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2012!
One leg of a right triangle has length 15.
The area of the triangle is 60.
What is the length of the hypotenuse?
Answer: 17
What is the sum of the roots of
2
6x + x - 2
Answer: -1/6
Calculate:
3 (3 )  2 (2 )
2
3
3
2
Answer: 65
Given that x and y are integers,
what is the value of y for the
following system of equations:
xy = 30
2x +3y = 28
Answer: y = 6
Calculate the mean of the prime
numbers between 60 and 80.
Answer: 70.2
When a  3, b  4 and c  5, the
ab  bc  ac
the expression
can be
ab  bc  ac
expressed as a fraction in simplest
p
form as . Find p  q.
q
Answer: 54
Solve for x
 2(3  5(2 x  3))  1
 13
5
Answer: x  2
The two shorter sides of a rightangled triangle are 7 and 24. What
is the length of the side of the
square that has the same
perimeter as this triangle?
Answer: 14
Make b the subject of the formula:
ab  t
p
cb  q
t  pq
Answer: b 
(or equivalent)
pc  a
The sum of the first N prime
numbers is 129, what is the value
of N?
Answer: N = 10
Calculate (21  9 )  (19  1 )
2
2
2
2
Answer: 0
What is the Least Common
Multiple (LCM) of 16, 18 and 20?
Answer: 720
A students takes 6 tests and
achieves a mean score of 72. He
takes two more tests. What must
the mean score in these tests be so
that his mean for all 8 tests is 75?
Answer: 84
The sum 2  4  5 can be
expressed in the form n where n
is an integer. Find n.
5
3
2
n9
Answer: n = 11
A man born in the year n2 died at
the age of 89. Given that he died in
2
the year (n+1) , in what year was
he born?
Answer: 1936
x
64
The equation
has two

1 9
1
x
solutions, a and b. Calculate ab.
 64
Answer:
9
A bag contains 5 white balls and 7
black balls. Yoona draws two balls
from the bag at the same time. The
probability that she draws two
p
p
different colored balls is where
q
q
is a fraction in its simplest form.
What is the value of p  q ?
Answer: 101
8! 2! 3!
Calculate the value of
5! 6! 7!
1
Answer:
900
ab b
Given a * b 
, find 2*(3*4)
b a
2
2
2
Answer: 2
Alice drives from A to B at a speed
of 60km/h. The distance from A to
B is 150km. She then drives from B
to C at a speed of 80km/h. The
distance from B to C is 250km.
What was her average speed for
the entire journey? Give your
answer correct to the nearest
1km/h.
Answer: 71km/h
A cube of ice with side length 4cm
is melted and then frozen in the
shape of a cone with radius 3cm.
What is the height of this cone?
Give your answer in terms of .
64
Answer:
3
35% of 50 - 45% of 30
Calculate
35% of 40
giving your answer as a fraction in
its simplest form.
2
Answer:
7
The complement of angle P is 15
less than one quarter of its
supplement. Find P.
Answer: P = 80
A rectangle has a length that is
three times bigger than its width.
The sum of the diagonals of the
rectangle is 40. What is the area of
the rectangle?
Answer: 120
The slope of the line perpendicular
1
to x  3y  4 is?
4
Answer: 12
1 + 3 + 5 + …… + (2n – 1) = 676.
What is the value of n?
Answer: n = 26
What value of a makes
a perfect square?
2
9x
+ 144x + 64
Answer: 81
A convex decagon has 8 angles that
are 150 degrees. The two
remaining angles are equal. What
size is each of the remaining
angles?
Answer: 120 degrees
A pair of fair 6 sided dice are
rolled. What is the probability of a
sum of 6 or 7?
11
Answer:
36
3
1
7
The equation


2 x  1 3x  2 20
has two solutions. Find the product
of these solutions.
Answer: 3
A cube has a diagonal of length 6.
Calculate the surface area of this
cube?
Answer: 72
2
If the ratio of (3x + y) to (x – y) is .
3
What is the ratio of x to y?
5
Answer:
7
1
2 3 4 5 6 a

