Years 5 and 6 sit the Australian Mathematics Competition in the Upper 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 Upper Primary · Warm-up
Tom is in a line for the slide. 14 children are ahead of him and three times as many are behind him. How many children are in the line?
45
48
51
54
57
Show the answer and the working
Answer: E (57)
Behind: 3 × 14. How many are behind? 42
Ahead + the person + behind: 14 + 1 + 42. How many in the line? 57
Fastest method: Count the people ahead, the person themself, and the people behind — three groups.
The trap: forgetting to count the person in the line.
2 · AMC Upper Primary · Warm-up
A bag of 140 counters holds red, blue and green counters in the ratio 5:4:1. How many green counters are there?
12
14
28
46
126
Show the answer and the working
Answer: B (14)
Add the ratio numbers to see how many equal parts there are. What is 5 + 4 + 1? 10
140 is shared over those 10 parts, so one part is 140 ÷ 10. How big is one part? 14
The asked share is 1 part. What is 14 × 1? 14
Fastest method: Add the ratio numbers to get the total number of parts, find the size of ONE part, then multiply by the part asked for.
The trap: dividing the total by the number of items in the ratio instead of the sum of the parts.
3 · AMC Upper Primary · Middle of the paper
Two friends' scores in a quiz have an average of 28, and one score is 8 higher than the other. What is the lower score?
0
8
16
24
32
Show the answer and the working
Answer: D (24)
The average 28 sits exactly halfway between the two numbers, so each is 8 ÷ 2 away from it. What is 8 ÷ 2? 4
The smaller number is the average minus that. What is 28 − 4? 24
Fastest method: Average of two = the middle. Half the difference above the middle is the larger, half below is the smaller.
The trap: adding the whole difference to the average.
4 · AMC Upper Primary · Middle of the paper
A courier charges $30 for the first 5 kg of a parcel and $5 for every 5 kg, or part of 5 kg, after that. How many dollars does it cost to send a 19 kg parcel?
18
27
36
45
54
Show the answer and the working
Answer: D (45)
The base covers the first 5; what is left is 19 − 5. How much is charged in blocks? 14
14 in blocks of 5, 'or part' means round UP. How many blocks? 3
Base plus 3 blocks at 5. What is 30 + 3 × 5? 45
Fastest method: Take off what the base covers; what remains is charged in blocks — if 'or part', round UP to whole blocks.
The trap: charging the base amount again for the first block, or rounding down 'or part'.
5 · AMC Upper Primary · The hard end
Ada's chess club have played 34 games this season and won 25 of them. There are 36 games still to play. How many of those must they win to have won exactly 70% of all their games for the season?
8
16
24
32
40
Show the answer and the working
Answer: C (24)
The percentage is of the WHOLE season, so count all the games first. How many games are there in the season altogether? 70
70% of that is the number of wins wanted. How many wins is 70% of the season? 49
25 are already won. How many more wins are needed? 24
Fastest method: Work out the target number of wins for the whole season first, then take away the wins already banked.
The trap: taking the percentage of the games left instead of the whole season.
6 · AMC Upper Primary · The hard end
On a farm, a horse eats one bale of hay every 12 days, a cow eats one bale of hay every 2 days and a sheep eats one bale of hay every 3 days. For how many days will 33 bales feed one horse, one cow and one sheep together?
0
12
24
36
48
Show the answer and the working
Answer: D (36)
Use a block of 12 days (a number all three of 12, 2, 3 divide into). In 12 days the horse eats 12 ÷ 12 bales, the cow 12 ÷ 2, the sheep 12 ÷ 3. How many bales do the three eat together in 12 days? 11
So 11 bales last 12 days. Scale to 33 bales. How many days do the bales last? 36
Fastest method: Turn each 'one bale every d days' into a share of a bale per day, add the shares, then divide the bales by the daily total.
Number: working backwards, fractions and ratios in stories, divisibility, digits and place value puzzles.
Space: area and perimeter puzzles, nets and cubes, angles, paths on grids.
Reasoning: counting systematically, logic, patterns that continue, 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 5 and 6 sit Upper Primary; Years 3 and 4 sit Middle Primary.
How do you prepare for the AMC hard questions?
By learning the handful of methods the last questions keep using — working backwards, counting systematically, looking for the pattern — one at a time, on fresh questions.
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.