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junior Division Competition paper
instruCtions anD information
GeneraL
1. Do not open the booklet until told to do so by your teacher.
2. NO calculators, slide rules, log tables, maths stencils, mobile phones or other calculating aids are
permitted. Scribbling paper, graph paper, ruler and compasses are permitted, but are not essential.
3. Diagrams are NOT drawn to scale. They are intended only as aids.
4. There are 25 multiple-choice questions, each with 5 possible answers given and 5 questions that
require a whole number answer between 0 and 999. The questions generally get harder as you
work through the paper. There is no penalty for an incorrect response.
5. This is a competition not a test; do not expect to answer all questions. You are only competing
against your own year in your own State or Region so different years doing the same paper
are not compared.
6. Read the instructions on the answer sheet carefully. Ensure your name, school name and school
year are entered. It is your responsibility to correctly code your answer sheet.
7. When your teacher gives the signal, begin working on the problems.
tHe ansWer sHeet
1. Use only lead pencil.
2. Record your answers on the reverse of the answer sheet (not on the question paper) by FULLY
colouring the circle matching your answer.
3. Your answer sheet will be scanned. The optical scanner will attempt to read all markings even
if they are in the wrong places, so please be careful not to doodle or write anything extra on
the answer sheet. If you want to change an answer or remove any marks, use a plastic eraser
and be sure to remove all marks and smudges.
inteGritY of tHe Competition
The AMT reserves the right to re-examine students before deciding whether to grant official status
to their score.
a u s t r a l i a n s c h o o l Y e a r s 7 a n d 8
t i m e a l l o w e d : 7 5 m i n u t e s
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ublishing2012
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A u s T r A l i A n
M A T h e M A T i c s
T r u s T
t h u r s daY 2 au g u s t 2 01 2
Junior Division
Questions 1 to 10, 3 marks each
1.
The value of 99
− 2 + 1 + 102 is
(A) 0
(B) 100
(C) 198
(D) 200
(E) 202
2.
The size, in degrees, of
6
Q is
......... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
55
◦
Q
R
45
◦
P
(A) 40
(B) 55
(C) 60
(D) 80
(E) 90
3.
Yesterday it rained continuously from 9:45 am until 3:10 pm. For how long did it
rain?
(A) 3 hours 25 minutes
(B) 3 hours 35 minutes
(C) 5 hours 25 minutes
(D) 6 hours 25 minutes
(E) 6 hours 35 minutes
4.
The value of 8
× 3.1 is
(A) 11.1
(B) 16.8
(C) 8.31
(D) 24.1
(E) 24.8
5.
The change you should receive from a $20 note after paying a bill of $9.45 is
(A) $10.55
(B) $10.45
(C) $11.55
(D) $9.55
(E) $10.65
6.
Three-fifths of a number is 48. What is the number?
(A) 54
(B) 60
(C) 64
(D) 80
(E) 84
7.
Which of the following is closest to 100?
J 2
8.
The adjacent sides of the decagon shown meet at right angles and all dimensions
are in metres.
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...... ... ... ... ...... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .8
7
8
6
16
What is the perimeter, in metres, of this decagon?
(A) 45
(B) 60
(C) 34
(D) 90
(E) cannot be calculated
9.
If
5
9
of the children in a choir are boys and the rest are girls, the ratio of boys to
girls is
(A) 4 : 9
(B) 4 : 5
(C) 5 : 4
(D) 9 : 4
(E) 5 : 9
10.
By what number must 6 be divided to obtain
1
3
as a result?
(A) 18
(B)
1
2
(C)
1
18
(D) 2
(E) 9
Questions 11 to 20, 4 marks each
11.
In the diagram, the size of three angles are
given. Find the value of x.
(A) 90
(B) 95
(C) 100
(D) 110
(E) 120
... ... ... ... ... ... ... ... ... ... ... ... ... ...... ...... ...... ...... ...... ...... ...... ...... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... ...30
◦
50
◦
40
◦
x
◦
12.
A jar of mixed lollies contains 100 g of jellybeans, 30 g of licorice bullets and 20 g
of bilby bears. Extra bilby bears are added to make the mix 50% bilby bears by
weight. How many grams of bilby bears are added?
J 3
13.
