| Code | Content | Pri | Notes | |
|---|---|---|---|---|
| 1.1 | Standard Form | — | ||
| 1.2 | Arithmetic Sequences & Series | — | ||
| 1.3 | Geometric Sequences & Series | — | ||
| 1.4 | Financial Applications (compound interest, annual depreciation) | — | ||
| 1.5 | Exponents & Logarithms | — | ||
| 1.6 | Approximation & Percentage Error | — | ||
| 1.7 | Amortization & Annuities | — | ||
| 1.8 | Systems of Linear Equations (up to 3 variables, polynomial equations, GDC) | — | ||
| 1.9 | Laws of Logarithms | — | ||
| 1.10 | Rational Exponents | — | ||
| 1.11 | Infinite Geometric Series | — | ||
| 1.12 | Complex Numbers (Cartesian) (modulus, argument, conjugate, complex plane, quadratic roots) | — | ||
| 1.13 | Complex Numbers (Polar & Euler) (cis form, exponential form, sinusoidal addition) | — | ||
| 1.14 | Matrices (multiplication, determinants, inverses, solving systems Ax=b) | — | ||
| 1.15 | Eigenvalues & Eigenvectors (characteristic polynomial, diagonalization, matrix powers) | — |
| Code | Content | Pri | Notes | |
|---|---|---|---|---|
| 2.1 | Equation of a Straight Line | — | ||
| 2.2 | Functions: Domain, Range & Graph (function notation, inverse concept) | — | ||
| 2.3 | Graph of a Function | — | ||
| 2.4 | Key Features of Graphs (intersections, asymptotes, maxima, minima) | — | ||
| 2.5 | Modelling with Functions (linear, quadratic, exponential, cubic, sinusoidal, direct/inverse variation) | — | ||
| 2.6 | Modelling Skills (fitting models, choosing parameters, testing reasonableness) | — | ||
| 2.7 | Composite & Inverse Functions | — | ||
| 2.8 | Transformations of Graphs (translations, reflections, stretches, composite transformations) | — | ||
| 2.9 | Advanced Modelling (half-life, natural log models, logistic models, piecewise functions) | — | ||
| 2.10 | Scaling with Logarithms (linearizing data, log-log graphs, semi-log graphs) | — |
| Code | Content | Pri | Notes | |
|---|---|---|---|---|
| 3.1 | 3D Geometry, Volume & Surface Area (pyramid, cone, sphere, hemisphere, angle between line and plane) | — | ||
| 3.2 | Trig Ratios, Sine & Cosine Rules (area of triangle, right-angled triangles) | — | ||
| 3.3 | Applications of Trigonometry (elevation, depression, bearings, labelled diagrams) | — | ||
| 3.4 | Arc Length & Sector Area | — | ||
| 3.5 | Perpendicular Bisectors | — | ||
| 3.6 | Voronoi Diagrams (sites, vertices, edges, cells, nearest neighbour interpolation, toxic waste problem) | — | ||
| 3.7 | Radians | — | ||
| 3.8 | Unit Circle & Trig Identities (Pythagorean identity, tan definition, ambiguous case) | — | ||
| 3.9 | Matrix Transformations (reflections, stretches, rotations, determinant interpretation) | — | ||
| 3.10 | Vectors (unit vectors, position vectors, column representation, magnitude) | — | ||
| 3.11 | Vector Equation of a Line | — | ||
| 3.12 | Vector Kinematics (constant velocity, variable velocity, displacement in 2D/3D) | — | ||
| 3.13 | Scalar & Vector Products (dot product, cross product, area of parallelogram, angle between vectors) | — | ||
| 3.14 | Graph Theory Basics (vertices, edges, degree, simple/complete/weighted/directed graphs, trees) | — | ||
| 3.15 | Adjacency Matrices & Walks (k-length walks, weighted tables, transition matrices) | — | ||
| 3.16 | Graph Algorithms (Eulerian trails, Hamiltonian cycles, Kruskal, Prim, Chinese postman, TSP) | — |
| Code | Content | Pri | Notes | |
|---|---|---|---|---|
| 4.1 | Population, Sample & Data Types | — | ||
| 4.2 | Frequency Distributions & Histograms (cumulative frequency, box plots, quartiles, percentiles) | — | ||
| 4.3 | Central Tendency & Dispersion (mean, median, mode, standard deviation, variance, grouped data) | — | ||
| 4.4 | Linear Correlation & Regression (Pearson's r, scatter diagrams, line of best fit, prediction) | — | ||
| 4.5 | Probability Concepts (sample space, complementary events, expected occurrences) | — | ||
| 4.6 | Venn Diagrams, Trees & Tables (conditional probability, combined events, independence) | — | ||
| 4.7 | Discrete Random Variables | — | ||
| 4.8 | Binomial Distribution | — | ||
| 4.9 | Normal Distribution | — | ||
| 4.10 | Spearman's Rank Correlation | — | ||
| 4.11 | Hypothesis Testing (chi-squared, t-test, goodness of fit, p-values, significance levels) | — | ||
| 4.12 | Data Collection Methods (surveys, reliability, validity, categorizing data) | — | ||
| 4.13 | Non-linear Regression (least squares curves, sum of square residuals, R-squared) | — | ||
| 4.14 | Linear Combinations of Random Variables (E(X), Var(X), unbiased estimates of mean and variance) | — | ||
| 4.15 | Normal Combinations (distribution of sample mean, central limit theorem) | — | ||
| 4.16 | Confidence Intervals | — | ||
| 4.17 | Poisson Distribution | — | ||
| 4.18 | Critical Values & Regions (test for mean, proportion, Poisson mean, Type I/II errors) | — | ||
| 4.19 | Transition Matrices & Markov Chains (steady state, long-term probabilities, regular chains) | — |
| Code | Content | Pri | Notes | |
|---|---|---|---|---|
| 5.1 | Introduction to Limits | — | ||
| 5.2 | Increasing & Decreasing Functions | — | ||
| 5.3 | Derivative of x^n | — | ||
| 5.4 | Tangents & Normals | — | ||
| 5.5 | Integration as Anti-differentiation (boundary conditions, definite integrals, area under curve) | — | ||
| 5.6 | Stationary Points | — | ||
| 5.7 | Optimisation | — | ||
| 5.8 | Trapezoidal Rule | — | ||
| 5.9 | Derivatives of Trig, Exp & Log Functions (chain rule, product rule, quotient rule, related rates) | — | ||
| 5.10 | Second Derivative | — | ||
| 5.11 | Definite & Indefinite Integration (trig, exp, 1/x, integration by inspection/substitution) | — | ||
| 5.12 | Area Under & Between Curves (volumes of revolution about x and y axes) | — | ||
| 5.13 | Kinematics | — | ||
| 5.14 | Differential Equations (modelling from context, separation of variables) | — | ||
| 5.15 | Slope Fields | — | ||
| 5.16 | Euler's Method (first order DEs, coupled systems) | — | ||
| 5.17 | Coupled Differential Equations (phase portraits, equilibrium points, eigenvalue analysis) | — | ||
| 5.18 | Second Order DEs (Euler's method for second order) | — |