1. PAPER
E
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.
You are NOT allowed to use a calculator.

2. 1. Below is a temperature scale ranging from 4. Blake made up the following code.
0 °C to 100 °C.
0 1 2 3 4 5 6 7 8 9
Which point on the scale would be closest
to the temperature of an ice-cream?
(A) (B) (C) (D)
To read his coded numbers you start
at the top left corner and read each line
from left to right.
0 °C 37 °C 100 °C 0 1 2 3 4 5 6 7 8 9
freezing human body boiling point Which of the following codes correctly
point of temperature of water shows the (A)
number 957 286 304?
water (B)
2. 5 × 50 = ?
(A) 2 500
(B) 1 000 (A) (B)
(C) 250 (C) (D)
(D) 100
3. Which one of the following numbers is
four hundred thousand, six hundred and
two? (C) (D)
(A) 400 062
(B) 400 602
(C) 406 002
(D) 406 602
ICAS Mathematics Practice Questions Paper E © EAA 2

3. 5. Lyn built a model of a shed. It had no 7. A snail travelled 1.5 metres in 4 hours.
floor and no door. It looked like this when
it was finished.
If the snail continued at the same speed,
Which of the following shows the shapes how far would it travel in 160 minutes?
that Lyn used to build the shed?
(A) 60 cm
(B) 100 cm
(C) 150 cm
(D) 600 cm
8. A set of three cogs turns as shown below.
Cog Y
4
Cog Z
Cog X
6. Look at the number grid below. 8 12
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
If Cog X makes 15 complete revolutions,
how many revolutions do Cog Y and
Trent shaded the numbers 1, 4, 8,13
Cog Z make at the same time?
and 19 in that order.
Which number would he shade next if he Cog Y Cog Z
followed the same pattern?
(A) 71 22 1
2 2
(A) 24 (B) 30 10
(B) 25
(C) 26 (C) 71 10
2
(D) 27
(D) 30 22 1
2
3 ICAS Mathematics Practice Questions Paper E © EAA

4. 9. This sign can turn about its centre.
It makes a three-quarter turn in a
clockwise direction and then a half turn in
an anticlockwise direction.
Which picture shows the sign after
these turns?
(A) (B) (C) (D)
(A) (B) (C) (D)
QUESTION 10 IS FREE RESPONSE.
Write your answer in the boxes provided on
the ANSWER SHEET and fill in the ovals that
match your answer.
10. A cube has a volume of 343 cm3.
What is the sum of the lengths of the
edges of the cube, in cm ?
END OF PAPER
ICAS Mathematics Practice Questions Paper E © EAA 4

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

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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 *045907* 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 A B C D
10
0 0 0
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7 7
8 8 8
9 9 9
PaPer
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Inter national
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9. LEVEL OF
QUESTION KEY SOLUTION STRAND
DIFFICULTY
The temperature of an ice-cream is very close
to the freezing point of water (0 °C). Noticing
1 A Measurement Easy
the given scale, the closest point to 0 °C is
option A.
Number and
2 C Multiplying 5 by 50 gives 250. Easy
Arithmetic
This number should have 6 digits. If we write it
using expanded notation, we should have Number and
3 B Easy
400 000 + 600 + 2. In other words, it is Arithmetic
400 602.
Reading the code from left to right from the
upper left corner and using the key provided, Number and
4 C Easy
option C is the only code that shows correctly Arithmetic
all digits of the given number.
The 3D shape is made of four rectangles and
5 A Measurement Medium
two pentagons.
Trent made his pattern by skipping squares
systematically by 2, then 3, then 4, then
5 squares. Number and
6 C Medium
Following this pattern, he will skip 6 squares Arithmetic
to shade the next square. Therefore, the next
shaded number in Trent’s pattern will be 26.
Convert hours to minutes and m to cm first.
The snail travelled 1.5 m in 4 hours. That is
equal to 150 cm in 240 min. Number and
7 B Hard
150 150
Distance travelled in 1 min = cm × 160 Arithmetic
240 240
150 150
Distance travelled in 160 min = × 160 cm
240 240
= 100 cm
ICAS Mathematics Practice Questions Paper E © EAA

10. The ratio of the number of teeth on the
cogs can be expressed as a ratio of their
circumference which in turn can be expressed
as a ratio of their radii.
X:Y:Z = 8 : 4 : 12 = 1 : ½ : 3/2
Cog X has twice the number of teeth as cog Y,
Algebra and
8 B so when cog X makes a complete revolution, Medium/Hard
Pattern
cog Y must make 2 revolutions.
Cog X has 2/3 of the number of teeth of
cog Z, so when cog X makes a complete
revolution, cog Z makes 2/3 revolutions. When
cog X makes 15 revolutions, cog Y makes 30
revolutions and cog Z makes 10 revolutions.
The difference between ¾ and ½ is ¼.
Therefore, if we turn the sign ¾ turn clockwise,
Space and
9 A , then ½ turn anticlockwise, , then the Hard
Geometry
result will be the same as just turning the sign
¼ turn clockwise.
If a cube has a volume of 343 cm3 then its edge
length is 7 cm. There are 12 edges on a cube,
10 84 Measurement Hard
so the total length of the edges is 7 × 12 =
84 cm
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 E © EAA