A square piece of paper is folded in half. The resulting rectangle has a perimeter
of 18 cm. What is the area, in square centimetres, of the original square?
(A) 9
(B) 16
(C) 36
(D) 81
(E) 144
14.
If 750
× 45 = p, then 750 × 44 equals
(A) p
− 45
(B) p
− 750
(C) p
− 1
(D) 44p
(E) 750p
15.
The grid shown is part of a cross-number puzzle.
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...... ...... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .... .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. . .. ... .. .. .. .. . .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .... .. .. .. .. . .. .. .. .. .. .. .. . .. .. .. .. .. . .. ... .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. ... .. . .. ...
1
2
3
6
7
11
12
13
16
17
20
21
22
2
Clues
16 across is the reverse of 2 down
1 down is the sum of 16 across and 2 down
7 down is the sum of the digits in 16 across
What is 7 down?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
16.
I can ride my bike 3 times as fast as Ted can jog. Ted starts 40 minutes before me
and then I chase him. How long does it take me to catch Ted?
(A) 20 min
(B) 30 min
(C) 40 min
(D) 50 min
(E) 60 min
17.
Five towns are joined by roads, as shown in the diagram.
...... ...... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... ... .... .... .... .... .... .... .... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
P
Q
R
S
T
How many ways are there of travelling from town P to town T if no town can be
visited more than once?
J 4
18.
What are the last three digits of 7777
× 9999?
(A) 223
(B) 233
(C) 333
(D) 323
(E) 343
19.
In how many ways can 52 be written as the sum of three prime numbers?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
20.
Four points P , Q, R and S are such that P Q = 10, QR = 30, RS = 15 and
P S = m. If m is an integer and no three of these points lie on a straight line, what
is the number of possible values of m?
(A) 5
(B) 49
(C) 50
(D) 54
(E) 55
Questions 21 to 25, 5 marks each
21.
A courier company has motorbikes that can travel 300 km starting with a full tank.
Two couriers, Anna and Brian, set off from the depot together to deliver a letter to
Connor’s house. The only refuelling is when they stop for Anna to transfer some
fuel from her tank to Brian’s tank. She then returns to the depot while Brian keeps
going, delivers the letter and returns to the depot. What is the greatest distance
that Connor’s house could be from the depot?
(A) 180 km
(B) 200 km
(C) 225 km
(D) 250 km
(E) 300 km
22.
The square P QRS has sides of 3 metres. The points X and Y divide P Q into 3
equal parts.
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...... ...... ...... ...... ...... ...... ...... ... ... ... ... .. ... ... ... .. ... ... ... ..P
X
Y
Q
R
S
Z
Find the area, in square metres, of
4XY Z.
(A)
3
8
(B)
1
2
(C)
3
16
(D)
1
3
(E)
1
4
J 5
23.
The product of three consecutive odd numbers is 226 737. What is the middle
number?
(A) 57
(B) 59
(C) 61
(D) 63
(E) 65
24.
A Meeker number is a 7-digit number of the form pqrstup, where p
× q = 10r + s
and s
× t = 10u + p and none of the digits are zero. For example, 6 742 816 is a
Meeker number. The value of s in the largest Meeker number is
(A) 2
(B) 3
(C) 5
(D) 7
(E) 8
25.
Four positive integers are arranged in a 2
×2 table. For each row and column of the
table, the product of the two numbers in this row or column is calculated. When
all four such products are added together, the result is 1001. What is the largest
possible sum of two numbers in the table that are neither in the same row nor in
the same column?
(A) 33
(B) 77
(C) 91
(D) 143
(E) 500
For questions 26 to 30, shade the answer as an integer from 0 to 999 in
the space provided on the answer sheet.
Question 26 is 6 marks, question 27 is 7 marks, question 28 is 8 marks,
question 29 is 9 marks and question 30 is 10 marks.
26.
This cube has a different whole number on each face, and has the property that
whichever pair of opposite faces is chosen, the two numbers multiply to give the
same result.
What is the smallest possible total of all 6 numbers on the cube?
27.
How many four-digit numbers containing no zeros have the property that whenever
any its four digits is removed, the resulting three-digit number is divisible by 3?
J 6
28.
A rhombus-shaped tile is formed by joining two equilateral triangles together.
Three of these tiles are combined edge to edge to form a variety of shapes as
in the example given.
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .
