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, B) PQR is a right triangle with the right angle, C) PQR is a right triangle with the right angle, 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?
A) 8000
B) 5000
C) 16000
D) 32000
E) 64000
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.
A) 30 cm.
B) 16 cm.
C) 25 cm.
D) 20 cm.
E) 24 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) 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) 13 C10 = 286
B) 11 C 8 =165
C) 2 X 11 C9 =110
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
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 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
