TCE General Mathematics Level 3 Notes

These are the 20 revision notes inside the TCE General Mathematics Mastery Pack. Open any note to see what it covers before you buy.

1. Modelling with data, sequences and finance: choosing the model, checking reasonableness and drawing conclusions (Criterion 3)Module 1 · Module 1: Mathematical modelling, problem solving and the statistical investigation process

   Mathematical modelling and problem solving

2. Two-way frequency tables, percentaged tables, divided bar graphs and describing associationModule 2 Topic 1 · Module 2 Topic 1: Statistical analysis

   Bivariate data analysis — categorical variables

3. Scatterplots, direction, form and strength, and the correlation coefficient rModule 2 Topic 1 · Module 2 Topic 1: Statistical analysis

   Bivariate data analysis — numerical variables

4. Fitting the least-squares line by formula and calculator; interpreting gradient and intercept in contextModule 2 Topic 1 · Module 2 Topic 1: Statistical analysis

   Bivariate data analysis — least-squares regression

5. Residual plots, the coefficient of determination, interpolation versus extrapolation and reliability; association versus causationModule 2 Topic 1 · Module 2 Topic 1: Statistical analysis

   Bivariate data analysis — residuals, r² and prediction

6. Time series plots, trend, seasonality and irregular fluctuation; moving averages, seasonal indices, deseasonalising and trend-line forecastingModule 2 Topic 1 · Module 2 Topic 1: Statistical analysis

   Time series analysis

7. Arithmetic sequences: recursion, the nth term, tables and graphs, and modelling linear growth and decayModule 2 Topic 2 · Module 2 Topic 2: Growth and decay in sequences

   The arithmetic sequence

8. Geometric sequences: the nth term, exponential growth and decay, and finding a, r and n from given termsModule 2 Topic 2 · Module 2 Topic 2: Growth and decay in sequences

   The geometric sequence

9. Arithmetic and geometric series: S_n formulas and the sum to infinity, and what S∞ means in contextModule 2 Topic 2 · Module 2 Topic 2: Growth and decay in sequences

   Series

10. First-order linear recurrence relations t_(n+1) = r t_n + d: generating terms, long-term behaviour and the steady state d/(1 − r)Module 2 Topic 2 · Module 2 Topic 2: Growth and decay in sequences

    Sequences generated by first-order linear recurrence relations

11. Compound interest FV = PV(1 + i)^n, compounding periods, effective annual rate and inflationModule 3 Topic 1 · Module 3 Topic 1: Investment, loans and annuities

    Compound interest investments and loans

12. Reducing balance loans: recurrence relations, the finance solver, repayments, term and total interestModule 3 Topic 1 · Module 3 Topic 1: Investment, loans and annuities

    Reducing balance loans

13. Straight line and reducing balance depreciation and comparing the two methodsModule 3 Topic 1 · Module 3 Topic 1: Investment, loans and annuities

    Depreciation

14. Annuities in advance and in arrears, sinking funds, present and future value, and perpetuities P = R/iModule 3 Topic 1 · Module 3 Topic 1: Investment, loans and annuities

    Annuities and perpetuities

15. Right-angled trigonometry, Pythagoras in 3D, and the area of a triangle (½ab sin C and Heron's rule)Module 3 Topic 2a · Module 3 Topic 2a: Trigonometry and Earth geometry

    Applications of trigonometry

16. The sine rule and cosine rule with angles of elevation and depression and bearings in navigationModule 3 Topic 2a · Module 3 Topic 2a: Trigonometry and Earth geometry

    Applications of trigonometry — non-right-angled triangles

17. Great and small circle distances, the spherical cosine rule, longitude and time, UTC, the date line and travel problemsModule 3 Topic 2a · Module 3 Topic 2a: Trigonometry and Earth geometry

    Earth geometry and time zones

18. Graph terminology, adjacency matrices, Euler's formula, Eulerian and Hamiltonian graphs and trailsModule 3 Topic 2b · Module 3 Topic 2b: Graphs, networks and decision mathematics

    Graphs, paths and cycles

19. Spanning trees and Prim's algorithm; project networks, EST/LST, critical paths and floatModule 3 Topic 2b · Module 3 Topic 2b: Graphs, networks and decision mathematics

    Trees and minimum connector problems; critical path analysis

20. Maximum-flow minimum-cut and optimum assignment with the Hungarian algorithmModule 3 Topic 2b · Module 3 Topic 2b: Graphs, networks and decision mathematics

    Flow networks and assignment problems