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) 0
(b) 2
(c) 3
(d) x
(e) 1
2.
Simplify (x3 + 2x2 + 2x + 1)

(x + 1)
(a) x2 - x + 1
(b) x2 + 1
(c) x2 - 2x + 1
(d) x2 + 2x + 1
(e) x2 + x + 1
3.
Evaluate
( 1

x
+ 3 ) ( 5 + 2

x2
).
(a)
5

x
+ 6

x2
(b)
5

x
+ 15 + 2

x3
+ 6

x2
(c)
11

x
+ 15 + 2

x2
(d) All of the other answers are incorrect.
(e)
4

x
+ 6

x2
4. The set of points (x,y) such that   x2 + y2 = 9   is
(a) an hyperbola
(b) a parabola
(c) a circle of radius 3 centered at (0,0)
(d) a circle of radius 3 centered at (1,1)
(e) a circle of radius 9 centered at (0,0)
5. The set of points (x,y) such that   x2 -4x + y2 -6y = 15   is a circle centered at
(a) (9,4)
(b) (0,0)
(c) (2,3)
(d) (3,2)
(e) (4,9)
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 is not equal to 0
(c) if and only if m > 0
(d) for no values of m
(e) for all values of m
7. If 3x + 6 = 12, what is x?
(a) All of the other answers are incorrect.
(b) x = 4
(c) x = -2
(d) x = 2
(e) x = 0
8. If x = y and x2y2 - 5xy + 6 = 0, then which of the following is possible?
(a) x = 6
(b) x = 2
(c) x2 = 6
(d) x = 3
(e) x2 = 3
9. Find the largest solution of x3 + 4x2 + 3x = 0.
(a) x = -2
(b) x = -1
(c) x = -3
(d) x = 1
(e) x = 0
10. log(3/2) equals
(a) log(3) - log(2)
(b) (1/2)log(3)
(c) 3 log(1/2)
(d) log(2) - log(3)
(e) log(2) + log(3)
11. log2(x2 y2) is equal to which of the following?
(a) 2log2(x) + 2log2(y)
(b) All of the other answers are incorrect.
(c) log2(x) + log2(y)
(d) [log2(x)]2 + [log2(y)]2
(e) log2(x2) log2(y2)
12. log(x2 - 2x +1) > log(25) reduces to
(a) x < -4 or x > 6
(b) x < 6
(c) x > 6
(d) x > -4
(e) x < -4
13. If f(x) = -5x - 2, what is f(0)?
(a) -3
(b) 0
(c) -2
(d) -1
(e) -5
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) 16
(c) 0
(d) 10
(e) 4
15. If f(x) = 3x + 3 what is f(f(2))?
(a) 30
(b) 9
(c) All of the other answers are incorrect.
(d) Not defined.
(e) 81
16.
The inequality
x
x2 +1
> 0
is equivalent to:
(a) x < 0
(b) x > 0
(c) x > 1
(d) x = 0
(e) x < 1
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 and x > 3/5
(c) x < 1/5 or x > 3/5
(d) x < -1/5
(e) x < -1/5 or x > 3/5
18. [x2 - 6x + 9]1/2 < | x - 1 | reduces to
(a) x < 1
(b) x > 3
(c) x < 3
(d) x < 2
(e) x > 2
19. If 3x + 4y = 7 and 5x-4y = 1, then xy is
(a) Cannot be determined
(b) 1
(c) 2
(d) 4
(e) 3
20. If 5x-6y = 4 and 3x + 4y = 10, then x/y is
(a) 2
(b) Cannot be determined
(c) 1
(d) 3
(e) 0
21. If y + 4x - 5 = 0 and y = x2, then there is a solution with y given by
(a) y = 20
(b) y = 25
(c) Cannot be determined
(d) y = 0
(e) y = 30
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) pi/2
(d) 1/2
(e) 1/(4pi)
23. If sin(a) = 1, cos(b) > 0, and sin(b) = 1/2, then sin(a + b) is
(a) 3/2
(b) 1/2
(c) 31/2/2
(d) 2/(31/2)
(e) 2/3
24. If sin(a + b) = 1 and tan(a) = 0, then tan(b) is
(a) 1/2
(b) undefined
(c) 1
(d) 0
(e) 1/4