Diagnostic Examination

Georgia O'Keeffe's Line and Curve

1. If you divide 12ab3 by 4b, the answer is
(a) ab3 - b
(b) 3ab2
(c) 8b2
(d) 0
(e) ab2
2. Find the product (2x+y)(y-3x).
(a) -6x2 + y2 - xy
(b) -6x2 + y2
(c) -xy
(d) 6x2 + y2 - xy
(e) All of the other answers are incorrect.
3.
Evaluate
( 1

x
+ 3 ) ( 5 + 2

x2
).
(a)
4

x
+ 6

x2
(b)
11

x
+ 15 + 2

x2
(c) All of the other answers are incorrect.
(d)
5

x
+ 15 + 2

x3
+ 6

x2
(e)
5

x
+ 6

x2
4. The set of points (x,y) such that   x2 + y2 = 9   is
(a) a circle of radius 9 centered at (0,0)
(b) a parabola
(c) a circle of radius 3 centered at (1,1)
(d) an hyperbola
(e) a circle of radius 3 centered at (0,0)
5. Find the equation of the line perpendicular to y = x/3 + 1 through the point (3,2).
(a) y = 3x - 7
(b) y = x/3 +1
(c) y = -x/3 + 3
(d) y = x/3 + 7
(e) y = - 3x + 11
6. The line containing the points (1,1) and (1,-1) is perpendicular to the line
(a) y = 5
(b) y = 2x +1
(c) y -1 = x -1
(d) y = -x -1
(e) x = 5
7. If 3x + 6 = 12, what is x?
(a) x = 4
(b) x = 0
(c) x = 2
(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) 0
(b) 3
(c) There is no smallest value.
(d) -3
(e) -6
9. Find the largest solution of x3 + 4x2 + 3x = 0.
(a) x = -2
(b) x = -3
(c) x = -1
(d) x = 0
(e) x = 1
10. If f(x) = 2-x, find f(4).
(a) -1/16
(b) -16
(c) 1/16
(d) 16
(e) 8
11. log(x) < log(x +1) reduces to
(a) x < 1
(b) x < x +1
(c) x < 0
(d) 1 < x
(e) 0 < x
12. Which of the following values of x satisfies log2(3x) + log2(2x) = 3?
(a) x = (3/2)1/2
(b) x = 5
(c) x = 3/5
(d) x = 4
(e) x = (4/3)1/2
13. If g(x) = 5x + 2, what is g(2)?
(a) 10
(b) 14
(c) 16
(d) 12
(e) 11
14. If h(x) = x3, g(x) = x2+1 and f(x) = x +1, then h(g(f(0))) + f(g(h(0))) is:
(a) 9
(b) 16
(c) 4
(d) 0
(e) 10
15. If f(x) = 3x2 + 4 and g(y) = 2y1/2 + 5, what is g(f(2))?
(a) 20
(b) 10
(c) 13
(d) 9
(e) All of the other answers are incorrect.
16. The inequality   x2 - 2x > -1   reduces to
(a) x > 1
(b) x < -1
(c) x is not equal to 1
(d) x > -1
(e) x < 1
17. The expression | 5x-2 | > 1 is equivalent to which of the following?
(a) x < 1/5 and x > 3/5
(b) There are no values of x which satisfy this expression.
(c) x < -1/5 or x > 3/5
(d) x < 1/5 or x > 3/5
(e) x < -1/5
18.
Under which of the following conditions does   x   satisfy
x + 2

| x - 1 |
> 0
(a) x - 1 > 0 and x + 2 > 0
(b) x + 2 > 0
(c) x is not equal to 1 and x + 2 > 0
(d) There are no values of x which satisfy this expression.
(e) All of the other answers are incorrect.
19. If 4x - y = 1 and 2x + y = 5, find x and y.
(a) x = 0 and y = 6
(b) x = 4 and y = 1
(c) x = 0 and y = 3
(d) x = -1 and y = 5
(e) x = 1 and y = 3
20. If x - y = 4 and 4x - y = 1, then 3xy is
(a) 15
(b) 6
(c) 12
(d) Cannot be determined
(e) 9
21. If y + 3x + 2 = 0 and y = x2, then there is a solution with x given by
(a) x = 0
(b) Cannot be determined
(c) x = 1
(d) x = 2
(e) x = -1
22. The radian measure of an angle of 60 degrees is
(a) 2(pi/3)
(b) pi/4
(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) 1/2
(c) 3/2
(d) 2/3
(e) 2/(31/2)
24. If sin(a + b) = 1 and cos(a) = 0, then cos(2b) is
(a) cannot be determined
(b) 1/2
(c) 1
(d) 0
(e) 2