Diagnostic Examination

Georgia O'Keeffe's Line and Curve

1. If you divide 12ab3 by 4b, the answer is
(a) 0
(b) ab2
(c) 3ab2
(d) ab3 - b
(e) 8b2
2.
Simplify
(3 a2 b-3)-4

(12ab3)-5
(a) 96a-13b27
(b) 48a-13b-27
(c) 48a-3b27
(d) All of the other answers are incorrect.
(e) 96a-3b27
3.
Simplify
x + 1

(x2 - 2x - 3)

x - 3

x + 1
(a)
1

x-3
(b) 12
(c)
1

x+1
(d)
( x+1

x - 3
) ( x2 - 2x - 3

x+1
)
(e)
x+1

(x-3)2
4. The area of a right triangle with sides 3, 4, and 5 is
(a) 12
(b) 6
(c) 10
(d) 15
(e) 20
5. Find the equation of the line through (-1,1) and (5,2).
(a) x + y = 0
(b) x - 2y - 1 = 0
(c) x - y + 2 = 0
(d) x - 6y + 7 = 0
(e) x - y - 2 = 0
6. The distance from the point (x,y) to the point (2,3) is twice the distance from the point (x,y) to the point (5,7). What is the maximum possible distance from (x,y) to (2,3)?
(a) 5
(b) 15
(c) 25
(d) 4
(e) 10
7. If 3x + 6 = 12, what is x?
(a) x = -2
(b) x = 4
(c) x = 0
(d) All of the other answers are incorrect.
(e) x = 2
8. If x = y and x2y2 - 5xy + 6 = 0, then which of the following is possible?
(a) x2 = 6
(b) x = 3
(c) x = 6
(d) x2 = 3
(e) x = 2
9. How many real solutions for x are there to the equation x2 + 3x + 8 = 0?
(a) 1
(b) 3
(c) It cannot be determined.
(d) 2
(e) 0
10. If log(x) = 4 then log(x2) is
(a) 4
(b) 1
(c) 10
(d) 2
(e) 8
11. log(x) < log(x +1) reduces to
(a) 1 < x
(b) x < 1
(c) x < x +1
(d) 0 < x
(e) x < 0
12. log(x2 - 2x +1) > log(25) reduces to
(a) x > 6
(b) x < -4 or x > 6
(c) x < 6
(d) x > -4
(e) x < -4
13. If h(x) = x2, g(x) = x+1, and f(x) = x +3, then what is h(g(f(0)))?
(a) 1
(b) 0
(c) 9
(d) 4
(e) 16
14. If f(x) = 3x + 3 and g(y) = 2y + 5, what is g(f(2))?
(a) All of the other answers are incorrect.
(b) 23
(c) 7
(d) 9
(e) 30
15. If f(x)=3x2 + 3, what is f(f(a))?
(a) 3(3a2 + 3)2 + 3
(b) 3a2 + 3
(c) Not defined.
(d) 0
(e) All of the other answers are incorrect.
16. The inequality   x2 - 2x > -1   reduces to
(a) x < 1
(b) x > 1
(c) x > -1
(d) x is not equal to 1
(e) x < -1
17. The inequality (x - 1)2 > 1 is equivalent to
(a) 0 < x and x < 2
(b) x < 0 or x > 2
(c) x > 2
(d) x < -2
(e) x < 0
18. The expression ( x + 1)(x + 2) > 0 is equivalent to which of the following?
(a) x > -1
(b) All of the other answers are incorrect.
(c) x < -2
(d) x < -2 or x > -1
(e) -1 > x > -2
19. If 3x + 4y = 7 and 5x-4y = 1, then xy is
(a) Cannot be determined
(b) 3
(c) 2
(d) 4
(e) 1
20. If x - y = 4 and 4x - y = 1, then 3xy is
(a) 12
(b) Cannot be determined
(c) 9
(d) 15
(e) 6
21. If y + 3x + 2 = 0 and y = x2, then there is a solution with x given by
(a) x = 2
(b) Cannot be determined
(c) x = 0
(d) x = -1
(e) x = 1
22. The radian measure of an angle of 60 degrees is
(a) pi/3
(b) pi/4
(c) pi
(d) pi/2
(e) 2(pi/3)
23. If sin(a) = 1, cos(b) > 0, and sin(b) = 1/2, then sin(a + b) is
(a) 2/3
(b) 3/2
(c) 2/(31/2)
(d) 1/2
(e) 31/2/2
24. A triangle has sides of length 5, 5 and 8. What is the sine of its smallest angle?
(a) 3/5
(b) 4/5
(c) 8/5
(d) 3/8
(e) 5/8