Years 3 and 4 sit the Australian Mathematics Competition in the Middle Primary division. Six practice questions at that level, from the opening questions to the hard end, each worked out step by step.
The paper30 questions: 25 multiple-choice (A to E) and 5 with a whole-number answer from 0 to 999. 60 minutes.
WhenEarly August at school; in 2026 it was sat from 4 to 6 August.
AwardsParticipation, Proficiency, Credit, Distinction, High Distinction and Prize, decided by rank across the country.
The rampQuestions get harder and are worth more marks as the paper goes on; the last questions decide the top awards.
Six practice questions, easy to hard
Try each one before opening the answer: the working shows the step where a wrong answer usually goes wrong.
1 · AMC Middle Primary · Warm-up
Each face of a cube is divided into a grid of equal small squares, with 3 squares along each side of the face. How many small squares are there on the outside of the cube altogether?
9
18
36
54
162
Show the answer and the working
Answer: D (54)
One face is a 3 by 3 grid of small squares. How many small squares on one face? 9
A cube has 6 faces, and every small square is on exactly one face. What is 6 × 9? 54
Fastest method: Count one face (k x k) and multiply by 6 faces — every small square is on exactly one face.
The trap: multiplying by 4 faces, or counting edges instead of faces.
2 · AMC Middle Primary · Warm-up
How many minutes are there in four twelfths of an hour?
15
20
25
33
40
Show the answer and the working
Answer: B (20)
An hour is 60 minutes. One twelfth of it is 60 ÷ 12. What is 60 ÷ 12? 5
You need 4 of those parts. What is 5 × 4? 20
Fastest method: An hour is 60 minutes; divide 60 by the denominator, then multiply by the numerator.
The trap: using 100 minutes in an hour.
3 · AMC Middle Primary · Middle of the paper
The pictograph shows the number of books for each year level. Each full symbol stands for 10 books; a half symbol stands for 5. How many books were there altogether?
9
70
75
80
85
Show the answer and the working
Answer: E (85)
Year 3: 4 full symbols × 10. How many books for Year 3? 40
Year 4: 2 full symbols × 10. How many books for Year 4? 20
Year 5: 1 full symbol × 10. How many books for Year 5? 10
Year 6: 1 full symbol × 10, plus a half symbol worth 5. How many books for Year 6? 15
Add every row. What is 40 + 20 + 10 + 15? 85
Fastest method: Multiply full symbols by the key, add half a key for a half symbol, then compare or add the rows.
The trap: counting symbols instead of what they stand for, or forgetting the half symbol.
4 · AMC Middle Primary · Middle of the paper
Ava has 23 stamps. Ben has 3 more than Ava. Cara has 10 more than Ben. How many stamps does Cara have?
13
23
36
37
59
Show the answer and the working
Answer: C (36)
One person at a time. Ben is '+3' compared with Ava, who has 23. How many does Ben have? 26
One person at a time. Cara is '+10' compared with Ben, who has 26. How many does Cara have? 36
Fastest method: Write each person's number on its own line, one step at a time, before adding anything.
The trap: answering the last person's number when the question asks for a total, or applying a step to the wrong person.
5 · AMC Middle Primary · The hard end
A rectangle is cut into four smaller rectangles by one line across and one line down. The top-left piece has an area of 24 square centimetres, the top-right piece 48 square centimetres and the bottom-left piece 9 square centimetres. What is the area of the bottom-right piece, in square centimetres?
12
18
24
30
36
Show the answer and the working
Answer: B (18)
The top two pieces share a height and the left two share a width. So top-left × bottom-right = top-right × bottom-left (each side is width × width × height × height). What is 48 × 9? 432
Divide by the top-left area. What is the bottom-right area? 18
Fastest method: Pieces in the same row share a height and pieces in the same column share a width, so the unknown area is (top-right x bottom-left) ÷ top-left.
The trap: adding or subtracting the areas.
6 · AMC Middle Primary · The hard end
A gardener plants rows of seedlings. Each row takes one minute longer than the row before it. The first 6 rows take 39 minutes in total. How long do the next 3 rows take, in minutes?
24
27
30
33
36
Show the answer and the working
Answer: D (33)
Row 2 takes 1 minute more than row 1, row 3 takes 2 more, … so the first 6 have step-ups of 0 + 1 + … + 5. What is 0 + 1 + … + 5? 15
Take the step-ups off the total; what is left is 6 copies of row 1. How many minutes does row 1 take? 4
The next 3 are row 7 to row 9: (4 + 6) + (4 + 7) + (4 + 8). How many minutes do the next 3 take? 33
Fastest method: Consecutive minutes are spread evenly: the middle hole is the average, so find the first hole, then continue the pattern.
The trap: dividing the total by the number of holes and using that for the next holes.
Number puzzles: working backwards, money and change, number patterns, counting carefully.
Space: shapes, folding and nets, stacked cubes, views from different sides.
Reasoning: logic and ordering, time and calendars, the multi-step problems at the end of the paper.
How the practice works
A free diagnostic first: it finds the skills not yet held and names the step behind every miss.
Then every week: a 20-question practice paper on those skills, a mock on Saturday on the real clock, and a report to you on Sunday.
Marked by code; a wrong answer is worked through step by step before the right one is shown.
Questions parents ask
Which AMC division does my child sit?
Years 3 and 4 sit Middle Primary; Years 5 and 6 sit Upper Primary.
Can a Year 3 child do the AMC?
Yes. Year 3 and Year 4 sit the same Middle Primary paper; a Year 3 child is ranked against the same paper, so the opening questions are the place to start.
Are these past AMC questions?
No. Each question is a fresh variation of a family modelled on an official past question; the original is never shown.