Diagnostic Examination

Georgia O'Keeffe's Line and Curve

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

(x2 - 2x - 3)

x - 3

x + 1
(a)
1

x+1
(b)
1

x-3
(c)
x+1

(x-3)2
(d)
( x+1

x - 3
) ( x2 - 2x - 3

x+1
)
(e) 12
4. The area of a right triangle with sides 3, 4, and 5 is
(a) 15
(b) 10
(c) 6
(d) 12
(e) 20
5. Which of the following points is closer to the point (1,1) than the point (2,2) is to (1,1)?
(a) (1, 5/2)
(b) (2,0)
(c) (0,0)
(d) (0,2)
(e) (0,1)
6. The circle with equation x2 + y2 - 2y = 0 intersects the line y = mx in two distinct points
(a) if and only if m < 0
(b) if and only if m > 0
(c) if and only if m is not equal to 0
(d) for no values of m
(e) for all values of m
7. If 2(2x-3) + 5(x + 1) = 6x-7, what is x?
(a) x = -2
(b) x = -4
(c) x = 8
(d) x = 4
(e) x = 2
8. If x = 3, find the smallest value of y which satisfies y2x + 3yx2 + 54 = 0.
(a) There is no smallest value.
(b) 3
(c) 0
(d) -6
(e) -3
9. How many real solutions for x are there to the equation x2 + 3x + 8 = 0?
(a) 1
(b) 3
(c) 2
(d) 0
(e) It cannot be determined.
10. [x2]1/2 reduces to
(a) 1
(b) |x|
(c) 0
(d) x
(e) x2
11. log2(3xy2) is equal to which of the following?
(a) log2(3x) log2(y2)
(b) 3 log2(x) + [log2(y)]2
(c) All of the other answers are incorrect.
(d) 3log2(x) + 2log2(y)
(e) log2(3) + log2(x) + log2(y2)
12. Which of the following values of x satisfies log2(3x) + log2(2x) = 3?
(a) x = 4
(b) x = (3/2)1/2
(c) x = (4/3)1/2
(d) x = 3/5
(e) x = 5
13. If h(x) = x4 +1, g(x) = x3+1 and f(x) = x2 +1, then f( g(0) + h(0) ) is:
(a) 1
(b) 11
(c) 5
(d) 0
(e) 9
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) 4
(c) 0
(d) 10
(e) 16
15. If f(x)=3x2 + 3, what is f(f(a))?
(a) 3a2 + 3
(b) 3(3a2 + 3)2 + 3
(c) 0
(d) Not defined.
(e) All of the other answers are incorrect.
16. The inequality |x -1| < |2 -x| is equivalent to
(a) 1 < x < 2
(b) x < 2
(c) x < 1/2
(d) 1 < x
(e) x < 3/2
17. The expression | 5x-2 | > 1 is equivalent to which of the following?
(a) There are no values of x which satisfy this expression.
(b) x < 1/5 or x > 3/5
(c) x < -1/5 or x > 3/5
(d) x < 1/5 and 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) There are no values of x which satisfy this expression.
(c) x + 2 > 0
(d) All of the other answers are incorrect.
(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 = 2 and y = 1
(b) x = 1 and y = 1
(c) x = 2 and y = 2
(d) x = 1 and y = -1
(e) x = -1 and y = 1
20. If x - y = 4 and 4x - y = 1, then 3xy is
(a) 12
(b) 15
(c) 6
(d) Cannot be determined
(e) 9
21. If y + 4x - 5 = 0 and y = x2, then there is a solution with y given by
(a) y = 0
(b) y = 25
(c) y = 20
(d) y = 30
(e) Cannot be determined
22. The radian measure of an angle of 60 degrees is
(a) pi/4
(b) 2(pi/3)
(c) pi
(d) pi/3
(e) pi/2
23. If sin(a) = 1, cos(b) > 0, and sin(b) = 1/2, then sin(a + b) is
(a) 3/2
(b) 31/2/2
(c) 1/2
(d) 2/(31/2)
(e) 2/3
24. A triangle has sides of length 5, 5 and 8. What is the sine of its smallest angle?
(a) 8/5
(b) 3/8
(c) 4/5
(d) 5/8
(e) 3/5