1. PAPER
G
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. In which picture does the slice match the 3. This is a sector graph (pie graph).
missing part of the cake?
Vehicles Passing the School
cake cake
15
9
slice slice Key
(A) (B) 21 cars
trucks
90
cake cake motorbikes
bicycles
slice What is the angle at the centre for the
slice
number of cars passing this school?
(C) (D)
(A) 296°
(B) 284°
2. This is a diagram of a triangle. (C) 257°
(D) 240°
4. In the toy car shown, the diameters of
the back wheels are one-and-a-half times
the diameters of the front wheels.
NOT TO SCALE
Which of these cannot be values for
NOT TO SCALE
x and y ? x y
(A) 70 120
(B)
x 50 y120 When the car travels one metre, the
(A) 70 120 back wheels go around 6 times.
(C) 70 100
(B) 50 120
(D) 50 100
How many times do the front wheels go
(C) 70 100
around when the car travels one metre?
(D) 50 100
(A) 4
(B) 6
(C) 9
(D) 12
ICAS Mathematics Practice Questions Paper G © EAA 2

3. 5. How many numbers between 301 and 400 7. This picture is based on the style of the
are divisible by both 3 and 4? Dutch artist Piet Mondrian (1872–1944).
(A) 6 6 2
(B) 8 2
(C) 12
(D) 25 4
6
6. Alan and Bill want to make a bottle that
will hold about twice as much as the 4
one shown.
NOT TO SCALE
height
Which expression gives the total area of the
three coloured rectangles in the picture?
(A) 6a2 + 48ab – 32b2
(B) 20a2 + 24b2
diameter (C) 4a2 + 36ab – 24b2
(D) 6a2 + 16b2
Alan wanted to double the height of the
bottle. Bill wanted to double the diameter of
the bottle. 8. A very large number is represented as
shown.
Who was correct?
(A) neither of them
(B) both of them
(C) Bill only
(D) Alan only What is the last digit (unit) of this number?
(A) 1
(B) 3
(C) 7
(D) 9
3 ICAS Mathematics Practice Questions Paper G © EAA

4. QUESTIONS 9 AND 10 ARE FREE RESPONSE.
10. Katya has a set of Russian dolls.
Write your answer in the boxes provided on The heights of her dolls are shown.
the ANSWER SHEET and fill in the ovals that They increase by a fixed ratio.
match your answer.
128 mm
9. Ricky is thinking of a positive 3-digit
96 mm
40.5 mm
72 mm
54 mm
number.
‘If I subtract 9 from the number,
the result will be divisible by 9.
If I subtract 10 from the number,
the result will be divisible by 10. The smallest doll fits in the next larger doll.
If I subtract 11 from the number, They both fit inside the next doll.
the result will be divisible by 11.’
128 mm
x
The largest doll shown fits all four of the
1.1603 10 mm
96 mm
40.5 mm
72 mm
other dolls inside it.
54 mm
Katya calculates the height of the doll
that can fit exactly 700 dolls inside it,
including the dolls shown.
She writes the answer as:
1.1603 10 x mm
What is the lowest possible number
What is the value of x?
Ricky is thinking of?
END OF PAPER
ICAS Mathematics Practice Questions Paper G © EAA 4

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

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7. PaPer
G M
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 *045909* 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
G M
Inter national
Competitions
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9. LEVEL OF
QUESTION KEY SOLUTION STRAND
DIFFICULTY
The missing part in C is one third which
Space and
1 C matches the slice (one third); altogether they Easy
Geometry
complete one whole.
The sum of x and y adds to 190° which is more Space and
2 A Easy
than the angle sum of a triangle (180°). Geometry
The total number of vehicles = 135
90 Chance and
3 D The angle at the centre for cars = × 360° Medium
135 Data
= 240°
Let D be the diameter of the big wheel (back
wheel).
Let d be the diameter of the small wheel (front
wheel).
According to the question information,
D = 3/2 × d.
When the car travels 1 m, the big wheel makes
6 turns. Therefore, 6 × the circumference of
the big wheel = 1
Circumference of the big wheel is πD,
therefore the equation can be presented as:
6 × πD = 1….(Equation 1).
4 C Measurement Medium
Let x be the number of turns the small wheel
makes when the car travels 1m.
Using the same logic, we can form the
equation x × πd = 1…. (Equation 2)
Dividing Equation 1 by Equation 2:
6D 6D 6×3
= 1, make x = subject of x = equation: 9
the the =
xd d 2
6D
=1 x = 6D x= 6×3 =9
xd d 2
Substitute D= 3/2 d
6D
=1 x = 6D x= 6×3 =9.
xd d 2
If the number is to be divisible by 3 and by 4, it
has to be divisible by 12. The first number that
is divisible by 12 between 300 and 400 is 312.
Then continue to add 12 to get the next
Number and
5 B number until you reach 396 (the last number Medium/Hard
Arithmetic
before 400).
Therefore, the numbers are 312, 324, 336,
348, 360, 372, 384, 396.
There are 8 numbers.
ICAS Mathematics Practice Questions Paper G © EAA

10. V = π
d  × h where dπis d  × h h is 2d
V =  the diameter, V = π  × h
2
2 2 2
the height of the bottle. d
V = π × 4 ×  × h
Alan suggested doubling the height, therefore 2
V = π
d  will be: V = π d  × h .
the new volume × h 2d 
V = π  × h
2 2 2
This is twice the original volume. In other
d
V = π × 4 ×  × h
words, by doubling the height of the bottle it 2
will hold twice as much content.
Bill suggested doubling the diameter, therefore Space and
6 D Hard
Geometry
the new volume will be:
d  × h V = π
d  ×  h 2d 2d
V = π
V = π  × h  × h
2 2 2 2
V = π × 4 ×  × h .
d
2
This is 4 times the original volume. In other
words, the bottle then will hold 4 times as
much content. Therefore, only Alan was
correct.
The green area is 2a × a = 2a2
The orange area is 4a × a = 4a2
The blue area is = length × width = (6b + 2b)
× (6a − 4b)
= 8b × (6a − 4b) Algebra and
7 A Hard
= 48ab − 32b2 Pattern
Therefore the total area that is coloured is =
green + orange + blue
= 2a2 + 4a2 + 48ab − 32b2
= 6a2 + 48ab − 32b2
ICAS Mathematics Practice Questions Paper G © EAA

11. This question relies on looking for a pattern.
333444 = (3 × 111)444 = 3444 × 111444
Let’s look at powers of 111 and try to find a
pattern:
1111 = 111
1112 = 12321
1113 = 1367631
It is clear that the last digit of 111 to the power
of 444 is 1.
For powers of 3 there is a different pattern:
31 = 3
32 = 9 Number and
8 A Hard
33 = 27 Arithmetic
34 = 81
35 = 243
36 = 729
37 = 2187
38 = 6561
From this pattern every 4th power of 3 results in
a number with the digit 1 in the units place.
Since 444 is a multiple of 4, then 3444 will end
in 1. If we multiply this number by 111444
(which also ends with the digit 1), the result
will also end with 1.
990 is the lowest common multiple of 9, 10 Number and
9 990 Hard
and 11. Arithmetic
Height of smallest doll is 40.5mm.
Rate of increase in height of successive dolls
700
is 128 . 128
96 96
Height of doll with 700 dolls inside Number and
10 89 Hard
700 Arithmetic
128 = 40.5 × 128
96 96
= 1.1603 × 1089 mm
Therefore, the value of x is 89.
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 G © EAA