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M
S
E
C
A
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each problem
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Trial Question
I have a cube and a squarebased pyramid.
What is the total number of
faces, edges and vertices?
A) 40
B) 42 C) 44 D) 46 E) 48
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1. Simplify
7
(22)
A) 10242
B) 163842
C) 128
D) 1024
E) 16384
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2. The line y = x + 1 undergoes the
following transformations:
1. Reflection in the x-axis, then…
2. Rotation of +90º about (0,0), then...
3. Reflection in the line x = -1
The final image line is:
A) y = x - 1
D) y = -x - 1
B) y = x + 3
E) y = -x - 3
C) y = -x + 1
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3. Solution A contains 45% salt.
Solution B contains 54% salt.
A and B are mixed in the ratio 2:1.
What is the percentage of salt in
the mixture?
A) 99%
B) 48%
C) 33%
D) 49.5% E) 72%
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4. If a T-shirt is sold for $40,
20% is lost. What is the
percentage gain or loss if it
is sold for $45?
A) loss of 5%
B) gain of 5%
C) gain of 10% D) loss of 10%
E) no gain or loss
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5. Three whole numbers, when
added two at a time, give sums of
39, 48 and 51.
What is the largest of the three
numbers?
A) 21
B) 30
D) 28
E) 14
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C) 18
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6. ABCD is a square.
A
The area of triangle
DOC is 4 square units.
The perimeter of
triangle DOC is:
B
O
D
A) 8
B) 82
D) 8 + 22
E) 4 + 42
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C) 42
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7. Calculate
2001 - 2000 + 1999 - … + 3 - 2 + 1
A) 999
B) 1000
C) 1001
D) 2001
E) none of these
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8. How many different
triangles have sides 6, 7 and
N, where N is a whole
number?
A) 9
B) 13
C) 10
D) 11
E) 12
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9. Given that y is 3 times the sum
of twice x plus the square of x,
what values of x will make y = 9?
A) x = 3, x = -3
B) x = 3, x = -1
C) x = 1, x = 0
D) x = 3, x = 0
E) x = 1, x = -3
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10. Simplify
9  10  6
10
4
6
15  16  3
5
A) 10
B) 15
11
C) 9
6
D) 5
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E) 2
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11. I pick a ball at random from a
bag containing 5 white, 2 blue, 1
red and 3 green balls.
What is the probability that the
ball is not white?
A) 5/11
B) 2/11
D) 8/121
E) 6/11
C) 4/11
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12. The mean height of the boys
in class T1 was 162cm.
When Tom, who is 165cm tall,
joined the class, the new mean
became 162.2cm.
How many boys are now in T1?
A) 11 B) 12 C) 13 D) 14 E) 15
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h (cm)
13. The graph shows
the change in height, 200
h, of the water level in 179
a pool against time.
At what time will the
water be 144cm high?
A) 4 min
B) 5 min
C) 8 min
D) 10 min
0 3
time
(min)
E) 12 min
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14. How many whole numbers are
perfect squares with four digits?
A) 32
D) 68
B) 99
E) 9801
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C) 67
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15. If
xy 3
y
 , then 
x
2
x
A) 7/2
B) 5/2
D) 1/2
E) -1/2
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C)3/2
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16.
x
y
If 2 .3
= 432,
find the value of x + y, where x
and y are positive integers.
A) 3
B) 7
D) 72
E) none of these
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C) 12
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17.
ab =
2
a
- (a -
2
b)
Find 52
A) 4
B) 1
D) 34
E) 16
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C) 74
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18. If p is the average of x and y,
q is the average of y and z, and
r is the average of x and z, then
what is the average of x, y and z?
A) (p + q + r)/3
B) (p + q + r)/2
C) 2(p + q + r)/3 D) p + q + r
E) 3(p + q + r)/2
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19. If f(x) = 5x + 6, then f(x) < 16
if and only if
A) x = 2
D) -2 < x < 2
B) x < 2
C) x > 2
E) 0 < x < 2
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20.
7 a b c
- d 1 2 8
c d 6 5
.
.
Each letter in the subtraction
above represents a single digit.
The letters in order a, b, c, d are
A) 4,9,3,6
B) 3,4,9,5
D) 4,9,3,5
E) 5,9,3,4
C) 4,3,9,5
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21. Simplify
1
1
1
1 1
1
A) x + 1
2x + 1
B) 3x + 2
2x + 1
D) x + 2
E) none of these
.
x
C) 2x + 1
3x + 2
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22. When two distinct circles and
three distinct lines intersect each
other, the maximum number of
points of intersection is:
A) 14
B) 15
D) 19
E) 17
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C) 21
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2
x
23. If
and
then
+
2
y
=8
xy = 7
(x +
2
y)
=
A) 14
B) 16
D) 30
E) 49
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C) 22
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24. If a watch is set at 2pm and
loses 1 21 minutes every two hours,
what will it read, on the following
day, when it is actually 2pm?
A) 1.30
B) 1.36
D) 1.42
E) 1.51
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C) 1.40
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25. A square ABCD contains an
equilateral triangle ABF.
The size of the angle CFD , in
degrees, is
A) 120
B) 150
D) 90
E) 180
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C) 75
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