2024 Official Past Papers · Free Download

2024 Australian AMC Mathematics Competition
Official Past Papers & Full Answers HD PDF

Complete collection of 2024 Australian AMC past papers for all five levels (A-E), with HD printable PDF papers, official standard answers, and bilingual detailed analysis.

2024Year
A-ELevels
MediumDifficulty
FreeAccess
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01 2024 Year Overview

Overall characteristics and difficulty level of the 2024 Australian AMC

The 2024 Australian AMC continued its classic format with an emphasis on engaging, real-world applications and moderate overall difficulty. The first 20 questions are standard foundational types, while the last 10 progressively deepen analytical thinking. This year strengthened geometry proofs and comprehensive number theory, with a notable emphasis on logical reasoning.

Overall Difficulty
Medium

02 Key Topics

Six core topic areas tested in 2024 Australian AMC

01

Geometry Proofs

Congruent triangle proofs, parallel line properties, cyclic quadrilaterals

Frequent
02

Number Theory

Prime properties, divisibility characteristics, modular arithmetic

Core
03

Algebraic Operations

Polynomial expansion, factorization, fraction simplification

Foundation
04

Probability & Statistics

Conditional probability, expected value, data analysis

Application
05

Sequences & Recursion

Arithmetic/geometric sequences, recurrence relations, series sums

Advanced
06

Solid Geometry

3D figure nets, surface area and volume calculations

Must-Know

03 Featured Problem Analysis

Q29 · Number Theory Challenge

Q29 · Number Theory Challenge

Find the smallest positive integer n such that the sum of digits of n equals the sum of digits of the sum of all divisors of n.
Solution Approach:
Let S(n) be the digit sum of n and σ(n) be the sum of divisors. We need the smallest n where S(n) = S(σ(n)). Starting from n=1, check each case using factorization and digit sum properties for systematic analysis. This problem tests deep understanding of divisor theory and patience in computation.

04 2024 Study Insights

Key observations based on 2024 exam characteristics

1
More Geometry Proofs

Pure geometry proof questions increased notably across all level papers compared to previous years.

2
Real-Life Problem Contexts

Multiple questions incorporated shopping, travel, and other real-world scenarios, emphasizing practical math.

3
More Comprehensive Number Theory

Number theory problems moved beyond pure computation, requiring cross-topic knowledge integration.

4
Clear Differentiation in Q21-30

The difficulty gradient in questions 21-30 was well-designed, effectively distinguishing different student levels.

05 2024 Australian AMC Study Guide

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

The 2024 Australian AMC had an overall difficulty of Medium. 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

Geometry Proofs

a high-frequency area this year — prioritise it and drill Congruent triangle proofs, parallel line properties, cyclic quadrilaterals for reliable marks.

Core

Number Theory

a core scoring area — master Prime properties, divisibility characteristics, modular arithmetic thoroughly.

Foundation

Algebraic Operations

a foundational area — lock in Polynomial expansion, factorization, fraction simplification to avoid easy losses.

Application

Probability & Statistics

application-focused — watch for Conditional probability, expected value, data analysis combined with real-life contexts.

Advanced

Sequences & Recursion

key to high scores — once the basics are solid, focus on Arithmetic/geometric sequences, recurrence relations, series sums.

Must-Know

Solid Geometry

appears almost every year — build a fixed method for 3D figure nets, surface area and volume calculations.

This year’s featured / final problem direction is “Q29 · Number Theory Challenge” — practise this problem type specifically and build complete analysis and write-up habits.

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