QCE General Mathematics Syllabus Notes

Original QCE General Mathematics notes for syllabus-aligned revision, worked examples, common mistakes and quick checks.

Unit 3: Bivariate data and time series analysis, sequences and Earth geometry

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.
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.

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.
Association and causation (6 hours)
Learn why association does not prove causation, including coincidence, confounding variables and cautious statistical communication.

Describing and interpreting patterns in time series data (3 hours)
Learn trend, seasonality and irregular fluctuations in QCE General Mathematics time series plots.
Analysing time series data (8 hours)
Learn moving averages, seasonal indices, deseasonalising and trend lines for QCE General Mathematics time series analysis.

The arithmetic sequence (5 hours)
Learn recursion, tables, graphs and nth-term rules for arithmetic sequences in QCE General Mathematics.
The geometric sequence (6 hours)
Learn recursion, common ratios, nth-term rules and practical growth or decay models for QCE General Mathematics.

Locations on the Earth (5 hours)
Learn great circles, latitude, longitude, angular distance and distance along meridians or parallels in QCE General Mathematics.
Time zones (5 hours)
Learn UTC, GMT, longitude and time differences, the International Date Line and travel-time calculations for QCE General Mathematics.

Compound interest loans and investments (6 hours)
Learn recurrence relations, compound interest formulae, effective annual interest and practical finance calculations for QCE General Mathematics.
Present value of ordinary annuities (6 hours)
Learn reducing-balance loans, present value annuity formulae and repayment interpretation for QCE General Mathematics.

Perpetuities and future value of ordinary annuities (8 hours)
Learn future value annuities, perpetuities and periodic-payment finance models for QCE General Mathematics.

Graphs, associated terminology and the adjacency matrix (4 hours)
Learn graph terminology, directed and weighted networks, and adjacency matrices for QCE General Mathematics.
Planar graphs, paths and cycles (8 hours)
Learn Euler's formula, walks, trails, paths, bridges, Eulerian and Hamiltonian routes for QCE General Mathematics.

Trees and minimum connector problems (4 hours)
Learn trees, spanning trees, minimum spanning trees and practical connector problems for QCE General Mathematics.
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.

Flow networks (4 hours)
Learn source nodes, sink nodes, cuts, minimum cuts and maximum flow for QCE General Mathematics flow networks.
Assigning order and the Hungarian algorithm (7 hours)
Learn allocation problems, bipartite graphs, inspection and the Hungarian algorithm for QCE General Mathematics.