General Mathematics: should I choose it?

Data analysis, probability and statistics

Algebra, number and structure

Functions, relations and graphs

Discrete mathematics

Data analysis, probability and statistics

Discrete mathematics

Functions, relations and graphs

Space and measurement

Data analysis

The largest area of study and the one that carries the most examination questions. It begins with classifying data as numerical or categorical, and categorical data as nominal or ordinal, then displaying it with dot plots, stem plots, histograms and boxplots and summarising it with mean, median, standard deviation, interquartile range and range. The normal distribution follows, using the 68-95-99.7% rule and standardised z-scores to move between a value and a percentage of the population. Bivariate work is the heart of the area: scatterplots, two-way frequency tables and segmented bar charts, correlation and the coefficient of determination, the least squares line with residual analysis, and interpolation as against extrapolation. Log and squared transformations linearise curved data. Time series closes the area with trend, seasonality, moving mean and median smoothing, seasonal indices and deseasonalising.

Recursion and financial modelling

Everything here is built on one idea: a starting value and a rule that generates the next term. You write first-order linear recurrence relations of the form u0 = a, un+1 = Run + d, and switch between that recursive form, an explicit rule and an amortisation table for the same situation. Simple and compound interest come first, with the effective annual interest rate used to compare accounts that compound at different frequencies. Then come the products themselves: reducing balance loans read through amortisation tables, annuities, perpetuities, and compound interest investments with regular deposits or withdrawals. Depreciation is the mirror image, using flat rate, reducing balance and unit cost methods. Questions frequently supply a partial table or a mid-term balance and expect you to work backwards to a missing rate, payment or number of periods.

Matrices

This area is largely about representing a real situation as a matrix and then letting matrix arithmetic do the work. You start with order and the named types — row, column, square, diagonal, identity, binary and permutation — then addition, subtraction, scalar multiplication and the row-by-column rule for matrix multiplication, including which products are defined at all. The determinant of a two-by-two matrix tells you whether an inverse exists, and the inverse solves systems written in matrix form. Applications take over from there: communication and adjacency matrices, dominance matrices for ranking round-robin results, permutation matrices for cyclical arrangements such as rotating timetables, transition matrices and Markov chains with their steady-state behaviour, matrix recurrence relations of the form Sn+1 = TSn + B, and Leslie matrices for age-structured populations.

Networks and decision mathematics

Networks turns diagrams into answers. The vocabulary comes first — vertices, edges, degree, walks, trails, paths and cycles — along with planar graphs, bridges and Euler's formula, v + f = e + 2. Then the traversal results: Eulerian trails and circuits, which depend on how many vertices have odd degree, and Hamiltonian paths and cycles, which visit vertices rather than edges. Weighted graphs bring the optimisation problems: minimum spanning trees found with Prim's algorithm, shortest path problems, flow problems solved through maximum flow-minimum cut, and assignment problems handled by the Hungarian algorithm's row and column reductions. Critical path analysis finishes the area, using activity networks, earliest and latest start times, float time, the critical path itself, and crashing to shorten a project at the least possible cost.