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Questions 1 to 10, 3 marks each
1.
The value of 95
− 83 is
(A) 2
(B) 8
(C) 11
(D) 12
(E) 22
2.
0.5 expressed as a fraction is
(A)
1
8
(B)
1
5
(C)
1
4
(D)
1
3
(E)
1
2
3.
In the diagram, x equals
(A) 70 (B) 80 (C) 90 (D) 100 (E) 110
... ... ... ... ... ... ... ... ... ... ... ... ... ...x
◦
70
◦
. . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . .4.
The value of
6
× 25
3
× 5 × 2
is
(A) 1
(B) 2
(C) 3
(D) 5
(E) 6
5.
When I start a journey, the tripmeter reads 789 km. When I finish it reads 901 km.
The distance travelled, in kilometres, is
(A) 102
(B) 108
(C) 110
(D) 112
(E) 288
6.
The change from $50 if you bought 7 bottles of orange juice at 70 c per bottle
should be
J 2
7.
A tetromino is a shape consisting of four squares joined along their edges. Here
are three different
tetrominoes:-Which of the tetrominoes below cannot be obtained by a rotation, in the plane,
of one of the above tetrominoes?
(A)
(B)
(C)
(D)
(E)
8.
The area, in square centimetres, of one face of a cube whose volume is 64 cm
3
is
(A) 8
(B) 16
(C) 24
(D) 32
(E) 64
9.
The value of
3
5
−
2
10
+
3
15
−
4
10
is
(A)
2
5
(B)
3
5
(C)
1
5
(D)
1
2
(E) 0
10.
The average of five numbers is 4. Four of them are 1, 2, 3 and 4. What is the
other?
Questions 11 to 20, 4 marks each
11.
Which of the spinners below would give a one-in-four chance of the arrow landing
in the shaded region?
(A)
... ...... ...... ......... ... ... ... ... ... ... .... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .. .. .. .. .. .. ... ... ... ... ... .... ...... ...... ...... ...... ...... ... ... ... ... ... ... ... .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. . .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. . .. ..... ... ... . .. .. . .. .. .. .. .. .. . .. .. .. .. .. .. .. .. . .. .. .. .. . .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . ... ... ... ... ... ... ... ... ...(B)
... ...... ...... ......... ... ... ... ... ... ... ... ... ... .. ... .. .. .. .. .. .. .. .. .. .. .. . .. . .. . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .. .. .. .. .. .. ... ... ... ... ... ... ...... ...... ...... ...... ...... ... ... ... ... ... ... ... ... . .. .. . .. .. .. .. .. .. . .. .. .. .. .. .. .. .. . .. .. .. .. . .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. . .. .. .. . .. .. .... ... ... ... ... ... ... ... ......... .. ...(C)
... ...... ...... ......... ... ... ... ... ... ... .... ... ... .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . .. .. .. . .. .. ... ... ... ... ... ... .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. . .. .. .. . .. .. .... ... . .. .. . .. .. .. .. .. .. . .. .. .. . .. .. .. .. . .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . ... ... ... ... ... ... ... ................... .... .......... .... .... .... .... .. .... .... . .... .... . .... ...(D)
...... ...... ...... ... ... ... ... ... ... .... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .. .. . .. .. .. ... ... ... ... ... ... ... ... ... ... ... ... ... ... . .. .. . .. .. .. .. .. .. . .. .. .. .. .. .. .. .. . .. .. .. .. . .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . ... ... ... ... ... ... ... .............. ...(E)
... ...... ...... ......... ... ... ... ... ... .... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .. .. .. .. ... .. .... ... ... ... ... ...... ...... ...... .. .... ... .... ... ... .... ... ... .... ... .... ... ... .... ... .... ... ... .... ... ... .. .. .. .. . .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. . .. .. .. . .. .. ....... ... ... ... ... ... ... ... ... .. ...12.
The numbers from 1 to 5 are placed one per square in the diagram shown, so that
the sum of the three numbers in the horizontal row is the same as the sum of the
3 numbers in the vertical column.
4
1
If the numbers 1 and 4 are placed as shown, then the sum of the row or column is
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
13.
Fifty L shaped tiles, each made out of three 1 cm by 1 cm squares,
are arranged as shown below.
