1. PAPER
J
ctice s
Pra stion
Que
inter national DO NOT OPEN THIS BOOKLET UNTIL INSTRUCTED.
competitions STUDENT’S NAME:
and assessments
for schools
Read the instructions on the ANSWER SHEET and fill in your
NAME, SCHOOL and OTHER INFORMATION.
Use a 2B or B pencil.
Do NOT use a pen.
Rub out any mistakes completely.
You MUST record your answers on the ANSWER SHEET.
Mark only ONE answer for each question.
MatheMatics Your score will be the number of correct answers.
Marks are NOT deducted for incorrect answers.
MULTIPLE-CHOICE QUESTIONS:
Use the information provided to choose the BEST answer from
the four possible options.
On your ANSWER SHEET fill in the oval that matches your answer.
FREE-RESPONSE QUESTIONS:
Write your answer in the boxes provided on the ANSWER SHEET
and fill in the oval that matches your answer
You may use a ruler and spare paper.
A CALCULATOR is required.

2. 1. The diagram below represents the 3. During 2001, Australia exported goods to
products of (x + 5) and (3x + 2). a total value of $123 000 million.
The graph shows the percentage of these
3x + 2 goods exported to different parts of the
world.
3x 2
x Key
19%
Japan
USA
x+5 41%
10% ASEAN
5
EU
12%
China
12% 6%
Other
What product is represented by the
NOT TO SCALE
shaded rectangle? What was the value, in millions of dollars,
of the goods exported to China?
(A) 2x
(B) 6x (A) 7 380
(C) x2 (B) 12 300
(D) 3x2 (C) 14 760
(D) 23 370
2. Jules has a package gift-wrapped, as
shown.
10 cm
10 cm
30 cm
What is the volume, in cm3, of the
package?
(A) 50
(B) 300
(C) 1400
(D) 3000
ICAS Mathematics Practice Questions Paper J © EAA 2

3. 4. Jane was tossing a coin, but one side of 6.
the coin was weighted more heavily than
X F
L=M 1–
the other. Y
Here are the results she obtained. Y = 5 F = 10 M =100 000 L = 120 000
What is the value of X correct to two
decimal places?
(A) – 0.09
(B) – 0.02
(C) 0.02
(D) 0.09
7. The area of one of these isosceles
triangles is 60 square units.
base
Based on her results, which of these is
the best estimate of the probability of The length of the base of the triangle is 10
getting a head in a single toss of Jane’s units.
coin? base
The grid below is made up of triangles
(A) 0.4 exactly the same size as the triangle
(B) 0.5 above.
(C) 0.6
(D) 0.7
5. This picture is based on the style of the
Dutch artist Piet Mondrian (1872–1944).
6 2
2
4 What is the perimeter of the shaded shape?
6
(A) 105 units
(B) 150 units
4 (C) 160 units
(D) 162 units
NOT TO SCALE
Which expression gives the total area of the
three coloured rectangles in the picture?
(A) 6a2 + 48ab – 32b2
(B) 20a2 + 24b2
(C) 4a2 + 36ab – 24b2
(D) 6a2 + 16b2
3 ICAS Mathematics Practice Questions Paper J © EAA

4. QUESTIONS 9 AND 10 ARE FREE RESPONSE.
8. Anna forgot the code of a 3-digit lock on
her case. The code was made of 3 digits Write your answer in the boxes provided on
ranging from 0 to 9. She remembered that the ANSWER SHEET and fill in the ovals that
the first digit was less than 5, the second match your answer.
digit was an odd number, and the third
one was either 7 or 8. There were no
identical digits in the code. 9. The diagram represents a regular octagon
of area 500 cm2.
How many different combinations could
possibly open her lock?
(A) 25
(B) 36
How long, to the nearest centimetre,
(C) 41
is one side of the octagon?
(D) 50
10. In the diagram H represents the position
of a hawk hovering above the ground, and
M the position of a mouse on the ground.
250
200
150 H
100
50
M
0
50 0
100 50
150 100
200 150
200
250
ALL MEASUREMENTS IN CENTIMETRES
The mouse moves to a new position N,
which is 50 cm from position M.
What is the maximum possible distance,
in cm, from H to the new position N
correct to the nearest whole number?
END OF PAPER
ICAS Mathematics Practice Questions Paper J © EAA 4

