Diagnostic Examination

Georgia O'Keeffe's Line and Curve

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

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

(x2 - 2x - 3)

x - 3

x + 1
(a) 12
(b)
1

x+1
(c)
( x+1

x - 3
) ( x2 - 2x - 3

x+1
)
(d)
1

x-3
(e)
x+1

(x-3)2
4. A line containing the point (0,0) defines an angle of 45 degrees with the x-axis. If the slope of the line is negative then the line must contain the point
(a) (1,-2)
(b) (1,3)
(c) (1,2)
(d) (1,-1)
(e) (1,1)
5. The line perpendicular to the line   x = 5   has slope
(a) 0
(b) -1
(c) 2
(d) -2
(e) 1
6. The circle with equation x2 + y2 - 2y = 0 intersects the line y = mx in two distinct points
(a) if and only if m is not equal to 0
(b) for no values of m
(c) for all values of m
(d) if and only if m > 0
(e) if and only if m < 0
7. If 2(2x-3) + 5(x + 1) = 6x-7, what is x?
(a) x = 8
(b) x = -2
(c) x = -4
(d) x = 2
(e) x = 4
8. If x = 8, find the largest value of y which satisfies y2x + yx2 + 128 = 0.
(a) There is no largest value.
(b) 4
(c) -4
(d) 8
(e) -8
9. Find the largest solution of x3 + 4x2 + 3x = 0.
(a) x = -2
(b) x = 0
(c) x = 1
(d) x = -1
(e) x = -3
10. If f(x)=2x, find f(3).
(a) All of the other answers are incorrect.
(b) 8
(c) 6
(d) 9
(e) 2
11.
Find the value of x that satisfies the equation
3 = 6x

2x
(a) 1
(b) 0
(c) 3
(d) 2
(e) 4
12. log(x2 - 2x +1) > log(25) reduces to
(a) x < -4 or x > 6
(b) x > 6
(c) x > -4
(d) x < 6
(e) x < -4
13. If f(x) = -5x - 2, what is f(0)?
(a) 0
(b) -1
(c) -2
(d) -5
(e) -3
14. If f(x) = 3x + 3 and g(y) = 2(y + 1) + 5, what is g(f(2))?
(a) 23
(b) 11
(c) 9
(d) 25
(e) All of the other answers are incorrect.
15. If f(x) = 3x2 + 4 and g(y) = 2y1/2 + 5, what is g(f(2))?
(a) All of the other answers are incorrect.
(b) 13
(c) 9
(d) 10
(e) 20
16. The expression 40 < 5x < 80 is equivalent to which of the following?
(a) All of the other answers are incorrect.
(b) 8 < x < 16
(c) 8 > x < 16
(d) 8 < x > 16
(e) 35 < x < 75
17.
The inequality
x4
x2 +1
> 0
is equivalent to:
(a) x < 1
(b) x > 1
(c) x is not equal to 0
(d) x > 0
(e) x < 0
18.
The inequality
x2- 2x + 1
x2 + x + 1
> 0
is equivalent to:
(a) x > 0
(b) x < 1
(c) x > 1
(d) x < 0
(e) x is not equal to 1
19. If 5x - 6y = 4 and 3x + 4y = 10, find x and y.
(a) x = 4 and y = 1
(b) x = 2 and y = 1
(c) x = 2 and y = -2
(d) x = -2 and y = -1
(e) x = -2 and y = 2
20. If 4x - y = 1 and 2x + y = 5, then 3xy is
(a) 6
(b) 9
(c) Cannot be determined
(d) 0
(e) 3
21. If y + 4x - 5 = 0 and y = x2, then there is a solution with y given by
(a) y = 0
(b) y = 30
(c) Cannot be determined
(d) y = 20
(e) y = 25
22. The radian measure of an angle of 45 degrees is
(a) pi
(b) pi/2
(c) pi/3
(d) 2pi/3
(e) pi/4
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) 3/2
(d) 1/2
(e) 31/2/2
24. If sin(a + b) = 1 and cos(a) = 0, then cos(2b) is
(a) 1
(b) 1/2
(c) 0
(d) 2
(e) cannot be determined