This is a free diagnostic for AMC Y7-8 (Australian Mathematics Competition) preparation. 12 multiple-choice plus 3 short-answer (Q26-28 level) questions sample Number Theory, Geometry, Combinatorics and Algebra.
It's an exam: answer all the questions first (you can change any answer freely), then submit the whole exam to see your report. The worked solutions and hints unlock only after you submit. Use the jump menu at the top to move around.
At the end you get a knowledge-point report: a bar for every topic you attempted, your weak spots flagged, and the exact lessons to revise.
Year 7–8 students preparing for the AMC (Australian Mathematics Competition).
A three-digit number n has digit sum s . It is known that n = 15 s + 27. Given that n is the largest such number, find n .
❓ Pick the best answer:
An AMC Number Theory problem. Read the conditions, set up the relationship and work to the answer — method beats guessing.
Work through the conditions step by step. Then check against the five options.
Revise: Number Theory lessons.
In the addition AB + BA = CC , where A, B and C are distinct non-zero digits, what is the value of the two-digit number CC ?
❓ Pick the best answer:
An AMC Number Theory problem. Read the conditions, set up the relationship and work to the answer — method beats guessing.
Work through the conditions step by step. Then check against the five options.
Revise: Number Theory lessons.
A square has side length 6. A smaller similar square sits inside it with side length 4. The remaining "frame" (large square minus small square) is then cut into 4 congruent rectangles. What is the total area of two of these rectangles?
❓ Pick the best answer:
An AMC Geometry problem. Read the conditions, set up the relationship and work to the answer — method beats guessing.
Work through the conditions step by step. Then check against the five options.
Revise: Geometry lessons.
A rectangle has sides 10 and 6. The midpoints of the longer sides are joined to the opposite corners, forming two crossing diagonals inside the rectangle. The four triangular regions formed have areas a, b, c, d . What is the area of the central quadrilateral region (the inner region created by the four lines)?
❓ Pick the best answer:
An AMC Geometry problem. Read the conditions, set up the relationship and work to the answer — method beats guessing.
Work through the conditions step by step. Then check against the five options.
Revise: Geometry lessons.
A box contains red, blue and green balls. The numbers of red, blue and green balls are three different positive integers that sum to 10. How many different (unordered) combinations of (red count, blue count, green count) are possible?
❓ Pick the best answer:
An AMC Combinatorics problem. Read the conditions, set up the relationship and work to the answer — method beats guessing.
Work through the conditions step by step. Then check against the five options.
Revise: Combinatorics lessons.
A 4-digit PIN uses the digits 1, 2, 3, 4 and 5 only. No digit may repeat, and the PIN must start with an odd digit. How many such PINs are possible?
❓ Pick the best answer:
An AMC Combinatorics problem. Read the conditions, set up the relationship and work to the answer — method beats guessing.
Work through the conditions step by step. Then check against the five options.
Revise: Combinatorics lessons.
Anna and Ben paint a wall. Working alone, Anna would finish in 6 hours. Working alone, Ben would finish in 4 hours. They start together but after 1 hour Ben leaves and Anna continues alone. How many additional hours, after Ben leaves, does Anna need to finish the wall? Give your answer in hours (decimal allowed).
❓ Pick the best answer:
An AMC Algebra problem. Read the conditions, set up the relationship and work to the answer — method beats guessing.
Work through the conditions step by step. Then check against the five options.
Revise: Algebra lessons.
A shop sells stamps in two denominations: 5 cents and 8 cents. Customers pay in exact change with no change given back. What is the largest postage amount (in cents, integer ≥ 1) that cannot be paid using a combination of these stamps?
❓ Pick the best answer:
An AMC Algebra problem. Read the conditions, set up the relationship and work to the answer — method beats guessing.
Work through the conditions step by step. Then check against the five options.
Revise: Algebra lessons.
How many of these numbers are divisible by 3? 1,   12,   123,   1234,   12345,   123456,   1234567,   12345678,   123456789
❓ Pick the best answer:
An AMC Number Theory problem. Read the conditions, set up the relationship and work to the answer — method beats guessing.
Work through the conditions step by step. Then check against the five options.
Revise: Number Theory lessons.
James chooses two electives — one from each group: Group A: Mandarin, Japanese, Indonesian Group B: Mandarin, German, Arabic, Italian How many different pairs are possible?
❓ Pick the best answer:
An AMC Combinatorics problem. Read the conditions, set up the relationship and work to the answer — method beats guessing.
Work through the conditions step by step. Then check against the five options.
Revise: Combinatorics lessons.
I have four consecutive odd numbers. The largest is one less than twice the smallest. Which of the following is the largest of the four numbers?
❓ Pick the best answer:
An AMC Algebra problem. Read the conditions, set up the relationship and work to the answer — method beats guessing.
Work through the conditions step by step. Then check against the five options.
Revise: Algebra lessons.
Amy designed this rectangular flag for her fleet of yachts. What fraction of the flag is shaded?
❓ Pick the best answer:
An AMC Algebra problem. Read the conditions, set up the relationship and work to the answer — method beats guessing.
Work through the conditions step by step. Then check against the five options.
Revise: Algebra lessons.
I start with a number, multiply it by 10, and then subtract a multiple of 9 that is less than 100. My answer is 5347. What number did I start with?
❓ Enter your answer (a whole number):
An AMC Number Theory problem (a harder Q26-28 short-answer). Read the conditions, set up the relationship and work to the answer — method beats guessing.
Work through the conditions step by step. The answer is a whole number.
Revise: Number Theory lessons.
Amelia noticed that the names of three friends, Mei, Emma and Liam, were all made from letters of 'Amelia'. She chose different values from 0 to 9 for each of A, E, I, L and M so that M + E + I = E + M + M + A = L + I + A + M. What is the largest possible value of A + M + E + L + I + A ?
❓ Enter your answer (a whole number):
An AMC Combinatorics problem (a harder Q26-28 short-answer). Read the conditions, set up the relationship and work to the answer — method beats guessing.
Work through the conditions step by step. The answer is a whole number.
Revise: Combinatorics lessons.
There are three sets of three parallel lines in a plane. Lines in different sets are not parallel, and every pair of non-parallel lines intersect. Find the largest possible number of intersection points and the smallest possible number of intersection points, then multiply these two numbers .
❓ Enter your answer (a whole number):
An AMC Number Theory problem (a harder Q26-28 short-answer). Read the conditions, set up the relationship and work to the answer — method beats guessing.
Work through the conditions step by step. The answer is a whole number.
Revise: Number Theory lessons.
Go back and change any answers you like. When you're ready, submit the whole exam to lock it in and see your knowledge report — then you can revisit every question to read the full worked solution.
The report stays locked until you submit — you can't open it early.
Here is how you performed on every knowledge area you attempted. Bars show your accuracy per topic — green is strong, amber is shaky, red needs work. Only questions you answered are scored.
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