| 1) If xy =1 and x is greater than 0, which of
the following statements is true?
A)When x is greater than 1, y is negative.
B)When x is greater than 1, y is greater than 1.
C)When x is less than 1, y is less than 1.
D)As x increases, y increases.
E) As x increases, y decreases. _______________________________________________________________________________
|
| 2) In how
many ways can one arrange on a bookshelf 5 thick books, 4 medium\par sized books
and 3 thin books so that the books of the same size remain together?
A)5! 4! 3! 3! = 103,680
B)5! 4! 3! = 17,280
C) (5! 4! 3!) x 3 = 51,840
D) 5 x 4 x 3 x 3 =180
E) 2 12 x 3 =12,288
_______________________________________________________________________________
|
| 3) The acceleration
of an object moving in a straight line can be determined from
A) the slope of the distance-time graph
B) the area below the distance-time graph
C) the slope of the velocity-time graph
D) the area below the velocity-time graph _______________________________________________________________________________
|
| 4)
The value of 
is:
A) 0 B)
C) 1/2
D) 
E) 
_______________________________________________________________________________
|
| 5)
Which of the following graphs has these features:? f'(0) >0, f'(1) <0 and f''(x)
is always negative. 
A) B)
C) D)
E) _______________________________________________________________________________
|
| 6)
The line l in the figure is the graph of y = f(x). 
A) 3
B) 4
C)
4.5
D) 5
E) 5.5 _______________________________________________________________________________
|
| 7)
The vertices of the triangle PQR are the points P(1, 2), Q(4, 6) and R(- 4, 12).
Which one of the following statements about triangle PQR is true?
A) PQR is a right triangle with the right angle, P.
B) PQR is a right triangle with the right angle,Q.
C) PQR is a right triangle with the right angle, R.
D) PQR is not a right triangle. _______________________________________________________________________________
|
8)
Which one of the following conics is represented by the equation (x-3y)(x+3y)
= 36 ? A)
Circle
B) Ellipse
C) Parabola
D) Hyperbola _______________________________________________________________________________
|
| 9)
Determine the distance between the x -intercept and the z-intercept
of the plane whose equation is 3x + 2y - 4z = 12.
A) 
B) 1
C)
5
D) 7 _______________________________________________________________________________
|
10)
AB is the diameter of a semicircle
k, C is an arbitrary point on the semicircle (other than A or B), and S is the
centre of the circle inscribed into triangle ABC. Then the measure of
A)angle ASB changes as C moves on k.
B)angle ASB is the same for all positions of C but it cannot be determined
without knowing the radius.
C) angle ASB = 135° for all C.
D) angle ASB = 150° for all C. _______________________________________________________________________________
|
11)
A set of 24 cards is numbered with the positive integers from 1 to 24. If the
cards are shuffled and if only one is selected at random, what is the probability
that the number on the card is divisible by 4 or 6?
A) 1/6
B)
5/24
C) 1/4
D) 1/3
E) 5/12 _______________________________________________________________________________
|
12)
A translation maps A (2, -3) onto A' (-3, -5). Under the same translation, find
the coordinates of B', the image of B (1,4).
A) (-5, -2)
B)
(6,6)
C) (-2,
-4)
D) (-4, 2)
_______________________________________________________________________________
|
| 13)
The number of bacteria in a colony was growing exponentially. At 1 pm yesterday
the number of bacteria was 1000 and at 3 pm yesterday it was 4000. How many bacteria
were there in the colony at 6 pm yesterday?
|
| 14 The rectangle labeled Q CANNOT be obtained
from the rectangle labeled P by means of 
A) reflection (about an axis in the plane of the page)
B) rotation (in the plane of the page)
C) translation
D) translation followed by a reflection _______________________________________________________________________________
|
| 15)
Determine all complex number z that satisfy the equation 
where  denotes the conjugate of z.
A) ( -1/3 + 5/3i)
B) ( -3 -i)
C)
(1 -i)
D) answer
not given _______________________________________________________________________________
|
16
The graph of the function g passes through the point (1,2). The slope of the tangent
to the graph at any point (x, y) is given by g'(x) = 6x - 12. What is g(x)?
A) 6x2 -12x +11
B) 6x2 -12x -11
C) 3x2 - 12x +11
D) 3x2 -12x _______________________________________________________________________________
|
| 17)
What are the values of x for which the inequality 
is true?
A) x is less than or equal to -7/9
B) x is less than or equal to -1/3
C) x is greater than or equal to 0
D) x is greater than or equal 7/3
E) x is greater than or equal 9/3 _______________________________________________________________________________
|
18)
Given logb2 = 1/3, then logb32 is equal to
A) 2
B) 5
C)
-3/5
D) 5/3
E) 3/log232
_______________________________________________________________________________
|
19)
The sum of the infinite series 1- (1/2) + (1/4) - (1/8) + ... is
A) 5/8
B)
2/3
C) 3/5
D) 3/2
E) infinite _______________________________________________________________________________
|
| 20)
The velocity v of a body moving in a straight line t seconds after
starting from rest is v = 4t3 - 12 t2
meters/second . How many seconds after starting does its acceleration
become zero? seconds
|
| 21) A warning system installation consists of two independent
alarms probabilities of operating in an emergency of 0.95 and 0.90 respectively.
Find the probability that at least one alarm operates in an emergency.
A) 0.995
B)
0.975
C) 0.95
D) 0.90
E) 0.855 _______________________________________________________________________________
|
22
An examination consists of 13 questions. A student must answer only one of the
first two questions and only nine of the remaining ones. How many choices of questions
does the student have?
A) 13C10 = 286
B) 11C 8 =165
C) 2 X 11C9 =110
D) 2 X 11P 2 = 220
E) some other number _______________________________________________________________________________
|
| 23
For what real value of k will the equation below describe of circle of radius
equal to 3? x2 + y2+2x-4y+k = 0
A) K=2
B) K=8
C)
K= -4
D) K= -9
E) K= 4
_______________________________________________________________________________
|
| 24
Find all real values of x which satisfy the equation. 
A) x=1
B) x=4, x=1
C)
x=4
D) x=2, x=
-1
E) x=2
_______________________________________________________________________________
|
| 25)
A string is wound symmetrically around a circular rod. The string goes exactly
4 times around the rod. The circumference of the rod is 4 cm. and its length is
12 cm.  Find the length of the
string. cm.
|
