2021 Official Past Papers · Free Download

2021 Australian AMC Mathematics Competition
Official Past Papers & Full Answers HD PDF

Complete collection of 2021 Australian AMC past papers for all five levels (A-E), with HD printable PDF papers, official standard answers, and bilingual detailed analysis.

2021Year
A-ELevels
Medium-AboveDifficulty
FreeAccess
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01 2021 Year Overview

Overall characteristics and difficulty level of the 2021 Australian AMC

The 2021 Australian AMC used online format in some regions due to the pandemic, but maintained stable question quality. This year featured excellent number theory and combinatorics problems, emphasizing divisibility properties and counting techniques. The geometry section introduced coordinate methods, while algebra focused on function graph analysis.

Overall Difficulty
Medium-Above

02 Key Topics

Six core topic areas tested in 2021 Australian AMC

01

Divisibility & Factors

Divisibility tests, factor count formula, sum of factors

Frequent
02

Counting Principles

Step-by-step counting, bundling method, gap method

Core
03

Coordinate Geometry

Distance formula, midpoint formula, triangle area via coordinates

Foundation
04

Function Graphs

Linear/quadratic function graph analysis, graph transformations

Application
05

Statistical Analysis

Mean, median, standard deviation concepts and calculations

Must-Know
06

Equations & Inequalities

System solving, integer solutions, inequality proofs

Advanced

03 Featured Problem Analysis

Q29 · Factor Counting

Q29 · Factor Counting

Let n be a positive integer from 1 to 100 such that n has an even number of factors and the sum of all factors of n is also even. How many such values of n are there?
Solution Approach:
An even number of factors means n is not a perfect square (perfect squares have an odd factor count). An even factor sum requires analyzing the prime factorization of n. If n=2^a·p1^a1·p2^a2…, then σ(n)=(1+2+…+2^a)·∏(1+pi+…+pi^ai). Requires systematic parity analysis, counting after excluding perfect squares.

04 2021 Study Insights

Key observations based on 2021 exam characteristics

1
Some Regions Used Online Format

Due to the pandemic, some regions adopted online testing, but difficulty remained consistent.

2
Outstanding Number Theory Problems

Divisibility and factor theory were highlights, with cleverly designed questions.

3
Function Graph Analysis Added

Advanced papers featured questions requiring analysis of function graph trends.

4
Diverse Counting Techniques

Combinatorial counting covered bundling, gap, inclusion-exclusion, and other techniques.

05 2021 Australian AMC Study Guide

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

The 2021 Australian AMC had an overall difficulty of Medium-Above. 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

Divisibility & Factors

a high-frequency area this year — prioritise it and drill Divisibility tests, factor count formula, sum of factors for reliable marks.

Core

Counting Principles

a core scoring area — master Step-by-step counting, bundling method, gap method thoroughly.

Foundation

Coordinate Geometry

a foundational area — lock in Distance formula, midpoint formula, triangle area via coordinates to avoid easy losses.

Application

Function Graphs

application-focused — watch for Linear/quadratic function graph analysis, graph transformations combined with real-life contexts.

Must-Know

Statistical Analysis

appears almost every year — build a fixed method for Mean, median, standard deviation concepts and calculations.

Advanced

Equations & Inequalities

key to high scores — once the basics are solid, focus on System solving, integer solutions, inequality proofs.

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

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