2015 Official Past Papers · Free Download

2015 Australian AMC Mathematics Competition
Official Past Papers & Full Answers HD PDF

Complete collection of 2015 Australian AMC past papers for all five levels (A-E), with HD printable PDF papers, official standard answers, and bilingual detailed analysis.

2015Year
A-ELevels
MediumDifficulty
FreeAccess
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01 2015 Year Overview

Overall characteristics and difficulty level of the 2015 Australian AMC

The 2015 Australian AMC emphasized layered question design, transitioning smoothly from basic computation to advanced reasoning. This year focused on sequence patterns and logical reasoning, with geometry emphasizing angle calculations and area relationships. An excellent year for transitioning from basic to intermediate training.

Overall Difficulty
Medium

02 Key Topics

Six core topic areas tested in 2015 Australian AMC

01

Sequence Patterns

Pattern finding, general terms, periodicity

Frequent
02

Logical Reasoning

Conditional reasoning, elimination, enumeration

Core
03

Angles & Area

Angle calculations, area formulas, area ratios

Foundation
04

Divisibility & Remainders

Divisibility tests, remainder calculations, number patterns

Must-Know
05

Equation Solving

Single-variable equations, word-to-equation, system solving

Application
06

Probability Basics

Simple probability, dice problems, ball-drawing problems

Basic

03 Featured Problem Analysis

Q29 · Sequence & Periodicity

Q29 · Sequence & Periodicity

Define a₁=1, a₂=2, and aₙ₊₂ as the units digit of aₙ·aₙ₊₁. Find the value of a₁+a₂+…+a₂₀₁₅.
Solution Approach:
Computing initial terms: 1,2,2,4,8,2,6,2,2,4,8,2,6… Starting from a₂, a periodic pattern emerges with period [2,2,4,8,2,6], length 6, period sum=24. From a₂ to a₂₀₁₅ there are 2014 terms, 2014÷6=335 remainder 4. Total=1+335×24+(2+2+4+8)=1+8040+16=8057. Core method: periodicity analysis.

04 2015 Study Insights

Key observations based on 2015 exam characteristics

1
Sequence Pattern-Finding Is the Highlight

Sequence patterns and periodicity were the year's most distinctive question types.

2
Rich Layers in Logical Reasoning

From simple elimination to complex reasoning chains, well-structured progression.

3
Geometry Focuses on Area Relationships

Area ratios and area formulas were the geometry core.

4
Ideal for Transitional Training

Well-designed difficulty gradient, suited for basic-to-intermediate transition.

05 2015 Australian AMC Study Guide

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

The 2015 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

Sequence Patterns

a high-frequency area this year — prioritise it and drill Pattern finding, general terms, periodicity for reliable marks.

Core

Logical Reasoning

a core scoring area — master Conditional reasoning, elimination, enumeration thoroughly.

Foundation

Angles & Area

a foundational area — lock in Angle calculations, area formulas, area ratios to avoid easy losses.

Must-Know

Divisibility & Remainders

appears almost every year — build a fixed method for Divisibility tests, remainder calculations, number patterns.

Application

Equation Solving

application-focused — watch for Single-variable equations, word-to-equation, system solving combined with real-life contexts.

Basic

Probability Basics

a foundational area — lock in Simple probability, dice problems, ball-drawing problems to avoid easy losses.

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

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