2025 Official Past Papers · Free Download

2025 Australian AMC Mathematics Competition
Official Past Papers & Full Answers HD PDF

Complete collection of 2025 Australian AMC past papers for all five levels (A-E), with HD printable PDF papers, official standard answers, and bilingual detailed analysis.

2025Year
A-ELevels
Medium-HardDifficulty
FreeAccess
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01 2025 Year Overview

Overall characteristics and difficulty level of the 2025 Australian AMC

The 2025 Australian AMC featured broad knowledge coverage and higher demands on mathematical thinking, with intense competition among top students. It maintained its classic difficulty gradient — the first two-thirds are foundational questions, while the final third are challenging problems. The last five high-value questions account for approximately 30% of the total score and are the decisive factor in differentiating top performers.

Overall Difficulty
Medium-Hard

02 Key Topics

Six core topic areas tested in 2025 Australian AMC

01

Number Theory & Divisibility

Prime factorization, GCD/LCM, divisibility rules

Frequent
02

Geometry & Area

Triangle area, circle area, composite figure decomposition

Core
03

Algebra & Equations

Linear equations, inequalities, sequence terms and sums

Foundation
04

Combinatorics & Probability

Permutations and combinations, classical probability, pigeonhole principle

Advanced
05

Logical Reasoning

Conditional reasoning, chart analysis, elimination and enumeration

Must-Know
06

Measurement & Unit Conversion

Length/area/volume unit conversion, time and speed problems

Basic

03 Featured Problem Analysis

Q30 · Combinatorics Challenge

Q30 · Combinatorics Challenge

Divide the 20 positive integers from 1 to 20 into two groups such that the sum of all numbers in each group is equal. How many different ways are there to do this?
Solution Approach:
The sum of 1 to 20 is 210, so each group must sum to 105. This problem requires systematic enumeration or generating functions. Let S be the set of all subsets satisfying the condition; compute the number of subsets with sum 105 via recursion. Due to symmetry (choosing vs. not choosing), the final answer is half the total number of valid subsets. This problem tests students' mastery of combinatorial counting and recursive thinking, requiring rigorous case analysis.

04 2025 Study Insights

Key observations based on 2025 exam characteristics

1
Broader Knowledge Coverage

This year covered a broader range of knowledge, demanding greater flexibility and integrated application of mathematical thinking.

2
Increased Competition for Top Awards

Competition for top awards (Prize and High Distinction) was more intense than before, with performance on the final high-value questions proving decisive.

3
Last Five Questions Are Decisive

The final five questions account for ~30% of the total score, with top award winners showing significantly higher accuracy on these.

4
Foundation Questions Remain Stable

Mid-to-low award cutoffs remained consistent with 2024, maintaining the competition's high participation and encouraging nature.

05 2025 Australian AMC Study Guide

Targeted preparation tips by topic, based on this year’s difficulty and focus areas

The 2025 Australian AMC had an overall difficulty of Medium-Hard. Prepare in order — secure the high-frequency and foundational areas first, then break through the advanced topics — with timed practice on this year’s papers.

Frequent

Number Theory & Divisibility

a high-frequency area this year — prioritise it and drill Prime factorization, GCD/LCM, divisibility rules for reliable marks.

Core

Geometry & Area

a core scoring area — master Triangle area, circle area, composite figure decomposition thoroughly.

Foundation

Algebra & Equations

a foundational area — lock in Linear equations, inequalities, sequence terms and sums to avoid easy losses.

Advanced

Combinatorics & Probability

key to high scores — once the basics are solid, focus on Permutations and combinations, classical probability, pigeonhole principle.

Must-Know

Logical Reasoning

appears almost every year — build a fixed method for Conditional reasoning, chart analysis, elimination and enumeration.

Basic

Measurement & Unit Conversion

a foundational area — lock in Length/area/volume unit conversion, time and speed problems to avoid easy losses.

This year’s featured / final problem direction is “Q30 · Combinatorics Challenge” — practise this problem type specifically and build complete analysis and write-up habits.

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