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Australian AMC 2012 - Junior

Question 1

The value of $99-2+1+102$ is
  1. 0
  2. 100
  3. 198
  4. 200
  5. 202

Question 2

The size, in degrees, of $\angle Q$ is

Question illustration
  1. 40
  2. 55
  3. 60
  4. 80
  5. 90

Question 3

Yesterday it rained continuously from 9:45 am until 3:10 pm. For how long did it rain?
  1. 3 hours 25 minutes
  2. 3 hours 35 minutes
  3. 5 hours 25 minutes
  4. 6 hours 25 minutes
  5. 6 hours 35 minutes

Question 4

The value of $8\times3.1$ is
  1. 11.1
  2. 16.8
  3. 8.31
  4. 24.1
  5. 24.8

Question 5

The change you should receive from a \$20 note after paying a bill of \$9.45 is
  1. \$10.55
  2. \$10.45
  3. \$11.55
  4. \$9.55
  5. \$10.65

Question 6

Three-fifths of a number is 48. What is the number?
  1. 54
  2. 60
  3. 64
  4. 80
  5. 84

Question 7

Which of the following is closest to 100?
  1. $99+2.01$
  2. $98+3.011$
  3. $97+4.0111$
  4. $101-1.01$
  5. $102-2.011$

Question 8

The adjacent sides of the decagon shown meet at right angles and all dimensions are in metres.

Question illustration

What is the perimeter, in metres, of this decagon?
  1. 45
  2. 60
  3. 34
  4. 90
  5. cannot be calculated

Question 9

If $\frac59$ of the children in a choir are boys and the rest are girls, the ratio of boys to girls is
  1. 4 : 9
  2. 4 : 5
  3. 5 : 4
  4. 9 : 4
  5. 5 : 9

Question 10

By what number must 6 be divided to obtain $\frac13$ as a result?
  1. 18
  2. $\frac12$
  3. $\frac1{18}$
  4. 2
  5. 9

Question 11

In the diagram, the sizes of three angles are given. Find the value of x.

Question illustration
  1. 90
  2. 95
  3. 100
  4. 110
  5. 120

Question 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?
  1. 20
  2. 30
  3. 60
  4. 110
  5. 600

Question 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?
  1. 9
  2. 16
  3. 36
  4. 81
  5. 144

Question 14

If $750\times45=p$, then $750\times44$ equals
  1. $p-45$
  2. $p-750$
  3. $p-1$
  4. $44p$
  5. $750p$

Question 15

The grid shown is part of a cross-number puzzle.

Question illustration

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?
  1. 11
  2. 12
  3. 13
  4. 14
  5. 15

Question 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?
  1. 20 min
  2. 30 min
  3. 40 min
  4. 50 min
  5. 60 min

Question 17

Five towns are joined by roads, as shown in the diagram.

Question illustration

How many ways are there of travelling from town $P$ to town $T$ if no town can be visited more than once?
  1. 3
  2. 5
  3. 6
  4. 7
  5. 9

Question 18

What are the last three digits of $7777\times9999$?
  1. 223
  2. 233
  3. 333
  4. 323
  5. 343

Question 19

In how many ways can 52 be written as the sum of three prime numbers?
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

Question 20

Four points $P$, $Q$, $R$ and $S$ are such that $PQ=10$, $QR=30$, $RS=15$ and $PS=m$. If $m$ is an integer and no three of these points lie on a straight line, what is the number of possible values of $m$?
  1. 5
  2. 49
  3. 50
  4. 54
  5. 55