AMC-style maths competition practice for Years 3 to 8
The Australian Mathematics Competition (AMC) is a problem solving competition run by the Australian Maths Trust. Learnest has AMC-style problem solving questions for Years 3 to 8, and timed AMC-style papers you can set from your parent page.
A$10 a month for one child, A$5 for each extra child.
What the AMC is
- Divisions
- Middle Primary for Years 3 and 4, Upper Primary for Years 5 and 6, and Junior for Years 7 and 8. Older students sit the Intermediate and Senior divisions.
- The paper
- 30 questions: 25 multiple choice and 5 with a whole-number answer.
- How long
- 60 minutes for the primary divisions and 75 minutes for the secondary divisions.
Source: Australian Mathematics Competition on amt.edu.au, checked 3 October 2026.
When the AMC runs
The 2026 competition ran from Tuesday 4 to Thursday 6 August 2026. The Australian Maths Trust had not published the 2027 date when we checked on 3 October 2026.
Source: Australian Mathematics Competition on amt.edu.au, checked 3 October 2026.
How Learnest helps
- One strategy at a time: working backwards, guess and improve, drawing a diagram, making an organised list, splitting into cases and finding the pattern, with bar models and digit puzzles from Year 5, and algebra, systematic counting and remainders in Years 7 and 8.
- A stretch question on maths days: problem solving on some days in Years 3 to 6 and every day in Years 7 and 8. In Settings you can make it problem solving every day in Years 3 to 6 as well.
- AMC-style papers: 30 questions in 60 minutes for Years 3 to 6, or in 75 minutes for Years 7 and 8, the same count and time as the real paper. A quick paper of 10 questions in 20 minutes suits a school night.
- Daily work underneath: the maths follows the NSW syllabus for your child's year, which teaches the number skills the problems need.
How Learnest's papers differ: each multiple-choice question has four options, where the AMC's have five, and the review after a paper shows the right answer rather than a full solution.
Each year has a page with what your child works on and sample questions: Year 3, Year 4, Year 5, Year 6, Year 7 and Year 8.
Sample questions
These come from Learnest's own question bank. Try each one, then open the worked answer.
Pick an answer to check it. Try a wrong one too: you see the mistake that usually leads to it.
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Middle Primary: work backwards
Jack spent half his money on a book, then $4 on a drink, and has $6 left. How many dollars did he start with?
Your child types the answer.
See the worked answer
Answer: 20
Add the $4 back to reach $10, which is the half he did not spend on the book, so he started with $20.
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Middle Primary: draw it
At assembly Priya stands 10th from one end of her row and 8th from the other end. How many children make up the row?
- Option A: 18
- Option B: 16
- Option C: 17
- Option D: 10
See the worked answer
Answer: C, 17
Priya is inside both counts, the 10th from one end and the 8th from the other, so one place is counted twice.
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Upper Primary: find the pattern and jump ahead
The word SYDNEY is written again and again with no spaces: SYDNEYSYDNEY... What is the 2026th letter?
- Option A: N
- Option B: Y
- Option C: E
- Option D: D
See the worked answer
Answer: A, N
The pattern repeats every 6 letters. 2026 = 337 × 6 + 4, so after 337 whole repeats the 2026th letter is the 4th letter of the next repeat, which is N.
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Upper Primary: digit puzzles
A 2-digit number is added to the number made by swapping its digits, and the total is 132. How many different 2-digit numbers could it be?
- Option A: 7
- Option B: 3
- Option C: 6
- Option D: 4
See the worked answer
Answer: A, 7
A number with digits a and b plus its swap is 10a + b + 10b + a, which is 11 lots of a + b, so the digits add to 132 รท 11 = 12. The numbers are 39, 48, 57, 66, 75, 84 and 93, which is 7.
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Junior: remainders
Find the smallest positive whole number with remainder 2 on division by 3, remainder 3 on division by 4, and remainder 4 on division by 5.
- Option A: 59
- Option B: 61
- Option C: 119
- Option D: 9
See the worked answer
Answer: A, 59
Each remainder is one less than the divisor, so the number plus 1 is a multiple of 3, 4 and 5. The lowest common multiple is 60, so the number is 59.
Questions parents ask
When is the AMC in 2027?
The Australian Maths Trust had not published the 2027 date when we checked on 3 October 2026. The 2026 competition ran from Tuesday 4 to Thursday 6 August 2026.
Which AMC division is my child in?
Middle Primary is for Years 3 and 4, Upper Primary for Years 5 and 6, and Junior for Years 7 and 8.
How long is the AMC?
30 questions: 25 multiple choice and 5 with a whole-number answer. Primary divisions have 60 minutes and secondary divisions 75 minutes.
Is Learnest connected to the Australian Maths Trust?
No. Learnest is not affiliated with the Australian Maths Trust. AMC-style means the questions follow the competition's problem solving style. Every question is Learnest's own.
Fifteen to twenty minutes a day, planned for your child.
Learnest finds the level, teaches the gap and tells you that night which skill is slipping. The test-style practice adds to that daily work.
Learnest is not affiliated with ACARA, NESA, the NSW Department of Education or the Australian Maths Trust. Every question on this page is Learnest's own, written for practice. None comes from a past paper.