Diagnostic Examination

Georgia O'Keeffe's Line and Curve

1. Factor   x2 - 5x + 6.
(a) (x - 2)(x + 3)
(b) (x - 2)(x - 3)
(c) (x + 2)(x + 3)
(d) x2 - 5 x + 6
(e) (x + 3)(x - 2)
2. Find the product (2x+y)(y-3x).
(a) -6x2 + y2
(b) -xy
(c) All of the other answers are incorrect.
(d) 6x2 + y2 - xy
(e) -6x2 + y2 - xy
3.
Evaluate
( 1

x
+ 3 ) ( 5 + 2

x2
).
(a)
5

x
+ 15 + 2

x3
+ 6

x2
(b) All of the other answers are incorrect.
(c)
11

x
+ 15 + 2

x2
(d)
5

x
+ 6

x2
(e)
4

x
+ 6

x2
4. The line perpendicular to the line which contains the points (1,1) and (2,2) has slope
(a) -1
(b) 1
(c) 0
(d) 2
(e) -2
5. The parabola with equation y = x2 +1 intersects the line y = mx if and only if
(a) m < 0
(b) 4 less than or equal m2
(c) m > 0
(d) m = 2
(e) 2 less than or equal m
6. The line containing the points (1,1) and (1,-1) is perpendicular to the line
(a) y = 5
(b) y -1 = x -1
(c) y = -x -1
(d) y = 2x +1
(e) x = 5
7. If 3x + 6 = 12, what is x?
(a) x = -2
(b) x = 0
(c) x = 4
(d) x = 2
(e) All of the other answers are incorrect.
8. If x = 3, find the smallest value of y which satisfies y2x + 3yx2 + 54 = 0.
(a) There is no smallest value.
(b) -6
(c) 0
(d) -3
(e) 3
9. How many real solutions for x are there to the equation x2 + 3x + 8 = 0?
(a) 2
(b) 1
(c) 3
(d) It cannot be determined.
(e) 0
10. If f(x)=2x, find f(3).
(a) 9
(b) All of the other answers are incorrect.
(c) 2
(d) 6
(e) 8
11. log2(3xy2) is equal to which of the following?
(a) 3 log2(x) + [log2(y)]2
(b) log2(3x) log2(y2)
(c) All of the other answers are incorrect.
(d) 3log2(x) + 2log2(y)
(e) log2(3) + log2(x) + log2(y2)
12. log(x2 - 2x +1) > log(25) reduces to
(a) x < -4
(b) x < -4 or x > 6
(c) x > 6
(d) x > -4
(e) x < 6
13. If h(x) = x4 +1, g(x) = x3+1 and f(x) = x2 +1, then f( g(0) + h(0) ) is:
(a) 5
(b) 1
(c) 0
(d) 9
(e) 11
14. If f(x) = 3x + 3 and g(y) = 2y + 5, what is f(g(2))?
(a) 23
(b) 9
(c) 3
(d) 30
(e) 7
15. If f(x) = 3x2 + 4 and g(y) = 2y1/2 + 5, what is g(f(2))?
(a) 10
(b) 13
(c) 20
(d) All of the other answers are incorrect.
(e) 9
16.
The inequality
x
x2 +1
> 0
is equivalent to:
(a) x > 0
(b) x = 0
(c) x < 0
(d) x > 1
(e) x < 1
17.
The inequality
x4
x2 +1
> 0
is equivalent to:
(a) x > 0
(b) x is not equal to 0
(c) x < 1
(d) x < 0
(e) x > 1
18. The expression ( x + 1)(x + 2) > 0 is equivalent to which of the following?
(a) -1 > x > -2
(b) x < -2
(c) x > -1
(d) x < -2 or x > -1
(e) All of the other answers are incorrect.
19. If 3x + 4y = 7 and 5x-4y = 1, then xy is
(a) 2
(b) 1
(c) Cannot be determined
(d) 4
(e) 3
20. If 5x-6y = 4 and 3x + 4y = 10, then x/y is
(a) 1
(b) 3
(c) Cannot be determined
(d) 2
(e) 0
21. If y + 4x - 5 = 0 and y = x2, then there is a solution with y given by
(a) y = 25
(b) y = 20
(c) y = 30
(d) Cannot be determined
(e) y = 0
22. The radian measure of an angle of 60 degrees is
(a) pi/4
(b) pi
(c) pi/3
(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) 2/(31/2)
(c) 1/2
(d) 31/2/2
(e) 3/2
24. If sin(a + b) = 1 and cos(a) = 0, then cos(2b) is
(a) 1
(b) cannot be determined
(c) 1/2
(d) 0
(e) 2