Diagnostic Examination

Georgia O'Keeffe's Line and Curve

1.
Simplify
1

1+ 1

x+1
(a)
1

x+2
(b)
x+1

x+2
(c)
x+1
(d)
x+1

2
(e)
1

x+1
2.
Simplify
(3 a2 b-3)-4

(12ab3)-5
(a) 48a-3b27
(b) 48a-13b-27
(c) 96a-3b27
(d) All of the other answers are incorrect.
(e) 96a-13b27
3.
Evaluate
( 1

x
+ 3 ) ( 5 + 2

x2
).
(a)
4

x
+ 6

x2
(b)
5

x
+ 6

x2
(c) All of the other answers are incorrect.
(d)
11

x
+ 15 + 2

x2
(e)
5

x
+ 15 + 2

x3
+ 6

x2
4.
The graph
would best approximate the graph of which of the following equations for on the interval [-1.5,1.5]?
(a) y = x1/2
(b) y2 + x2 = 1
(c) y = x3
(d) y = x
(e) y = x2
5. Find the equation of the line through (-1,1) and (5,2).
(a) x - y - 2 = 0
(b) x - y + 2 = 0
(c) x - 6y + 7 = 0
(d) x - 2y - 1 = 0
(e) x + y = 0
6. The line containing the points (1,1) and (1,-1) is perpendicular to the line
(a) y -1 = x -1
(b) y = 5
(c) x = 5
(d) y = -x -1
(e) y = 2x +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 = 3, find the smallest value of y which satisfies y2x + 3yx2 + 54 = 0.
(a) -6
(b) 0
(c) There is no smallest value.
(d) -3
(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) 1
(e) It cannot be determined.
10. log(3/2) equals
(a) (1/2)log(3)
(b) log(3) - log(2)
(c) log(2) - log(3)
(d) 3 log(1/2)
(e) log(2) + log(3)
11.
Find the value of x that satisfies the equation
3 = 6x

2x
(a) 4
(b) 3
(c) 1
(d) 0
(e) 2
12. log(x2 - 2x +1) > log(25) reduces to
(a) x < -4
(b) x < -4 or x > 6
(c) x > -4
(d) x > 6
(e) x < 6
13. If h(x) = x2, g(x) = x+1, and f(x) = x +3, then what is h(g(f(0)))?
(a) 16
(b) 0
(c) 9
(d) 1
(e) 4
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) 10
(b) 16
(c) 4
(d) 0
(e) 9
15. If f(x) = 3x + 3 what is f(f(2))?
(a) 81
(b) All of the other answers are incorrect.
(c) Not defined.
(d) 30
(e) 9
16. The inequality   x3 > y3   reduces to
(a) x > 2y
(b) x > y
(c) x = y
(d) x < y
(e) x < 2y
17.
The inequality
x4
x2 +1
> 0
is equivalent to:
(a) x < 0
(b) x < 1
(c) x > 0
(d) x > 1
(e) x is not equal to 0
18.
The inequality
x2- 2x + 1
x2 + x + 1
> 0
is equivalent to:
(a) x < 0
(b) x > 0
(c) x > 1
(d) x is not equal to 1
(e) x < 1
19. If 3x + 4y = 7 and 5x-4y = 1, find x and y.
(a) x = 2 and y = 2
(b) x = -1 and y = 1
(c) x = 1 and y = -1
(d) x = 2 and y = 1
(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) y = 0
(b) y = 1
(c) y = 2
(d) Cannot be determined
(e) y = 9/4
21. If y + 3x + 2 = 0 and y = x2, then there is a solution with x given by
(a) x = 2
(b) x = 0
(c) x = -1
(d) x = 1
(e) Cannot be determined
22. A right triangle has sides of length 3, 4, and 5. What is the cosine of its smallest angle?
(a) 5/3
(b) 4/5
(c) 4/3
(d) 3/5
(e) 3/4
23. Which of the following is correct?
(a) sin(.1) < cos(.1) < sin(.1)cos(.1)
(b) sin(.1)cos(.1) < sin(.1) < cos(.1)
(c) cos(.1) < sin(.1) < sin(.1)cos(.1)
(d) sin(.1) < sin(.1)cos(.1) < cos(.1)
(e) cos(.1) < sin(.1)cos(.1) < sin(.1)
24. If sin(a + b) = 1 and tan(a) = 0, then tan(b) is
(a) undefined
(b) 0
(c) 1/2
(d) 1
(e) 1/4