QCE General Mathematics Notes
Browse 38 free QCE General Mathematics notes across Units 1-4, organised by topic with syllabus points, worked examples and quick checks.
38 QCE General Mathematics notes across Units 1-4, covering 20 topics for syllabus revision, external exams and ATAR study.
Use these notes as the first pass for a QCE syllabus point, then test the same topic with practice questions, feedback or subject-specific study guides.
Unit 1: Money, measurement, algebra and linear equations
Consumer arithmetic
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Wages, income support and personal budgets
Learn income and budgets for QCE General Mathematics Unit 1 with worked reasoning, KaTeX, an original diagram and checked practice.
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Unit pricing, percentage change, exchange and shares
Learn consumer comparisons for QCE General Mathematics Unit 1 with worked reasoning, KaTeX, an original diagram and checked practice.
Shape and measurement
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Pythagoras, perimeter and area in context
Learn two-dimensional measurement for QCE General Mathematics Unit 1 with worked reasoning, KaTeX, an original diagram and checked practice.
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Surface area, volume, capacity and composite solids
Learn three-dimensional measurement for QCE General Mathematics Unit 1 with worked reasoning, KaTeX, an original diagram and checked practice.
Similarity and scale
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Similar figures, triangles and linear scale
Learn similarity and linear scale for QCE General Mathematics Unit 1 with worked reasoning, KaTeX, an original diagram and checked practice.
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Scale drawings, area, volume and capacity scaling
Learn scale drawings and powers of scale for QCE General Mathematics Unit 1 with worked reasoning, KaTeX, an original diagram and checked practice.
Algebra
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Substitution, evaluation and formula rearrangement
Learn substitution and transposition for QCE General Mathematics Unit 1 with worked reasoning, KaTeX, an original diagram and checked practice.
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Formula tables and two-variable spreadsheets
Learn spreadsheet formula tables for QCE General Mathematics Unit 1 with worked reasoning, KaTeX, an original diagram and checked practice.
Linear equations and their graphs
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Linear equations from words and practical models
Learn linear equation modelling for QCE General Mathematics Unit 1 with worked reasoning, KaTeX, an original diagram and checked practice.
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Straight-line graphs, gradient, intercepts and context
Learn straight-line models for QCE General Mathematics Unit 1 with worked reasoning, KaTeX, an original diagram and checked practice.
Unit 2: Applications of linear equations and trigonometry, matrices and univariate data analysis
Applications of linear equations and their graphs
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Simultaneous linear equations and intersections
Learn simultaneous equations for QCE General Mathematics Unit 2 with worked reasoning, KaTeX, an original diagram and checked practice.
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Piecewise-linear and step-graph models
Learn piecewise and step graphs for QCE General Mathematics Unit 2 with worked reasoning, KaTeX, an original diagram and checked practice.
Applications of trigonometry
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Right-triangle trigonometry, elevation and depression
Learn right-triangle applications for QCE General Mathematics Unit 2 with worked reasoning, KaTeX, an original diagram and checked practice.
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Non-right triangles, area, bearings and navigation
Learn non-right triangles and bearings for QCE General Mathematics Unit 2 with worked reasoning, KaTeX, an original diagram and checked practice.
Matrices
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Matrix types, addition, scalar multiplication and dimensions
Learn matrix structure and arithmetic for QCE General Mathematics Unit 2 with worked reasoning, KaTeX, an original diagram and checked practice.
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Matrix multiplication, powers and practical models
Learn matrix products and powers for QCE General Mathematics Unit 2 with worked reasoning, KaTeX, an original diagram and checked practice.
Univariate data analysis 1
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Variable types, data displays and distribution shape
Learn classifying and displaying data for QCE General Mathematics Unit 2 with worked reasoning, KaTeX, an original diagram and checked practice.
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Centre, spread, standard deviation and summary choice
Learn centre and spread for QCE General Mathematics Unit 2 with worked reasoning, KaTeX, an original diagram and checked practice.