The fraction      
 3 6 12 24 48  b
a
where is expressed in it simplest
b
form. Calculate
2
a
+ b.
Answer: 149
12 9
Given 4    0, find x.
x x
3
6
3
Answer: x 
2
3
Given that a number is positive and
that the number is equal to six
times its reciprocal plus one, what
is the number?
Answer: 3
A regular octagon has sides of length
10. Find the shortest distance
between opposite sides.
Give your answer in the form a  b c
Answer: 10  10 2
Calculate the sum of all of the
factors of 72.
Answer: 195
The volume of a sphere is
numerically twice its surface area.
What is the radius of the sphere?
Answer: 6
Given concentric circles where the
larger of the two has a diameter of
8, what diameter must the smaller
circle have if it occupies 40% of the
area of the larger one?
a
Give your answer in the form
b
Where a and b are integers.
16
Answer:
10
A triangle has vertices at (-1,-2),
(5,3) and (2,6). What is the area of
this triangle?
Answer: 16.5
The point (1, y) lies on the line
joining the points (-2, 8) and (3, -2).
What is the value of y?
Answer: y = 2
The number of digits in the
number 243546 is?
Answer: 8
When 1.412412….. is expressed in
a
the form the value of a + b is?
b
Answer: 2410
b  3c c  b
Given that a 

bc
c b
find the value of a when b = 2 and c = 5 .
3
2
2
Answer: 6
The equation x  4  3x  1 has two
solutions. Find their product.
 15
Answer:
8
f (x)  2 x  x  3.
2
f (n  2)  an  bn  c.
Find a  b  c.
2
Answer: 6
Given the system of equations:
 3x  4 y  14
4 x  5y  17
find the value of x  y.
Answer: 7
2 x 1
Given 27
 81
x 2
find x.
Answer: x = 5.5
A regular convex polygon has
interior angles that are 156
degrees bigger than its exterior
angles. How many sides does the
polygon have?
Answer: 30
The probability that it snows
tomorrow is 0.7. If it snows, the
probability that I will go out for a
walk is 0.2. If it does not snow
tomorrow, the probability that will go
out for a walk is 0.65. What is the
probability that I will go out for a
walk tomorrow?
Answer: 0.335
An equilateral triangle has an area
of 100√3. What is the length of its
sides?
Answer: 20
3
4
Simplify

giving your answer
1 3 2 3
with a rational denominator.
Answer: 6( 3  1)
In a class of 40 students, 25 like
pasta, 30 like rice and 4 like
neither. What is the probability
that a student chosen at random
likes both pasta and rice?
19
Answer:
40
12  30 can be written in the form
2  3  5 , find a  b  c.
2
a
3
b
c
Answer: 15
The mean of the first 8 fibonacci
numbers is?
Answer: 6.75
The expression  2 x  6 x  1 can be
written in the form  2(x  a)  b
a
What is the value of ?
b
2
2
3
Answer:
7
If a1 = 1 and a2 = 3 and
an = 2an-1 + an-2 for n > 2,
calculate 100 – a6
Answer: 1
The decimal number 42 is written
in binary as what?
Answer: 101010
3!( 16)! 

Calculate 

5!


1

2
Answer: 2
What is the product of the first
three composite numbers divided
by the sum of the first two prime
numbers? Give your answer as a
decimal.
Answer: 38.4
Two sides of a triangle are 12 and
15. The third side of the triangle is
also an integer. What is the
difference between the smallest
and largest perimeters that this
triangle can have?
Answer: 22
f (x)  2 x  3 and g(x)  25  5x.
2
f (4)
Calculate
.
g(4)
Answer: 7
(6.25)(0.16)

0.008
Answer: 125
20  20  20  .... 
Answer: 5
The number 2222 in base three is
written in base 2. What is sum of
the digits?
Answer: 2
The mean of 6 numbers is 52.5.
What number would have to be
added to these 6 so that the mean
becomes 62.5?
Answer: 122.5
What is difference between 60% of
65 and 55% of 60?
Answer: 6
A bag contains 7 blue, 5 red and 3
yellow discs. Two discs are drawn
from the bag simultaneously. What
is the probability that both discs
are red? Your answer must be a
fraction in its simplest form.
Answer: 2/21
How many numbers from 1 to 100
have the figure ‘4’, the figure ‘5’ or
both in them?
Answer: 36
How big is the acute angle between
the hands of a clock at 2:45?
Answer: 172.5 degrees
A high school has 517 students.
312 students are in Grade 10 or
below. 321 students are in Grade
10 or above. How many students
are in Grade 10?
Answer: 116
7x
The mean of x and y is
calculate
6
x y
the value of  .
y x
25
Answer:
12
Anne, Bill and Cole receive a gift
which they divide in a ratio of 3:4:8
respectively. Bill receives $40 more
than Anne. How much was the
original gift?
Answer: $600
In how many different ways can 5
students sit in a row of 5 seats if
the oldest student cannot sit at the
beginning or end of the row?
Answer: 72