.. . .. . .. . . .. . .. . .. . . .. . .. . .. . . .. . .. . .. . .. . . .. . .. . .. . . .. . .. . .. . . .. . .. . .. . . .. . .. . .. . . .. . .. . .. . . .. . .. . ... ... ... ... ... ...... . . . .. . . .. . . . .. . . .. . . . .. . . .. . . . .. . . .. . . . .. . . .. . . . ...... ... .. . .. . .. . . .. . .. . .. . .. . .. . .. . .. . . ... . ... ... ... ... ...... ... . . .. . . .. . . . .. . . .. . . . .. . . .. . . . .. . . ...... ......... . .. . .. . .. . .. . . .. . .. . .. . .. . .. . .. . .. . . .. . .. . ... . ... ... ... ... ...... ... . .. . . .. . . . .. . . .. . . . .. . . . .. . . .. . . ...... ......... . .. . .. . . .. . .. . .. . .. . .. . .. . .. . . .. . .. . .. . .. . ... ... ... ... ... ...... ... . . .. . . . .. . . .. . . . .. . . .. . . . .. . . .. . . ...... ......... . . .. . .. . .. . .. . .. . .. . .. . . .. . .. . .. . .. . .. . .. . . ... ... ... ... ...... ... . . . .. . . .. . . . .. . . .. . . . .. . . .. . . . .. . ...... ........ .. . .. . .. . .. . .. . .. . .. . . .. . .. . .. . .. . .. . .. . .. . ... ... ... ... ... ...... ... . . .. . . .. . . . .. . . .. . . . .. . . .. . . . .. . ...... ... . .. . . .. . .. . .. . .. . .. . .. . .. . . .. . .. .
q
q
q
The perimeter of the resulting shape, in centimetres, is
J 4
14.
Using only 5 c, 10 c and 20 c coins, in how many ways can you make up 35 cents?
(A) 4
(B) 6
(C) 5
(D) 8
(E) 7
15.
In the diagram, P OR = 120
◦
and QOS = 145
◦
.
The size of T OV is
(A) 45
◦
(B) 60
◦
(C) 85
◦
(D) 90
◦
(E) 95
◦
... ...... ...... ...... ...... ...... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...T
V
P
Q
R
S
O
16.
The middle date of the year in 2006 is
(A) 29th June
(B) 30th June
(C) 1st July
(D) 2nd July
(E) 3rd July
17.
Gina has three children and one of them is a teenager. When she multiplies their
ages together the result is 770. How old is the teenager?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
18.
A 1
× 1 × 1 cube is cut out of a 10 × 10 × 10 cube. Then a 2 × 2 × 2 cube is cut
from the remainder followed by a 3
× 3 × 3 cube and so on. What is the largest
cube which can be cut out?
(A) 3
× 3 × 3
(B) 4
× 4 × 4
(C) 6
× 6 × 6
(D) 7
× 7 × 7
(E) 5
× 5 × 5
19.
The digits 3, 4, 5 and 6 can be put together to form 24 different four-digit numbers.
If these numbers are arranged from smallest to largest, which number is in the
thirteenth position?
20.
The corner of a rectangular piece of paper is folded as shown in figure 1, then
folded again, so the corner A just touches the first fold line as shown in figure 2.
A
4
4
@I
First fold line
f igure 1
... ... ... ... ... ... ... .. ... ... ... ...A
@R
Second fold line
f igure 2
... . .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. . ... ... ... ... ... ... ... ... ... ..The area, in square units, of the shaded triangle is
(A) 4
(B) 2
(C) 6
(D) 2
1
3
(E) 1
2
3
Questions 21 to 30, 5 marks each
21.
In aerial view, an apartment block is composed of a number of square apartments
and a number of square gardens, joined to form a rectangular block. Apartments
must have at least one window, either to the outside or to one of the gardens. For
example, in the 3
× 4 block below, the apartment marked ∗ has a window onto the
internal garden G, whilst all other apartments have outside windows.
... ... ... ... ... ... .... . . . . . . . ... ... ... ... ... ... .... . . . . . . . ... ... ... ... ... ... .... . . . . . . . ... ... ... . . . . . . . ... ... ... ... ... ... ... ... ... . . . . . . . ... ... ... ... ... ... ... ... ... ... ... ... . . . . . . . ... ... ... ... ... ... ... ... ...
