FURTHER MATHEMATICS

Units 1 & 2 (Year 11) – Foundation Topics

Data Analysis and Statistics

  • Types of data (categorical, numerical)

  • Measures of central tendency (mean, median, mode)

  • Measures of spread (range, IQR, standard deviation)

  • Boxplots, histograms, and stem-and-leaf plots

  • Outliers and their impact on data

  • Correlation and regression (scatterplots, line of best fit)

Financial Mathematics

  • Simple interest and compound interest

  • Depreciation and appreciation

  • Loans, investments, and annuities

  • Effective and nominal interest rates

Graphs and Networks

  • Types of graphs (directed, undirected, weighted)

  • Eulerian and Hamiltonian paths and circuits

  • Planar graphs and Euler’s formula

  • Shortest path and minimal spanning trees

Matrices

  • Types of matrices (row, column, square, identity)

  • Matrix addition, subtraction, and multiplication

  • The inverse of a matrix

  • Transition matrices and Markov chains

Units 3 & 4 (Year 12) – Core and Modules

Core: Data Analysis

  • Univariate and bivariate data analysis

  • Measures of location, spread, and shape

  • Standard deviation and z-scores

  • Normal distribution and standard normal curve

  • Correlation coefficient (r) and coefficient of determination (r²)

  • Least squares regression line and residual analysis

  • Time series analysis (trend, seasonal, cyclic, irregular)

  • Moving averages and smoothing techniques

  • Seasonal indices and deseasonalising data

Core: Recursion and Financial Modelling

  • First-order linear recurrence relations

  • Depreciation models (reducing balance, flat rate)

  • Compound interest and annuities

  • Perpetuities and amortisation of loans

  • Reducing balance loans and repayment schedules

Module Options (Two Must Be Studied)

1. Matrices

  • Matrix operations (addition, subtraction, multiplication)

  • The identity and inverse matrix

  • Solving simultaneous equations using matrices

  • Transition matrices and steady-state probabilities

2. Networks and Decision Mathematics

  • Graphs, edges, and vertices

  • Eulerian and Hamiltonian paths and circuits

  • Shortest path algorithms (Dijkstra’s algorithm)

  • Minimal spanning trees (Kruskal’s and Prim’s algorithm)

  • Critical path analysis and project scheduling

3. Geometry and Measurement

  • Units of measurement and conversions

  • Pythagoras’ theorem and trigonometry

  • Sine rule, cosine rule, and area of a triangle

  • Surface area and volume of 3D shapes

  • Bearings and navigation

4. Graphs and Relations

  • Linear and non-linear graphs

  • Equations of straight lines

  • Quadratic, exponential, and other functions

  • Simultaneous equations and inequalities

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