Diagnostic Examination

Georgia O'Keeffe's Line and Curve

1. If you divide 12ab3 by 4b, the answer is
(a) 3ab2
(b) ab2
(c) ab3 - b
(d) 8b2
(e) 0
2.
Simplify (x3 + 2x2 + 2x + 1)

(x + 1)
(a) x2 + 1
(b) x2 - x + 1
(c) x2 - 2x + 1
(d) x2 + x + 1
(e) x2 + 2x + 1
3.
Evaluate
( 1

x
+ 3 ) ( 5 + 2

x2
).
(a)
5

x
+ 15 + 2

x3
+ 6

x2
(b)
4

x
+ 6

x2
(c)
11

x
+ 15 + 2

x2
(d)
5

x
+ 6

x2
(e) All of the other answers are incorrect.
4. What is the slope of the line through (1,2) and (2,-1)?
(a) -3
(b) 1/3
(c) 3
(d) -1/3
(e) 0
5. A triangle has a side of length 3, a side of length 4, and a side of length x. The possible values of x are
(a) x > 7
(b) 1 < x < 7
(c) x = 5
(d) 0 < x < 5
(e) 0 < x
6. The line containing the points (1,1) and (1,-1) is perpendicular to the line
(a) x = 5
(b) y -1 = x -1
(c) y = 5
(d) y = 2x +1
(e) y = -x -1
7. Let f(x) = 3x + 2. For which x is f(x) = -2?
(a) -4/3
(b) -2/3
(c) 0
(d) -3/2
(e) 4/3
8. If x = 3, find the smallest value of y which satisfies y2x + 3yx2 + 54 = 0.
(a) 0
(b) -6
(c) -3
(d) 3
(e) There is no smallest value.
9. Find the largest solution of x3 + 4x2 + 3x = 0.
(a) x = -1
(b) x = 0
(c) x = 1
(d) x = -3
(e) x = -2
10. [x2]1/2 reduces to
(a) 1
(b) 0
(c) x2
(d) |x|
(e) x
11. log2(3xy2) is equal to which of the following?
(a) All of the other answers are incorrect.
(b) 3log2(x) + 2log2(y)
(c) log2(3) + log2(x) + log2(y2)
(d) log2(3x) log2(y2)
(e) 3 log2(x) + [log2(y)]2
12. log(x2 - 2x +1) > log(25) reduces to
(a) x > -4
(b) x < -4
(c) x < 6
(d) x > 6
(e) x < -4 or x > 6
13. The function f(x) = x2 has range
(a) The set of all numbers x such that x is less than or equal to 1
(b) The set of all numbers x such that x is greater than or equal to 1
(c) The set of all numbers
(d) The set of all numbers x such that x is less than or equal to 0
(e) The set of all numbers x such that x is greater than or equal to 0
14. If f(x) = 3x + 3 and g(y) = 2y + 5, what is f(g(2))?
(a) 9
(b) 7
(c) 3
(d) 30
(e) 23
15. If f(x)=3x2 + 3, what is f(f(a))?
(a) 0
(b) Not defined.
(c) 3a2 + 3
(d) 3(3a2 + 3)2 + 3
(e) All of the other answers are incorrect.
16. The expression -18 < -6x < 12 is equivalent to which of the following?
(a) -2 > x > -3
(b) 3 > x > 2
(c) 2 > x > -3
(d) 3 > x > -2
(e) All of the other answers are incorrect.
17.
Simplify
-10 < 4x + 2

5
< 10
(a) All of the other answers are incorrect.
(b) -12 < x < 13
(c) -13 < x < 12
(d) -13 < x < 13
(e) -12 < x < 12
18.
The inequality
x2- 2x + 1
x2 + x + 1
> 0
is equivalent to:
(a) x < 0
(b) x > 1
(c) x > 0
(d) x < 1
(e) x is not equal to 1
19. If 3x + 4y = 7 and 5x-4y = 1, find x and y.
(a) x = 2 and y = 1
(b) x = -1 and y = 1
(c) x = 1 and y = -1
(d) x = 1 and y = 1
(e) x = 2 and y = 2
20. If y + 4x - 18 = 0 and y2 = x, then there is a solution with y given by
(a) y = 2
(b) y = 0
(c) Cannot be determined
(d) y = 1
(e) y = 9/4
21. If y + 3x + 2 = 0 and y = x2, then there is a solution with x given by
(a) Cannot be determined
(b) x = -1
(c) x = 1
(d) x = 2
(e) x = 0
22. The radian measure of an angle of 60 degrees is
(a) pi/4
(b) 2(pi/3)
(c) pi/2
(d) pi
(e) pi/3
23. If sin(a) = 1, cos(b) > 0, and sin(b) = 1/2, then sin(a + b) is
(a) 31/2/2
(b) 3/2
(c) 2/(31/2)
(d) 2/3
(e) 1/2
24. If sin(a + b) = 1 and cos(a) = 0, then cos(2b) is
(a) cannot be determined
(b) 0
(c) 1/2
(d) 1
(e) 2