Diagnostic Examination

Georgia O'Keeffe's Line and Curve

1. The remainder of dividing the polynomial   x3-x2+x-1   by   x-1   is
(a) x
(b) 2
(c) 0
(d) 1
(e) 3
2. The remainder of dividing the polynomial   x3 + x2   by   x2 +1   is
(a) x
(b) x +1
(c) 0
(d) 1
(e) -x -1
3.
Evaluate
( 1

x
+ 3 ) ( 5 + 2

x2
).
(a)
4

x
+ 6

x2
(b)
5

x
+ 6

x2
(c)
11

x
+ 15 + 2

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

x
+ 15 + 2

x3
+ 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 circle of radius 3 centered at (0,0)
(c) a circle of radius 3 centered at (1,1)
(d) an hyperbola
(e) a parabola
5. What is the slope of a line parallel to 5x - 7y + 2 = 0?
(a) 2
(b) 5
(c) 7/5
(d) -7
(e) 5/7
6. The line containing the points (1,1) and (1,-1) is perpendicular to the line
(a) y = 2x +1
(b) x = 5
(c) y = -x -1
(d) y = 5
(e) y -1 = x -1
7. Find all solutions to x2-3x + 2 = 0.
(a) x = 1.1 and x = 2.1
(b) x = 1 and x = 2
(c) x = 1 and x = -2
(d) x = -1 and x = -2
(e) x = -1 and x = 2
8. If x = 8, find the largest value of y which satisfies y2x + yx2 + 128 = 0.
(a) -4
(b) -8
(c) 4
(d) 8
(e) There is no largest value.
9. How many real solutions for x are there to the equation x2 + 3x + 8 = 0?
(a) 3
(b) 1
(c) 0
(d) It cannot be determined.
(e) 2
10. log(6) equals
(a) log(2) + log(3)
(b) 3 log(2)
(c) 3
(d) 2 log(3)
(e) 2
11. Which of the following values of x satisfies log2(x) - log2(x+1) = -1?
(a) x = 2
(b) x = 1/3
(c) x = 1
(d) x = -1/3
(e) x = 3
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 = 3/5
(d) x = 5
(e) x = (4/3)1/2
13. The function f(x) = x2 has range
(a) The set of all numbers x such that x is less than or equal to 1
(b) The set of all numbers x such that x is less than or equal to 0
(c) The set of all numbers x such that x is greater than or equal to 0
(d) The set of all numbers
(e) The set of all numbers x such that x is greater than or equal to 1
14. If f(x) = 3x + 3 and g(y) = 2y + 5, what is g(f(2))?
(a) 7
(b) All of the other answers are incorrect.
(c) 30
(d) 9
(e) 23
15. If f(x)=3x2 + 3, what is f(f(a))?
(a) All of the other answers are incorrect.
(b) 3a2 + 3
(c) Not defined.
(d) 0
(e) 3(3a2 + 3)2 + 3
16. The inequality |x -1| < |2 -x| is equivalent to
(a) 1 < x < 2
(b) 1 < x
(c) x < 3/2
(d) x < 2
(e) x < 1/2
17.
Simplify
-10 < 4x + 2

5
< 10
(a) -13 < x < 13
(b) -12 < x < 12
(c) All of the other answers are incorrect.
(d) -12 < x < 13
(e) -13 < x < 12
18.
The inequality
x2- 2x + 1
x2 + x + 1
> 0
is equivalent to:
(a) x > 1
(b) x is not equal to 1
(c) x < 1
(d) x > 0
(e) x < 0
19. If 4x - y = 1 and 2x + y = 5, find x and y.
(a) x = 0 and y = 3
(b) x = 0 and y = 6
(c) x = -1 and y = 5
(d) x = 4 and y = 1
(e) x = 1 and y = 3
20. If 4x - y = 1 and 2x + y = 5, then 3xy is
(a) 6
(b) Cannot be determined
(c) 3
(d) 9
(e) 0
21. If y + 4x - 5 = 0 and y = x2, then there is a solution with y given by
(a) Cannot be determined
(b) y = 20
(c) y = 0
(d) y = 25
(e) y = 30
22. The radian measure of an angle of 45 degrees is
(a) pi/4
(b) pi/2
(c) pi/3
(d) 2pi/3
(e) pi
23. Which of the following is correct?
(a) cos(.1) < sin(.1)cos(.1) < sin(.1)
(b) cos(.1) < sin(.1) < sin(.1)cos(.1)
(c) sin(.1)cos(.1) < sin(.1) < cos(.1)
(d) sin(.1) < cos(.1) < sin(.1)cos(.1)
(e) sin(.1) < sin(.1)cos(.1) < cos(.1)
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) 0
(b) 8
(c) 1/8
(d) 1
(e) 2