 6 mph and finally returns from B to A at 4 mph. If
her round trip time was 6 hours then her total round trip distance, in miles, was
a) 12
b) 6
c) 24
d) cannot be determined
e) none of these
C
13. An equilateral triangle ABC is inscribed in a circle with center O. If the
triangle area is 3 , then the circle area is
a) 3 π /2
b)
π 3
c)
2π 3 / 3
d) 3π 3 / 4
e) none of these
O
A
B
14. A coin, 1/2 inch in diameter, is tossed onto a black and red checkerboard. The center of the
coin lands randomly on one of the squares of the board. If the squares have 2 inch sides, then the
probability that the entire coin is within one of the black squares is
a) 1/2
b) 9/16
c) 1/4
d) 9/32
e) none of these
15. The trapezoid ABCD shown has AB parallel to CD, AD perpendicular to AB,
AD = 12, AB = 18, and an area of 186. The perimeter of the trapezoid is
a) 56
b) 54
c) 62
e) 60
e) none of these
D
A
C
B
PAGE IV
16. If f ( x) = 1 + x 3 and [ g ( x)]3 = x − 1 , then the sum of all possible values of
g ( f (2 )) is
a) 0
b) 2
c) 4
d) 6
e) none of these
Let A = x 2 − 6 x − 6 and B = x 2 + 4 x − 60 . Find all possible values of x that satisfy the
equation A B = 1 . The sum of all these x values is
17.
a) -4
b) 6
c) 2
d) 0
e) none of these
18. In the 4 × 4 grid shown, three coins are randomly placed in different squares. The
probability that no two coins lie in the same row or column is
a) 9/64
b) 6/35
c) 7/40
e) 9/65
e) none of these
19. A rectangular piece of paper, PQRS, has PQ = 15 and QR = 20. The
piece of paper is glued on the surface of a large cube so that P and R are on
vertices of the cube. (Note that PQR and PSR lie at on the front and top faces
of the cube, respectively.) The shortest distance from Q to S, as measured
through the cube, is
a)
384
b)
337
c)
342
d)
386
S
P
R
Q
e) none of these
20. Given the rectangle ABCD with AB = 8 inches and AD = 4 inches. The
rectangle is folded so that vertices A and C coincide. What is the length, in inches, of
the crease?
a) 3 6 / 2
b) 2 5 / 3
c) 2 6 / 3
d) 2 5
e) none of these