2022 Official Past Papers · Free Download

2022 Australian AMC Mathematics Competition
Official Past Papers & Full Answers HD PDF

Complete collection of 2022 Australian AMC past papers for all five levels (A-E), with HD printable PDF papers, official standard answers, and bilingual detailed analysis.

2022Year
A-ELevels
Medium-HardDifficulty
FreeAccess
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01 2022 Year Overview

Overall characteristics and difficulty level of the 2022 Australian AMC

The 2022 Australian AMC showed further improved question quality. This year strengthened algebraic inequalities and geometric transformations, with multiple-choice questions featuring rotation and symmetry analysis. Short-answer questions demanded more complete solution processes.

Overall Difficulty
Medium-Hard

02 Key Topics

Six core topic areas tested in 2022 Australian AMC

01

Geometric Transformations

Rotational symmetry, translation mapping, reflection properties

Frequent
02

Inequalities

Basic inequalities, Cauchy-Schwarz inequality, AM-GM inequality

Core
03

Integer Properties

Parity analysis, perfect squares, factorization

Foundation
04

Probability

Geometric probability, conditional probability, tree diagrams

Application
05

Sequences

Recursive sequences, limit concepts, summation techniques

Advanced
06

Coordinate Geometry

Distance and midpoint in coordinate systems, line equations

Must-Know

03 Featured Problem Analysis

Q30 · Geometric Transformation

Q30 · Geometric Transformation

Point P is inside equilateral triangle ABC. Rotating triangle ABP 60° counterclockwise around B gives triangle CBQ. Given PA=3, PB=4, PC=5, find the side length of equilateral triangle ABC.
Solution Approach:
After 60° rotation, BP=BQ and ∠PBQ=60°, so △BPQ is equilateral with PQ=4. By rotation invariance, AP=CQ=3. Thus △PQC has sides 3, 4, 5, making it a right triangle. Using the converse of the Pythagorean theorem to confirm ∠PQC=90°, then applying the law of cosines in △BQC to find BC²=BQ²+CQ²-2·BQ·CQ·cos∠BQC, yielding the side length.

04 2022 Study Insights

Key observations based on 2022 exam characteristics

1
Algebraic Inequalities in Focus

Combined use of algebraic inequalities and geometric transformations became key to high scores, with short-answer questions emphasizing complete solutions.

2
Geometric Transformations as New Focus

Rotation, reflection, and translation became mandatory content for advanced-level papers.

3
Stronger Inequality Applications

Flexible use of AM-GM and Cauchy-Schwarz inequalities became key differentiators.

4
Higher Standards for Solution Completeness

Grading placed notably higher demands on solution rigor and completeness.

05 2022 Australian AMC Study Guide

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

The 2022 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

Geometric Transformations

a high-frequency area this year — prioritise it and drill Rotational symmetry, translation mapping, reflection properties for reliable marks.

Core

Inequalities

a core scoring area — master Basic inequalities, Cauchy-Schwarz inequality, AM-GM inequality thoroughly.

Foundation

Integer Properties

a foundational area — lock in Parity analysis, perfect squares, factorization to avoid easy losses.

Application

Probability

application-focused — watch for Geometric probability, conditional probability, tree diagrams combined with real-life contexts.

Advanced

Sequences

key to high scores — once the basics are solid, focus on Recursive sequences, limit concepts, summation techniques.

Must-Know

Coordinate Geometry

appears almost every year — build a fixed method for Distance and midpoint in coordinate systems, line equations.

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

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