5. This page may be used for working.
5 ICAS Mathematics Practice Questions Paper J © EAA

6. Acknowledgment
copyright in this booklet is owned by educational
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acknowledge copyright. educational assessment australia
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The following year levels should sit THIS Paper:
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7. PaPer
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Inter national
Competitions
and Assessments THE UNIVERSITY OF NEW SOUTH WALES
for Schools
HOW TO FILL OUT THIS SHEET:
EXAMPLE 1: Debbie Bach EXAMPLE 2: Chan Ai Beng EXAMPLE 3: Jamal bin Abas
FIRST NAME LAST NAME FIRST NAME LAST NAME FIRST NAME LAST NAME
• Rub out all mistakes completely.
• Print your details clearly A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A
in the boxes provided. B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B
C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C
• Make sure you fill in only D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D
one oval in each column.
FIRST NAME to appear on certificate LAST NAME to appear on certificate
A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A
B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B
S
C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C
N
D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D
E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E
IO
F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F
G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G
T
H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H
S
I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I
E
J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J J
K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K
U
L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L
Q
M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M
N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N
E
O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P
I C
Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q
R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R
T
S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S
C
T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T
A
U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U
V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V V
R
W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W W
P
X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y
Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z
’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’
– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /
DATE OF BIRTH CLASS
Day Month Year (optional)
Are you male or female?
Male Female *045912* 0
1
0
1
0
1
0
1
0
1
0
1
A
B
K
L
Does anyone in your home usually speak a language other than English? 2 2 2 2 2 C M
Yes No 3 3 3 3 3 D N
4 4 4 4 E O
School name: 5 5 5 5 F P
6 6 6 6 G Q
Town / suburb: 7 7 7 7 H R
8 8 8 8 I S
Today’s date: Postcode: 9 9 9 9 J T

8. TO ANSWER THE QUESTIONS
MULTIPLE CHOICE FREE RESPONSE
Example: 4 + 6 = Example: 6 + 6 =
(A) 2 ● The answer is 12, so WRITE your 1 2
(B) 9 answer in the boxes. 0 0 0
(C) 10 ● Write only ONE digit in each box, 1 1 1
2 2 2
(D) 24 as shown, and fill in the correct oval, 3 3 3
as shown. 4 4 4
5 5 5
The answer is 10, so fill in the oval , as shown.
C
6 6 6
7 7 7
A B C D 8 8 8
9 9 9
START
1 A B C D
2 A B C D
3 A B C D
4 A B C D
5 A B C D
6 A B C D
7 A B C D
8 A B C D
9 10
0 0 0 0 0 0
1 1 1 1 1 1
2 2 2 2 2 2
3 3 3 3 3 3
4 4 4 4 4 4
5 5 5 5 5 5
6 6 6 6 6 6
7 7 7 7 7 7
8 8 8 8 8 8
9 9 9 9 9 9
PaPer
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Inter national
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9. LEVEL OF
QUESTION KEY SOLUTION STRAND
DIFFICULTY
The shaded rectangle has a side of 2 and a side
Algebra and
1 A of x. Therefore, the product of these two sides Easy
Pattern
is 2x.
Volume of a box = length × width × height
2 D V = 30 × 10 × 10 Measurement Easy
V = 3000 cm3
6% of the total products are exported to China.
Chance and
3 A 6% of 123 000 million = 0.06 × 123 000 Easy
Data
million = $7380 million
Experimental Probability equals:
Number of times an event has occurred
Number of times an event has occurred
Number of trials
Number of trials
Chance and
4 C Applying this formula: Medium
Data
67 + 286 + 581 + 2989
67 + 286 + 581 + 2989 = 0.59
100 + 500 + 1000 + 5000
100 + 500 + 1000 + 5000
Therefore, the best estimate is 0.6.
The green area is 2a × a = 2a2
The orange area is 4a × a = 4a2
The blue area is = length × width = (6b + 2b)
× (6a − 4b)
5 A = 8b × (6a − 4b) Algebra and
Medium
= 48ab − 32b2 Pattern
Therefore the total area that is coloured is =
green + orange + blue
= 2a2 + 4a2 + 48ab − 32b2
= 6a2 + 48ab − 32b2
Substitute all values in the given expression:
120000 = 100000(1− )10
X
120000 = 100000(1− X)10
X 10
5
120000 = 100000(1− get: 5)
By simplifying you will 5
X
6 = 5(1− )10
X)10
5
120000 = X 10
X
6 = 5(1− 100000(1− 5 )10 by 5 to get:
6 = 5(1− 5 ) , then divide
5
120000 = X)10
6 100000(1− )10
X
= (1−X 5
6= 5(1− 5 10
5
66 = (1− X)10 10
5 = (1− 5 )
5 X 5X 10 6 Algebra and
6 A By= 5(1−X the tenth root to the two sides of
6
1− =10 5 ) Medium/Hard
6 applying5
X =10 6 10
5 Pattern
= (1− 6
1− X )
the equation:
1− 5 =10 55
5
6 5 X
5
X = 5(1−10 66 )
= (1− )10
5 X 10 6 5
X = 5 = 105 65
1− 5(1−10 )
X = 5(1− 5 )
X 65
1− =10 subject of the equation:
Make5X the 5
X = 5(1−10 6 )
5
10 6
X = 5(1− )
5
X = −0.09
ICAS Mathematics Practice Questions Paper J © EAA

