Diagnostic Examination

Georgia O'Keeffe's Line and Curve

1. Factor   x2 - 5x + 6.
(a) x2 - 5 x + 6
(b) (x - 2)(x + 3)
(c) (x + 2)(x + 3)
(d) (x - 2)(x - 3)
(e) (x + 3)(x - 2)
2. Simplify [a4 - 4a2 +4]1/2
(a) a2 +2
(b) |a2-2|
(c) a2 + 2a + 2
(d) a2-2
(e) |a2 +2|
3.
Evaluate
( 1

x
+ 3 ) ( 5 + 2

x2
).
(a)
4

x
+ 6

x2
(b)
5

x
+ 15 + 2

x3
+ 6

x2
(c)
11

x
+ 15 + 2

x2
(d)
5

x
+ 6

x2
(e) All of the other answers are incorrect.
4.
The graph
would best approximate the graph of which of the following equations for on the interval [-1.5,1.5]?
(a) y = x3
(b) y2 + x2 = 1
(c) y = x1/2
(d) y = x
(e) y = x2
5. Find the equation of the line perpendicular to y = x/3 + 1 through the point (3,2).
(a) y = x/3 +1
(b) y = 3x - 7
(c) y = x/3 + 7
(d) y = -x/3 + 3
(e) y = - 3x + 11
6. How many points are in the intersection of y = x2 + 3x + 1 and y = 2x + 5?
(a) 1
(b) 2
(c) infinitely many
(d) 3
(e) 0
7. If 3x + 6 = 12, what is x?
(a) All of the other answers are incorrect.
(b) x = 0
(c) x = 4
(d) x = -2
(e) x = 2
8. If x = y and x2y2 - 5xy + 6 = 0, then which of the following is possible?
(a) x2 = 6
(b) x = 2
(c) x = 3
(d) x = 6
(e) x2 = 3
9. Find the largest solution of x3 + 4x2 + 3x = 0.
(a) x = 1
(b) x = -2
(c) x = -3
(d) x = 0
(e) x = -1
10. If f(x) = log2 x, find f(8).
(a) 1
(b) 4
(c) 3
(d) 0
(e) 2
11. log(x) < log(2) reduces to
(a) x < 10
(b) 10 < x
(c) 0 < x < 2
(d) x < 2
(e) x is not equal to 2
12. Which of the following values of x satisfies log2(3x) + log2(2x) = 3?
(a) x = (3/2)1/2
(b) x = 3/5
(c) x = 4
(d) x = 5
(e) x = (4/3)1/2
13. If g(x) = 5x + 2, what is g(2)?
(a) 16
(b) 11
(c) 14
(d) 12
(e) 10
14. The function f(x) = [x2 -1]1/2 has domain
(a) The set of all numbers x such that either x is less than or equal to -1 or 1 is less than or equal to x
(b) The set of all numbers x such that 1 is less than or equal to x
(c) The set of all numbers x such that either x < -1 or 1 < x
(d) The interval [-1,1]
(e) The set of all numbers x such that 1 < x
15. If f(x) = 3x2 + 4 and g(y) = 2y1/2 + 5, what is g(f(2))?
(a) 13
(b) All of the other answers are incorrect.
(c) 20
(d) 10
(e) 9
16. The expression -18 < -6x < 12 is equivalent to which of the following?
(a) All of the other answers are incorrect.
(b) -2 > x > -3
(c) 2 > x > -3
(d) 3 > x > -2
(e) 3 > x > 2
17.
The expression -1 <
1-x2

1+x2
< 1 is satisfied by
what values of x?
(a) x not equal to 0
(b) There are no values of x which satisfy this expression.
(c) -1 < x < 1
(d) All of the other answers are incorrect.
(e) All values of x satisfy this expression.
18. The expression ( x + 1)(x + 2) > 0 is equivalent to which of the following?
(a) x > -1
(b) All of the other answers are incorrect.
(c) -1 > x > -2
(d) x < -2
(e) x < -2 or x > -1
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 = 1 and y = -1
(d) x = 2 and y = 2
(e) x = 2 and y = 1
20. If x - y = 4 and 4x - y = 1, then 3xy is
(a) Cannot be determined
(b) 9
(c) 6
(d) 15
(e) 12
21. If y + 3x + 2 = 0 and y = x2, then there is a solution with x given by
(a) x = 1
(b) x = 0
(c) x = 2
(d) x = -1
(e) Cannot be determined
22. If a circle has radius 2, then what is the radian measure of an angle whose vertex is at the center of circle and which cuts an arc of length 1 along the circle?
(a) 2pi
(b) 2
(c) 1/(4pi)
(d) pi/2
(e) 1/2
23. If sin(a) = 1, cos(b) > 0, and sin(b) = 1/2, then sin(a + b) is
(a) 3/2
(b) 2/3
(c) 1/2
(d) 2/(31/2)
(e) 31/2/2
24. A line containing the point (0,0) defines an angle of 60 degrees with the x-axis. If the slope of the line is negative then the line must contain the point
(a) (1,31/2)
(b) (1,2)
(c) (1,-31/2)
(d) (1,-2)
(e) (1,-3)