Diagnostic Examination

Georgia O'Keeffe's Line and Curve

1. The equation, 4x2 - 6x + 10 = 0, has
(a) two real solutions
(b) one real solution
(c) three real solutions
(d) four real solutions
(e) no real solutions
2. The remainder of dividing the polynomial   x3 + x2   by   x2 +1   is
(a) 0
(b) 1
(c) -x -1
(d) x +1
(e) x
3.
Simplify
x + 1

(x2 - 2x - 3)

x - 3

x + 1
(a) 12
(b)
1

x-3
(c)
1

x+1
(d)
( x+1

x - 3
) ( x2 - 2x - 3

x+1
)
(e)
x+1

(x-3)2
4. Find the midpoint of the line segment between (-2,1) and (4,5).
(a) (-1,1)
(b) (3,-1)
(c) (3,3)
(d) (3,1)
(e) (1,3)
5. The set of points (x,y) such that   x2 -2x + y2 -6y = 6   is a circle of radius
(a) 5
(b) 4
(c) 6
(d) 51/2
(e) 61/2
6. The line containing the points (1,1) and (1,-1) is perpendicular to the line
(a) x = 5
(b) y = -x -1
(c) y -1 = x -1
(d) y = 5
(e) y = 2x +1
7. Let f(x) = 3x + 2. For which x is f(x) = -2?
(a) 4/3
(b) -2/3
(c) -3/2
(d) -4/3
(e) 0
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) -3
(d) 0
(e) 3
9. How many real solutions for x are there to the equation x2 + 3x + 8 = 0?
(a) 0
(b) 2
(c) 3
(d) It cannot be determined.
(e) 1
10. 163/2 is
(a) 32
(b) 8
(c) 83
(d) 128
(e) 64
11. Which of the following describes the domain of log(|x|)?
(a) x < 0
(b) x is any real number
(c) x is not equal to 0
(d) x > 0
(e) 1 > x > -1
12. Which of the following values of x satisfies log2(3x) + log2(2x) = 3?
(a) x = (3/2)1/2
(b) x = 4
(c) x = 5
(d) x = 3/5
(e) x = (4/3)1/2
13. If f(x) = x2 + 1 and g(x) = 2x - 1, then f(g(2)) =
(a) 5
(b) 10
(c) 26
(d) 9
(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) 0
(c) 4
(d) 16
(e) 10
15. If f(x) = 3x2 + 4 and g(y) = 2y1/2 + 5, what is g(f(2))?
(a) 20
(b) 9
(c) 13
(d) 10
(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 x3 < 2x2 -x reduces to
(a) x < 0
(b) x > 0
(c) x < 0 or x is not equal to 1
(d) x > 1
(e) x < 1
18.
Under which of the following conditions does   x   satisfy
x + 2

| x - 1 |
> 0
(a) All of the other answers are incorrect.
(b) x - 1 > 0 and x + 2 > 0
(c) There are no values of x which satisfy this expression.
(d) x + 2 > 0
(e) x is not equal to 1 and x + 2 > 0
19. If 3x + 4y = 7 and 5x-4y = 1, find x and y.
(a) x = 1 and y = -1
(b) x = -1 and y = 1
(c) x = 2 and y = 1
(d) x = 2 and y = 2
(e) x = 1 and y = 1
20. If y + 4x - 18 = 0 and y2 = x, then there is a solution with y given by
(a) Cannot be determined
(b) y = 2
(c) y = 0
(d) y = 1
(e) y = 9/4
21. If y + 4x - 5 = 0 and y = x2, then there is a solution with y given by
(a) y = 20
(b) Cannot be determined
(c) y = 25
(d) y = 30
(e) y = 0
22. The radian measure of an angle of 45 degrees is
(a) pi
(b) 2pi/3
(c) pi/3
(d) pi/4
(e) pi/2
23. If sin(a) = 1, cos(b) > 0, and sin(b) = 1/2, then sin(a + b) is
(a) 2/(31/2)
(b) 31/2/2
(c) 2/3
(d) 3/2
(e) 1/2
24. Two lines each contain the point (0,0). One line has slope 3 and the other line has slope 5. The tangent of the angle interior to the lines is
(a) 8
(b) 1/8
(c) 0
(d) 2
(e) 1