2020 Official Past Papers · Free Download

2020 Australian AMC Mathematics Competition
Official Past Papers & Full Answers HD PDF

Complete collection of 2020 Australian AMC past papers for all five levels (A-E), with HD printable PDF papers, official standard answers, and bilingual detailed analysis.

2020Year
A-ELevels
MediumDifficulty
FreeAccess
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01 2020 Year Overview

Overall characteristics and difficulty level of the 2020 Australian AMC

The 2020 Australian AMC was held before the pandemic and was one of the last large-scale in-person math competitions that year. The questions continued the AMC's tradition of engaging and thought-provoking design, emphasizing mathematical modeling and creative thinking. The probability and geometry sections were particularly outstanding.

Overall Difficulty
Medium

02 Key Topics

Six core topic areas tested in 2020 Australian AMC

01

Probability

Classical probability, geometric probability, addition and multiplication rules

Frequent
02

Circles & Triangles

Tangent lines, chord length, inscribed/circumscribed circles

Core
03

Number Theory Basics

Prime identification, GCD, LCM

Foundation
04

Algebraic Identities

Perfect square formula, sum/difference of cubes, factorization

Must-Know
05

Series Summation

Arithmetic sums, telescoping sums, method of differences

Advanced
06

Area & Volume

Irregular figure area, volume of solids of revolution

Application

03 Featured Problem Analysis

Q30 · Probability & Geometry

Q30 · Probability & Geometry

Two points are randomly chosen inside a unit square. Find the probability that the distance between them is less than 1.
Solution Approach:
Let the two points have coordinates (x₁,y₁) and (x₂,y₂), all uniformly distributed on [0,1]. The condition is (x₁-x₂)²+(y₁-y₂)²<1, a geometric probability problem in four-dimensional space. Using variable substitution u=x₁-x₂, v=y₁-y₂, the problem transforms to finding the area ratio of u²+v²<1 in [-1,1]×[-1,1], requiring a combination of integral calculus and geometric probability.

04 2020 Study Insights

Key observations based on 2020 exam characteristics

1
Last Large-Scale In-Person Event Pre-Pandemic

2020 was the last regular in-person Australian AMC before the COVID-19 pandemic.

2
Cleverly Designed Probability Questions

Probability problems incorporated geometric elements, requiring integrated analysis.

3
Flexible Use of Algebraic Identities

Factorization and identity manipulation were key themes this year.

4
Continued Tradition of Engaging Problems

Maintained the AMC's hallmark style of combining fun with mathematical insight.

05 2020 Australian AMC Study Guide

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

The 2020 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

Probability

a high-frequency area this year — prioritise it and drill Classical probability, geometric probability, addition and multiplication rules for reliable marks.

Core

Circles & Triangles

a core scoring area — master Tangent lines, chord length, inscribed/circumscribed circles thoroughly.

Foundation

Number Theory Basics

a foundational area — lock in Prime identification, GCD, LCM to avoid easy losses.

Must-Know

Algebraic Identities

appears almost every year — build a fixed method for Perfect square formula, sum/difference of cubes, factorization.

Advanced

Series Summation

key to high scores — once the basics are solid, focus on Arithmetic sums, telescoping sums, method of differences.

Application

Area & Volume

application-focused — watch for Irregular figure area, volume of solids of revolution combined with real-life contexts.

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

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