1. How many distinct real roots does the polynomial 10x 3 + 7x 2 − 8x have?
a) 0
b) 1
c) 2
d) 3
e) Cannot be determined
2. The largest possible value of the function f ( x ) = −4x 2 − 2x + 6 is
a) −
1
4
b)
1
4
c)
25
4
d)
27
95
e)
4
16
3. The second term of an arithmetic sequence is –2 and the eighth term is
40. What is the tenth term?
a) 56 b)38 c)61
d)54 e) none of these
4. For 1 ≤ x ≤ 3 , simplify 5 − 2x + 3 .
a) 1 − x
b) 8 + 2x
c) 2 − 2x
d) 2x − 2
e) 2 + 2x
5. How many different amounts of postage between 50 cents and $1.00,
inclusive, can be made using only 4-cent and 7-cent stamps?
a) 18 b) 20 c) 39 d) 50 e) 51
⎧5x − 2y = 6
6. The following system of equations ⎨
⎩3x + y = 11
a) has a unique solution (x, y) with x < y
b) has a unique solution (x, y) with x = y
c) has a unique solution (x, y) with x > y
d) has infinitely many solutions
e) does not exist
7. One angle of a triangle is three times as large as another. The measure of
the third angle is 40° more than that of the smallest angle. Find the
measure of the largest angle.
a) 68°
b) 72°
c) 76°
d) 80°
e) 84°
8. How many distinct real roots does the equation t 7 + 8t 4 + 16t have?
a) 7 b) 4 c) 3 d) 2 e) 1
3x − 2
defined?
x +1
⎛2 ⎞
⎡2 ⎞
c) ( −∞, −1) ∪ ⎜ , ∞ ⎟ d) ( −∞, −1) ∪ ⎢ , ∞ ⎟
⎝3 ⎠
⎣3 ⎠
9. For which values of x is the expression
a)
( −∞, −1) ∪ ( −1, ∞ )
b) ( −∞,1) ∪ (1, ∞ )
⎡ 2⎤
e) ⎢ −1, ⎥
⎣ 3⎦
10. The graph of the equation x 2 = 16 − 4 y 2 is which of the following?
a) hyperbola
b) ellipse c) circle
11. The base-10 unit digit in 33082008
a) 1
b) 3
c)4
is
d) parabola
d)7
e) none of these
e) 9
12. Find the center of the circle x 2 + y 2 − 10x + 2y + 17 = 0 .
a) (-5,-1)
b) (-10, 2)
c) (5, 1)
d) (5, -1)
e) (-5,1)
13. A group of applicants for training as air-traffic controllers consisted of
35 pilots, 20 veterans, 30 pilots who were not veterans, and 50 people who
were neither pilots nor veterans. How large was the group?
a) 60
b) 65
c) 100
d) 110
e) 135
14. Simplify
a) 3 ⋅ 5 −2
5
−2 + 5 −64 − 3 5 2 .
b)
5
−552
c) −4 ⋅ 5 2
15. Find all real solutions of
a) {−1, 2}
b) ∅ c) {11}
d) −6 ⋅ 5 2
e) 9 ⋅ 5 −2
3
1
.
=
x − x − 2 3x + 3
2
{
d) −1 − 3 2, −1 + 3 2
}
e) none of these
16. A cylinder with a radius of 3 inches and a height of 5 inches has its
height doubled. How many times greater is the volume of the larger cylinder
than the volume of the smaller cylinder?
a) 2 times b) 4 times c) 8 times d) 8π 3 times e) none of these
17. A set of books can be arranged on a shelf in 120 different ways, how
many books are there?
a) 5 b) 6 c) 7 d) 8 e) 9
18. An unfair coin is twice as likely to land “Heads” as “Tails”. If the coin is
tossed twice, what is the probability that it will land “Tails” both times?
a) 1/4
b) 1/6
c) 1/8
d) 1/9
e) 1/3
19. Find the coefficient of y in the expansion of ( 2x + y ) .
2
a) 4
b) 4x
c) 8
d) 8x
e) 8x 2
20. A 12 inch wire is bent into an equilateral triangle. Find the area of the
triangle.
a) 4 3
b) 4 c) 2 3
d) 8 e) 8 3
21. It normally takes 2 hours to fill a swimming pool. The pool has developed
a slow leak. If the pool were full, it would take 10 hours for all the water to
leak out. If the pool is empty, how long will it take to fill it?
a) 2hr 15 min b) 2hr 30 min c) 2hr 36 min d) 2hr 46 min e) none of these
22. When a small plane flies with the wind, it can travel 800 miles in 5
hours. When the plane flies in the opposite direction, against the wind, it
takes 7 hours to fly the same distance. Find the rate of the plane in still air.
a) 274 mph b) 137 mph c) 400/3 mph d) 960/7 mph e) 1920/7 mph
23. In a wrestling competition, the total weight of the two contestants is
700 lbs. If twice the weight of the first contestant is 275 pounds more than
the weight of the second contestant, what is the weight, in pounds, of the
first contestant?
a) 312.5
b) 212.5
c) 325
d) 425
e) none of these
24. A baked potato covered with cheddar cheese weighs 180 grams and
contains 10.5 grams of protein. If cheddar cheese contains 25% protein, and
a baked potato contains 2% protein, how many grams of cheddar cheese are
there?
a) 25
b) 30
c) 35
d) 40
e) 45
25. If three distinct positive integers have an arithmetic mean of 200, and
if the smallest of the three integers is 120, then the largest of the three
can be at most
a) 280
b) 350
c) 359
d) 360
e) 460