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Australian AMC 2020 - Junior

Question 1

How many $1\times1$ squares are in this diagram?

Question illustration
  1. 16
  2. 18
  3. 20
  4. 24
  5. 25

Question 3

What is the perimeter of this triangle?

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  1. 33 m
  2. 34 m
  3. 35 m
  4. 36 m
  5. 37 m

Question 4

I stepped on the train at 8.48 am and got off at 9.21 am. How many minutes did I spend on the train?
  1. 27
  2. 33
  3. 43
  4. 87
  5. 93

Question 5

What is the value of $y$ in this triangle?

Question illustration
  1. 10
  2. 30
  3. 50
  4. 70
  5. 90

Question 7

In the grid, the total of each row is given at the end of the row, and the total of each column is given at the bottom of the column.
The value of $N$ is

Question illustration
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

Question 8

A letter G is rotated clockwise by $135^\circ$. Which of the following pictures best represents the final image?
  1. Question illustration
  2. Question illustration
  3. Question illustration
  4. Question illustration
  5. Question illustration

Question 9

$\dfrac{1+2+3+4+5}{1+2+3+4}-\dfrac{1+2}{1+2+3}=$
  1. 3
  2. $\frac56$
  3. 1
  4. $\frac76$
  5. 2

Question 10

Sebastien is thinking of two numbers whose sum is 26 and whose difference is 14.
The product of Sebastien’s two numbers is
  1. 80
  2. 96
  3. 105
  4. 120
  5. 132

Question 11

A country consists of two islands as shown on this map.
In square kilometres, its area is

Question illustration
  1. between 100 and 1000
  2. between 1000 and 10000
  3. between 10000 and 100000
  4. between 100000 and 1000000
  5. greater than 1000000

Question 12

$123456-12345+1234-123+12-1=$
  1. 33333
  2. 101010
  3. 111111
  4. 122223
  5. 112233

Question 13

Lily is 2020 days old. How old was she on her last birthday?
  1. 4
  2. 5
  3. 6
  4. 7
  5. 8

Question 14

A piece of paper is folded twice as shown and cut along the dotted lines.
Once unfolded, which letter does the piece of paper most resemble?

Question illustration
  1. M
  2. O
  3. N
  4. B
  5. V

Question 15

An equilateral triangle is subdivided into a number of smaller equilateral triangles, as shown. The shaded triangle has side length 2. What is the perimeter of the large triangle?

Question illustration
  1. 24
  2. 27
  3. 30
  4. 33
  5. 36

Question 16

Triangle $XYS$ is enclosed by rectangle $PQRS$ as shown in the diagram.
In square centimetres, what is the area of triangle $XYS$?

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  1. 82
  2. 88
  3. 94
  4. 112
  5. 130

Question 17

Four teams play in a soccer tournament. Each team plays one game against each of the other three teams. Teams earn 3 points for a win,1 point for a draw and 0 points for a loss. After all the games have been played, one team has 6 points, two teams have 4 points and one team has 3 points. How many games ended in a draw?
  1. 0
  2. 1
  3. 2
  4. 3
  5. 4

Question 18

An isosceles triangle has a perimeter of 28 cm and sides of integer length. How many different such triangles can be made?
  1. 5
  2. 6
  3. 7
  4. 8
  5. 9

Question 19

In the grid shown, the numbers from 1 to 4 must appear once in each row and column. Also, the sum of numbers in each of the four regions separated by red lines must be the same.
What is the sum $x+y$?

Question illustration
  1. 8
  2. 7
  3. 6
  4. 5
  5. 4

Question 20

Anupam has a cardboard square with a perimeter of 400 centimetres. He draws a horizontal line and a vertical line on the square and cuts along these lines to create four rectangles. What is the largest possible sum of the perimeters of these four rectangles, in centimetres?
  1. 400
  2. 600
  3. 800
  4. 1000
  5. 1200