10. The perimeter of the shaded shape is made of
11 bases of the given triangle + 2 heights +
2 sides.
You need to calculate the height and the side
of the triangle first.
Calculating the height: the area is given
(60 square units), therefore you can find the
height using the formula: Area = ½ × height
h × 10
× base, 60 = 2 which gives
h = 12 units
Space and
7 C Calculating the side by cutting the triangle Hard
s middle, a right-angled triangle is Geometry
down the = 12 + 5
2 2
formed with base = 5 cm and height = 12 cm.
The unknown side is called s. Using Pythagoras’
h × 10
60 =
2
Theorem, h2 + 52 =s2. Substitute h = 12 and
find s:
s = 122 + 52 . Therefore, s = 13 units.
Now add all the values in the original
calculation: 11 bases of the given triangle +
2 heights + 2 sides.
11 × 10 + 2 × 12 + 2 × 13 = 160 units.
The first two digits filled 5 × 5 ways, the last
digit 2 ways BUT must delete Chance and
8 C Hard
117, 118, 337,338, 077,177,277,377 and 477. Data
5 × 5 × 2 – 9 = 41.
This item requires a lot of work and some
knowledge of Pythagoras’ Theorem and the
internal angles of an octagon.
There are several approaches, but they all work
by finding the area of triangles, rectangles
or trapeziums. From there, an equation that
relates the area of the octagon to the length of
the side can be written.
One method is to think of the octagon as a
rectangle between two trapeziums. A different
way is to think of it as a square with triangles
cut off. Space and
9 10 Hard
Geometry
x  2x
2
45°
x
2
x
y
y
ICAS Mathematics Practice Questions Paper J © EAA

11. x
y
y
x
x
y x
Either method results in the same answer.
Let’s approach it using x second way:
500 = 2(1+ 2) the 2
We need to calculate y first.
using Phythagoras’ Theorem:
y 2 + y 2 = x2
x
y=
2
The side of the square equals x + 2y
2x
that is x +
2
2
 2x 
The area of the square is
 x + 2
 
The area of each of the four triangles on the
1 1 x x x2
corners is × y × y = × × =
2 2 2 2 4
Therefore,
area of square – area of 4 triangles = 500
2
 2x 
x  − x = 500
2
 2
2x × 2x
x2  2 x2  − x2 = 500
2
 4 
x2  2   = 500
 2
Solving for x gives an answer of 10.176, cm.
Which is 10 to the nearest centimetre.
ICAS Mathematics Practice Questions Paper J © EAA

12. Apart from reading 3D coordinates the main
mathematics in this question is Pythagoras’
Theorem.
If we look at the mouse and the hawk from
above we would see this:
M
M
H
H
M
H
The line shows the hawk’s path. The distance
along the ground of this path (the horizontal
component)2is 1002 + 502 . This is about
M
111.8 cm.50 mouse runs 50 cm away from
1002 + The
H
the hawk M a new position ‘N’. The mouse can
to
H
run in any direction but wants to maximise the
1002 +from the hawk. This means he should
distance 502 N
N
run in the same direction as the line NH in the
H
diagram below. H
N
1002 + 502 H
1002 + 502
N H
10 190 H Measurement Hard
Along the ground H this gives a distance of
N
111.8+50=161.8 cm 100 cm
H 100 cm
H
This is just the horizontal distance. Fortunately
for the mouse, the hawk is further away than
N
N 161.8 cmcm
that because it is hovering above 100 ground at
the
161.8 cm
a height of 100 cm.
We can show this on a new diagram from a
H
N
different point of view.
161.8 cm H
161.82 + 1002 100 cm
161.82 + 1002
100 cm
N
161.8 cm
161.82 + 1002
N
161.8 cm
We can now use Pythagoras’ Theorem again to
find the distance from the hawk to the mouse.
161.82 + 1002
This gives an answer of 190.2 cm. To the
161.82 + 1002
nearest whole number this is 190.
Comment
The underlying mathematics in this problem is
not very difficult and boils down to two instances
of Pythagoras’ Theorem. As a problem, though,
the question is more difficult. Students have
to realise that Pythagoras’ Theorem is the
appropriate piece of mathematics to use and have
to extract information presented in an unusual
way. Also some insight is required to understand
in what direction the mouse should run.
ICAS Mathematics Practice Questions Paper J © EAA

13. Level of difficulty refers to the expected level of difficulty for the question.
Easy more than 70% of candidates will choose the correct option
Medium about 50–70% of candidates will choose the correct option
Medium/Hard about 30–50% of candidates will choose the correct option
Hard less than 30% of candidates will choose the correct option
ICAS Mathematics Practice Questions Paper J © EAA