Australian Mathematics Competition - 2022 - Middle Primary Years - Grade 3 & 4 - Questions

Problem 1:

How many dots are in this pattern?

(A) 20
(B) 21
(C) 22
(D) 23
(E) 24

Problem 2:

What number is one hundred more than \(465 \) ?

(A) 365
(B) 455
(C) 475
(D) 565
(E) 1465

Problem 3:

What fraction of this rectangle is shaded?

(A) \(\frac{1}{2}\)
(B) \(\frac{1}{4}\)
(C) \(\frac{1}{6}\)
(D) \(\frac{1}{8}\)
(E) \(\frac{1}{10}\)

Problem 4:

There were 17 dogs and 9 ran away. How many dogs were left?

(A) 7
(B) 8
(C) 12
(D) 26
(E) 27

Problem 5:

John is playing a board game. He moves his blue piece (>) one square up then three squares left. Which piece does he land on?

Problem 6:

Which shape is not used in this snowman picture?

(A) circle
(B) oval
(C) triangle
(D) square
(E) rectangle

Problem 7:

Eve starts at 20 and counts up by twos: (20,22,24) and so on. What is the tenth number she counts?

(A) 30
(B) 32
(C) 34
(D) 36
(E) 38

Problem 8:

This graph was made by a Year 3 class. How many students chose either Saturday or Sunday as their favourite day?

(A) 5
(B) 8
(C) 10
(D) 12
(E) 20

Problem 9:

I went for a bike ride this morning. These clocks show my start and finish times.
In minutes, how long was my ride?

(A) 9
(B) 13
(C) 47
(D) 52
(E) 62

Problem 10:

Edie and Louie are standing in a line with other children. Edie is fourth from the front and Louie is fourth from the back of the line. There are 15 children in the line. How many children are between Edie and Louie?

(A) 7
(B) 8
(C) 10
(D) 11
(E) 12

Problem 11:

There are 49 ten-cent coins in my pink piggy bank and 25 twenty-cent coins in my blue piggy bank.
How much money do I have altogether?

(A) \(\$ 7.40\)
(B) \(\$ 9.90\)
(C) \(\$ 12.30\)
(D) \(\$ 14.80\)
(E) \(\$ 990\)

Problem 12:

How many more small cubes are needed to complete this large cube?

(A) 6
(B) 8
(C) 9
(D) 12
(E) 20

Problem 13:

Ms Amali brings 100 stickers to share equally among her class of 23 students. How many stickers will she have left over?

(A) 3
(B) 8
(C) 12
(D) 17
(E) 21

Problem 14:

This card is flipped over its right-hand edge and then flipped again over its bottom edge. What does the card look like now?

Problem 15:

Chris wants to use the same number in both boxes to make this number sentence true. What number should she use?

(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

Problem 16:

Sally says to her brother, 'You are 10 years older than me'. Her brother says, 'You are right, and I am three times your age'. How old is Sally?

(A) 4 (B) 5 (C) 6 (D) 7 (E) 8

Problem 17:

How many of the small coloured tiles are needed to cover the large cross shape shown?

(A) 10
(B) 15
(C) 20
(D) 36
(E) 40

Problem 18:

Siobhan has seven cards, numbered 1 to 7 . She places six of them correctly in the three number sentences. Which card does she have left over?

(A) 1
(B) 2
(C) 3
(D) 5
(E) 7

Problem 19:

A long rectangular room 10 m long and 2 m wide has mirrors on all four walls. Any beam of light hitting these mirrors bounces back at the same angle as shown below. A guard standing at one end of the room shines a torch at an angle of \(45^{\circ}\) to the walls, making a narrow beam that bounces off the mirrors several times, stopping when it returns to her. How many times does the beam of light bounce off the mirrors?

(A) 7
(B) 9
(C) 10
(D) 11
(E) 22

Problem 20:

A can filled with 30 marbles weighs 115 g . The same can with 20 marbles weighs 85 g . How much does the empty can weigh?

(A) 10 g
(B) 20 g
(C) 25 g
(D) 30 g
(E) 55 g

Problem 21:

Peter wants to buy a length of ribbon to wrap around a box as shown. The box is 20 cm long, 20 cm wide and 20 cm high. It takes an extra 80 cm of ribbon to tie the bow. What is the best estimate of the amount of ribbon that Peter needs to buy to tie around the box?

(A) 160 cm
(B) 180 cm
(C) 240 cm
(D) 280 cm
(E) 320 cm

Problem 22:

In week 1, Hamish and Eliza open bank accounts for their savings. Hamish saves (\$ 12) every two weeks, starting in week 1 . Eliza saves (\$ 32) in week 1 and then (\$ 4) every week after that. When will they first have the same amount of money in the bank?

(A) week 3
(B) week 5
(C) week 7
(D) week 9
(E) week 11

Problem 23:

A different whole number is placed in each corner of a square. Two numbers joined by an edge must have a difference of more than 1. When the four numbers are added together, what is the smallest possible total?

(A) 10
(B) 11
(C) 12
(D) 13
(E) 14

Problem 24:

Three whole numbers add to 21 . When these same three numbers are multiplied together they equal 280 . What is the smallest of these three numbers?

(A) 1
(B) 2
(C) 4
(D) 7
(E) 10

Problem 25:

Steven made this cube from a paper net, then pushed a pin through it as shown. He then removed the pin, leaving holes in the cube, and unfolded the cube back to its net. Which of the following could be the net of Steven's cube?

Problem 25:

I notice that my electricity meter currently reads 896754 units, where all the digits are different. How many more units of electricity will I need to use before all the digits are again different?

Problem 27:

How many whole numbers between 200 and 500 contain the digit 3 ?

Problem 28:

On a digital display, a combination of bars light up to represent each digit as shown:

In some special numbers, the number of bars which light up in the digits is the same as the sum of the digits. For example, in 373 the number of bars is (5+3+5=13) which is the equal to (3+7+3=13). What is the largest such three-digit number?

Problem 29

Nguyen writes down some numbers according to the following rules. Starting with the number 1 , he doubles the number and adds 4 , so the second number he writes is 6 . He now repeats this process, starting with the last number written, doubling and then adding 4, but he doesn't write the hundreds digit if the number is bigger than 100 . What is the 2022nd number that Nguyen writes down?

Problem 30:

I choose three different numbers out of this list and add them together: 1, 3, 5, 7, 9,…, 105 How many different totals can I get?