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 ÐP.
B) PQR is a right triangle with the right angle ÐQ.
C) PQR is a right triangle with the right angle ÐR.
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).
Your Answer:
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?
Your Answer:
(ans. 32,000)
14) 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.
Your Answer:
(ans. 20 cm.)
15) Determine all complex number z that satisfy the equation
where 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 logb b
A) 2
B) 5
C) -3/5
D) 5/3
E) 3/log2 32
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 t 2 meters/second .
How many seconds after starting does its acceleration become zero?
A) 1
B) 2
C) 3
D) 4
E) 6
21) The ride with the cable car from station A to station B at the top
of Mt. Glacier takes 16 minutes. The average speed of the cable car is 2 meters per second
and it moves in a straight line forming a 25 degree angle with the
horizontal.
Find the height of Mt. Glacier (measured from the level of station A) to the
nearest whole meter.
Your Answer:
Answ =811
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) 13 C10 = 286
B) 11 C 8 =165
C) 2 X 11 C9 =119
D) 2 X 11 P 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
Your Answer:
Ans 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) answer not given
25 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