Univariate data analysis 2
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Parallel box plots, outliers and group comparisons
Learn comparing distributions for QCE General Mathematics Unit 2 with worked reasoning, KaTeX, an original diagram and checked practice.
Unit 3: Bivariate data and time series analysis, sequences and Earth geometry
Bivariate data analysis 1
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Identifying and describing associations between two categorical variables
Learn how QCE General Mathematics uses two-way frequency tables, row percentages and column percentages to describe associations between categorical variables.
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Identifying and describing associations between two numerical variables
Learn how to read scatterplots, identify explanatory and response variables, describe direction, form and strength, and interpret correlation in QCE General Mathematics.
Bivariate data analysis 2
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Fitting a linear model to numerical data (6 hours)
Learn least-squares lines, residual plots, interpolation, extrapolation and prediction for QCE General Mathematics bivariate data.
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Association and causation (6 hours)
Learn why association does not prove causation, including coincidence, confounding variables and cautious statistical communication.
Time series analysis
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Describing and interpreting patterns in time series data (3 hours)
Learn trend, seasonality and irregular fluctuations in QCE General Mathematics time series plots.
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Analysing time series data (8 hours)
Learn moving averages, seasonal indices, deseasonalising and trend lines for QCE General Mathematics time series analysis.
Growth and decay in sequences
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The arithmetic sequence (5 hours)
Learn recursion, tables, graphs and nth-term rules for arithmetic sequences in QCE General Mathematics.
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The geometric sequence (6 hours)
Learn recursion, common ratios, nth-term rules and practical growth or decay models for QCE General Mathematics.
Earth geometry and time zones
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Locations on the Earth (5 hours)
Learn great circles, latitude, longitude, angular distance and distance along meridians or parallels in QCE General Mathematics.
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Time zones (5 hours)
Learn UTC, GMT, longitude and time differences, the International Date Line and travel-time calculations for QCE General Mathematics.
Unit 4: Investing and networking
Loans, investments and annuities 1
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Compound interest loans and investments (6 hours)
Learn recurrence relations, compound interest formulae, effective annual interest and practical finance calculations for QCE General Mathematics.
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Present value of ordinary annuities (6 hours)
Learn reducing-balance loans, present value annuity formulae and repayment interpretation for QCE General Mathematics.
Loans, investments and annuities 2
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Perpetuities and future value of ordinary annuities (8 hours)
Learn future value annuities, perpetuities and periodic-payment finance models for QCE General Mathematics.
Graphs and networks
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Graphs, associated terminology and the adjacency matrix (4 hours)
Learn graph terminology, directed and weighted networks, and adjacency matrices for QCE General Mathematics.
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Planar graphs, paths and cycles (8 hours)
Learn Euler's formula, walks, trails, paths, bridges, Eulerian and Hamiltonian routes for QCE General Mathematics.
Networks and decision mathematics 1
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Trees and minimum connector problems (4 hours)
Learn trees, spanning trees, minimum spanning trees and practical connector problems for QCE General Mathematics.
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Project planning and scheduling using critical path analysis (CPA) (8 hours)
Learn activity-on-arc project networks, forward and backward scans, earliest and latest starting times, critical paths and float times.
Networks and decision mathematics 2
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Flow networks (4 hours)
Learn source nodes, sink nodes, cuts, minimum cuts and maximum flow for QCE General Mathematics flow networks.
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Assigning order and the Hungarian algorithm (7 hours)
Learn allocation problems, bipartite graphs, inspection and the Hungarian algorithm for QCE General Mathematics.
Questions about these General Mathematics notes
Are these notes free?
Yes. Every note on this subject page is public and can be read without an account.
What do these revision notes cover?
The current library covers Units 1-4 across 20 topics. Open a note to see its exact syllabus points and worked coverage.
Are they official curriculum notes?
No. Sylligence writes original study support around the published curriculum. Use the current authority syllabus and your school materials for official requirements.
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