# Diagnostic Examination

1. The remainder of dividing the polynomial   x3-x2+x-1   by   x-1   is
(a) 1
(b) 3
(c) 0
(d) 2
(e) x
2. Find the product (2x+y)(y-3x).
(a) All of the other answers are incorrect.
(b) -6x2 + y2 - xy
(c) -xy
(d) 6x2 + y2 - xy
(e) -6x2 + y2
3.
Evaluate
 ( 1 x + 3 ) ( 5 + 2 x2 ).
(a)
 11 x + 15 + 2 x2
(b) All of the other answers are incorrect.
(c)
 5 x + 15 + 2 x3 + 6 x2
(d)
 5 x + 6 x2
(e)
 4 x + 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) y = x2
(c) y = x3
(d) y = x
(e) y2 + x2 = 1
5. Which of the following points is on the line segment from (1,0) to (4,9)?
(a) (2,1)
(b) (2,4)
(c) (2,2)
(d) (2,0)
(e) (2,3)
6. The line containing the points (1,1) and (1,-1) is perpendicular to the line
(a) y = 5
(b) y = 2x +1
(c) x = 5
(d) y = -x -1
(e) y -1 = x -1
7. If 3x + 6 = 12, what is x?
(a) All of the other answers are incorrect.
(b) x = 4
(c) x = 2
(d) x = 0
(e) x = -2
8. If x = 8, find the largest value of y which satisfies y2x + yx2 + 128 = 0.
(a) There is no largest value.
(b) 8
(c) -4
(d) 4
(e) -8
9. Find the largest solution of x3 + 4x2 + 3x = 0.
(a) x = -3
(b) x = 1
(c) x = 0
(d) x = -1
(e) x = -2
10. log(3/2) equals
(a) log(2) - log(3)
(b) log(2) + log(3)
(c) 3 log(1/2)
(d) (1/2)log(3)
(e) log(3) - log(2)
11. log2(x2 y2) is equal to which of the following?
(a) log2(x2) log2(y2)
(b) log2(x) + log2(y)
(c) All of the other answers are incorrect.
(d) 2log2(x) + 2log2(y)
(e) [log2(x)]2 + [log2(y)]2
12. log(x2 - 2x +1) > log(25) reduces to
(a) x > -4
(b) x < 6
(c) x < -4
(d) x < -4 or x > 6
(e) x > 6
13. If h(x) = x4 +1, g(x) = x3+1 and f(x) = x2 +1, then f( g(0) + h(0) ) is:
(a) 0
(b) 11
(c) 5
(d) 1
(e) 9
14. The function f(x) = [x2 -1]1/2 has domain
(a) The set of all numbers x such that 1 < 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 is less than or equal to -1 or 1 is less than or equal to x
(d) The set of all numbers x such that either x < -1 or 1 < x
(e) The interval [-1,1]
15. If f(x) = 3x2 + 4 and g(y) = 2y1/2 + 5, what is g(f(2))?
(a) 9
(b) 10
(c) 13
(d) 20
(e) All of the other answers are incorrect.
16.
The expression
 -4 < 3x + 4 8 < 12
is equivalent to which of the following?
(a) -4 < x < 93
(b) -36 < 3x < 92
(c) -12 < x < 31
(d) -4 < x < 12
(e) All of the other answers are incorrect.
17.
The inequality
 x4x2 +1 > 0
is equivalent to:
(a) x > 0
(b) x < 0
(c) x < 1
(d) x > 1
(e) x is not equal to 0
18.
Under which of the following conditions does   x   satisfy
 x + 2 | x - 1 | > 0
(a) x - 1 > 0 and x + 2 > 0
(b) x is not equal to 1 and x + 2 > 0
(c) x + 2 > 0
(d) All of the other answers are incorrect.
(e) There are no values of x which satisfy this expression.
19. If 4x - y = 1 and 2x + y = 5, find x and y.
(a) x = -1 and y = 5
(b) x = 4 and y = 1
(c) x = 1 and y = 3
(d) x = 0 and y = 6
(e) x = 0 and y = 3
20. If y + 4x - 18 = 0 and y2 = x, then there is a solution with y given by
(a) y = 1
(b) y = 2
(c) y = 9/4
(d) Cannot be determined
(e) y = 0
21. If y + 4x - 5 = 0 and y = x2, then there is a solution with y given by
(a) y = 30
(b) Cannot be determined
(c) y = 20
(d) y = 25
(e) y = 0
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) 1/2
(b) 2
(c) 2pi
(d) pi/2
(e) 1/(4pi)
23. Which of the following is correct?
(a) cos(.1) < sin(.1) < sin(.1)cos(.1)
(b) sin(.1) < cos(.1) < sin(.1)cos(.1)
(c) cos(.1) < sin(.1)cos(.1) < sin(.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) 1
(b) 2
(c) 0
(d) 8
(e) 1/8