Diagnostic Examination

Georgia O'Keeffe's Line and Curve

1.
Simplify
1

1+ 1

x+1
(a)
x+1

x+2
(b)
x+1

2
(c)
x+1
(d)
1

x+1
(e)
1

x+2
2. Simplify [a4 - 4a2 +4]1/2
(a) a2 +2
(b) |a2 +2|
(c) |a2-2|
(d) a2-2
(e) a2 + 2a + 2
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)2
(e)
( x+1

x - 3
) ( x2 - 2x - 3

x+1
)
4. The line containing the points (1,1) and (1,3) has
(a) All of the other answers are incorrect.
(b) negative slope
(c) positive slope
(d) slope 0
(e) undefined slope
5. A triangle has a side of length 3, a side of length 4, and a side of length x. The possible values of x are
(a) x = 5
(b) 1 < x < 7
(c) x > 7
(d) 0 < x < 5
(e) 0 < x
6. The distance from the point (x,y) to the point (2,3) is twice the distance from the point (x,y) to the point (5,7). What is the maximum possible distance from (x,y) to (2,3)?
(a) 15
(b) 25
(c) 5
(d) 4
(e) 10
7. Find all solutions to x2-3x + 2 = 0.
(a) x = 1 and x = -2
(b) x = -1 and x = 2
(c) x = 1.1 and x = 2.1
(d) x = -1 and x = -2
(e) x = 1 and x = 2
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. How many real solutions for x are there to the equation x2 + 3x + 8 = 0?
(a) 0
(b) 3
(c) 1
(d) 2
(e) It cannot be determined.
10. If f(x) = 2-x, find f(4).
(a) -1/16
(b) -16
(c) 1/16
(d) 8
(e) 16
11. Which of the following describes the domain of log(|x|)?
(a) 1 > x > -1
(b) x is any real number
(c) x < 0
(d) x > 0
(e) x is not equal to 0
12. log(x2 - 2x +1) > log(25) reduces to
(a) x < -4 or x > 6
(b) x < -4
(c) x > 6
(d) x > -4
(e) x < 6
13. If g(x) = 5x + 2, what is g(2)?
(a) 11
(b) 16
(c) 10
(d) 14
(e) 12
14. If f(x) = 3x + 3 and g(y) = 2y + 5, what is f(g(2))?
(a) 9
(b) 30
(c) 23
(d) 3
(e) 7
15. If f(x) = 3x + 3 what is f(f(2))?
(a) All of the other answers are incorrect.
(b) 9
(c) 81
(d) 30
(e) Not defined.
16. The expression -18 < -6x < 12 is equivalent to which of the following?
(a) All of the other answers are incorrect.
(b) 3 > x > -2
(c) 2 > x > -3
(d) -2 > x > -3
(e) 3 > x > 2
17.
The expression -1 <
1-x2

1+x2
< 1 is satisfied by
what values of x?
(a) All of the other answers are incorrect.
(b) There are no values of x which satisfy this expression.
(c) -1 < x < 1
(d) All values of x satisfy this expression.
(e) x not equal to 0
18. The expression ( x + 1)(x + 2) > 0 is equivalent to which of the following?
(a) x < -2 or x > -1
(b) All of the other answers are incorrect.
(c) x > -1
(d) x < -2
(e) -1 > x > -2
19. If 3x + 4y = 7 and 5x-4y = 1, then xy is
(a) 3
(b) Cannot be determined
(c) 4
(d) 2
(e) 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 = 9/4
(e) y = 1
21. If y + 3x + 2 = 0 and y = x2, then there is a solution with x given by
(a) x = 1
(b) x = 2
(c) Cannot be determined
(d) x = -1
(e) x = 0
22. The radian measure of an angle of 60 degrees is
(a) 2(pi/3)
(b) pi/3
(c) pi
(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) 3/2
(b) 2/(31/2)
(c) 1/2
(d) 2/3
(e) 31/2/2
24. A triangle has sides of length 5, 5 and 8. What is the sine of its smallest angle?
(a) 8/5
(b) 5/8
(c) 3/8
(d) 3/5
(e) 4/5