QCE General Mathematics

Unit 1 of QCE General Mathematics covers four distinct topic areas that together build the foundational mathematical reasoning skills underpinning the entire course. Applied Trigonometry develops skills in right-angled and non-right-angled triangle trigonometry including the sine rule, cosine rule, and area formula, and applies these to practical measurement and navigation problems. Algebra covers linear and non-linear expressions and equations, substitution into formulae, and the use of algebraic skills to model and solve problems arising in real-world contexts. Matrices introduces matrix notation and arithmetic including addition, subtraction, scalar multiplication, and matrix multiplication, and applies matrix methods to practical situations including communication networks and systems. Univariate Data develops data literacy through classifying data, constructing and interpreting appropriate data displays, and calculating and comparing summary statistics including measures of centre and spread. Together these topics establish the breadth of mathematical reasoning expected across the General Mathematics course and directly prepare students for the content of Units 2, 3, and 4.

Unit 2 of QCE General Mathematics covers the Money, Measurement and Relations content that applies mathematical skills to practical financial, geometric, and algebraic contexts. The Money topic develops consumer arithmetic skills including percentage calculations, mark-ups, discounts, GST, simple and compound interest, and working with financial statements and budgets in everyday and business contexts. The Measurement topic extends and applies geometric and trigonometric skills to practical situations including area and volume of composite shapes and solids, error and accuracy in measurement, and applications of the metric system in practical trade and design contexts. The Relations topic develops graphical reasoning including plotting, interpreting, and applying linear, quadratic, and exponential relations in practical modelling contexts, identifying key features of graphs, and using graphs and equations to solve problems. Together these topic areas reflect the QCAA General Mathematics syllabus emphasis on applying mathematical skills to realistic, practical, and contextualised situations across personal finance, industry, and everyday life.

Unit 3 of QCE General Mathematics covers the Investing and Networking content that develops advanced financial and discrete mathematics skills. The Investing topic extends the compound interest and financial mathematics content from Unit 2 to include reducing balance loans, annuities, and the use of recurrence relations and technology to model and compare investment and loan scenarios over time including calculating future values, present values, and regular repayment amounts. The Networking topic introduces graph theory and network mathematics including the properties and terminology of graphs and networks, Eulerian and Hamiltonian paths, minimum spanning trees using Prim’s algorithm and Kruskal’s algorithm, the shortest path problem and Dijkstra’s algorithm, and an introduction to critical path analysis including identifying the critical path and calculating minimum project completion times. Investing and Networking is assessed in internal assessment tasks and contributes to the external examination, with the networking content rewarding students who can read and interpret network diagrams and apply graph algorithms methodically in unfamiliar contexts.

Unit 4 of QCE General Mathematics covers the Bivariate Data, Sequences and Change, and Earth Geometry content that rounds out and consolidates the General Mathematics course. Bivariate Data extends the Unit 1 univariate data skills to include scatter plots, the Pearson correlation coefficient and its interpretation, least-squares regression lines and their equations, making predictions using regression equations, and understanding the distinction between correlation and causation. Sequences and Change introduces arithmetic and geometric sequences and series, their general term formulae, and their applications to modelling practical situations involving growth and decay, including connecting sequence notation to the financial and investment content from Unit 3. Earth Geometry develops an understanding of the geometry of the sphere with applications to navigation, including latitude and longitude, calculating distances along great circles and small circles, and solving practical navigation problems on the surface of the Earth. Unit 4 is the capstone of the General Mathematics course and directly prepares students for the external examination, where all four units are assessed.