Revision notes.

Try this with General Mathematics

1. Close your notes and write the main idea in two sentences from memory.
2. Reopen the source and correct the first mistake or omission you find.
3. Add one example and one question to test whether you can apply the idea.

View General Mathematics resources on ATARMAXXING ↗

Topics in the resource inventory

• Modelling with data, sequences and finance: choosing the model, checking reasonableness and drawing conclusions (Criterion 3)
• Two-way frequency tables, percentaged tables, divided bar graphs and describing association
• Scatterplots, direction, form and strength, and the correlation coefficient r
• Fitting the least-squares line by formula and calculator; interpreting gradient and intercept in context
• Residual plots, the coefficient of determination, interpolation versus extrapolation and reliability; association versus causation
• Time series plots, trend, seasonality and irregular fluctuation; moving averages, seasonal indices, deseasonalising and trend-line forecasting
• Arithmetic sequences: recursion, the nth term, tables and graphs, and modelling linear growth and decay
• Geometric sequences: the nth term, exponential growth and decay, and finding a, r and n from given terms
• Arithmetic and geometric series: S_n formulas and the sum to infinity, and what S∞ means in context
• First-order linear recurrence relations t_(n+1) = r t_n + d: generating terms, long-term behaviour and the steady state d/(1 − r)
• Compound interest FV = PV(1 + i)^n, compounding periods, effective annual rate and inflation
• Reducing balance loans: recurrence relations, the finance solver, repayments, term and total interest
• Straight line and reducing balance depreciation and comparing the two methods
• Annuities in advance and in arrears, sinking funds, present and future value, and perpetuities P = R/i
• Right-angled trigonometry, Pythagoras in 3D, and the area of a triangle (½ab sin C and Heron's rule)
• The sine rule and cosine rule with angles of elevation and depression and bearings in navigation
• Great and small circle distances, the spherical cosine rule, longitude and time, UTC, the date line and travel problems
• Graph terminology, adjacency matrices, Euler's formula, Eulerian and Hamiltonian graphs and trails
• Spanning trees and Prim's algorithm; project networks, EST/LST, critical paths and float
• Maximum-flow minimum-cut and optimum assignment with the Hungarian algorithm