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Australian AMC 2014 - Junior

Question 1

What is the value of $17+16+14+13$?
  1. 60
  2. 61
  3. 63
  4. 68
  5. 70

Question 2

In the diagram, what is $x$ in degrees?

Question illustration
  1. 80
  2. 70
  3. 60
  4. 50
  5. 40

Question 3

What is the perimeter of the figure, in centimetres?

Question illustration
  1. 21
  2. 30
  3. 36
  4. 39
  5. 78

Question 4

This week my lemonade stand sold 29 dollars of lemonade. I spent 34 dollars on lemons and 14 dollars on sugar. What was my total loss?
  1. 1 dollars
  2. 9 dollars
  3. 19 dollars
  4. 21 dollars
  5. 29 dollars

Question 6

If $5/6$ of a number is 30, what is $3/4$ of that number?
  1. 22.5
  2. 24
  3. 25
  4. 27
  5. 40

Question 7

A map 40 cm wide and 20 cm high is folded along the dashed lines to form a 10 cm by 10 cm square that just fits its envelope. It is then pinned to a notice board. Which pattern A–E could show the pinholes on the unfolded map?

Question illustration

Question illustration
  1. A
  2. B
  3. C
  4. D
  5. E

Question 8

The diagram is an open square of order 4: three equal sides, each with four evenly spaced posts. How many posts are on an open square of order 10?

Question illustration
  1. 26
  2. 27
  3. 28
  4. 30
  5. 32

Question 9

A train is scheduled to leave at 10:14 am and takes 2 hours 47 minutes to reach its destination. If it leaves 8 minutes late, when does it arrive?
  1. 7:28 am
  2. 7:35 am
  3. 12:09 pm
  4. 1:01 pm
  5. 1:09 pm

Question 10

Five consecutive whole numbers are written on separate cards. The smallest three sum to 60. What is the sum of the largest three?
  1. 62
  2. 63
  3. 64
  4. 65
  5. 66

Question 11

A rectangle has width one third of its length and area $108\text{ cm}^2$. What is its perimeter in centimetres?
  1. 54
  2. 48
  3. 42
  4. 36
  5. 24

Question 12

Six people stand in a line. The first is 150 cm tall and the sixth is 180 cm tall. Every other person has height equal to the average of the heights directly in front and behind. How tall is the fourth person?
  1. 165 cm
  2. 168 cm
  3. 170 cm
  4. 172 cm
  5. 174 cm

Question 13

A tower uses 1 cube in its bottom layer, then 4 in the second, 9 in the third, then 16, and so on. It contains 91 cubes altogether. How many layers does it have?
  1. 7
  2. 6
  3. 5
  4. 4
  5. 3

Question 14

A school places 76 students as evenly as possible into six classes, with any two class sizes differing by at most one. How many classes have exactly 12 students?
  1. 2
  2. 3
  3. 4
  4. 5
  5. 6

Question 15

Four equal equilateral triangles with horizontal bases are arranged inside a larger equilateral triangle as shown. What fraction of the larger triangle is covered?

Question illustration
  1. $2/3$
  2. $1/2$
  3. $4/9$
  4. $4/7$
  5. $16/25$

Question 16

After 9 weekly spelling tests, Mikayla averages 5 marks out of 10. What is the minimum number of extra weeks needed to raise her average to 7?
  1. 4
  2. 5
  3. 6
  4. 7
  5. 8

Question 17

Anne has four cards, each with a different number. She lists all different totals obtained by choosing two or more cards and adding their numbers. What is the maximum number of different totals?
  1. 7
  2. 8
  3. 9
  4. 10
  5. 11

Question 18

In March, April and May, my lawn grows 0.7 cm daily. On the day it reaches 20 cm I mow it back to 2.5 cm. If I mow on 1 March, how many mowings are needed in these three months altogether?
  1. 2
  2. 3
  3. 4
  4. 5
  5. 6

Question 19

There are $n$ people equally spaced around a circle, numbered in order from 1 to $n$. Person 31 notices that people 7 and 14 are equally distant from him. How many people are there?
  1. 42
  2. 41
  3. 40
  4. 39
  5. 38

Question 20

A 3 by 5 grid of dots is shown. How many straight segments join two dots and pass through exactly one other dot?

Question illustration
  1. 14
  2. 20
  3. 22
  4. 24
  5. 30