TCE Mathematics Methods – Foundation Level 3 Notes

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

1. Substitution, rearranging formulae and function notation y = f(x)Area of study 1 · Algebra

   Review work and notation

2. Expanding, factorising, completing the square, the quadratic formula and the discriminantArea of study 1 · Algebra

   Quadratic functions (algebra)

3. Pascal's triangle and binomial expansions; factor theorem and sum/difference of cubes for cubicsArea of study 1 · Algebra

   Powers, polynomials and cubics

4. Index laws, rational indices, surds, scientific notation and solving index equationsArea of study 1 · Algebra

   Indices

5. Gradient, equations of lines, parallel and perpendicular linesArea of study 2 · Polynomial functions and graphs

   Linear functions

6. Turning-point, factorised and general forms; sketching from the signs of a, b, c and ΔArea of study 2 · Polynomial functions and graphs

   Quadratic functions (graphs)

7. Sketching cubics, repeated zeros, end behaviour and finding a cubic's equation from its graphArea of study 2 · Polynomial functions and graphs

   Cubic and other polynomial functions

8. Translations, dilations and reflections; functions versus relations; domain and rangeArea of study 2 · Polynomial functions and graphs

   Transformations and the language of functions

9. Graphs of y = a × bˣ + k, exponential equations and growth, decay and finance applicationsArea of study 3 · Exponential, logarithmic and circular (trigonometric) functions and graphs

   Exponential functions

10. Logarithms as indices, log laws, logarithmic equations and graphs of y = a log_n(x − h) + kArea of study 3 · Exponential, logarithmic and circular (trigonometric) functions and graphs

    Logarithmic functions

11. Radians, arc length, the unit circle, exact values, symmetry properties and the sine and cosine rulesArea of study 3 · Exponential, logarithmic and circular (trigonometric) functions and graphs

    Circular (trigonometric) functions: measure and identities

12. Graphs of y = a sin bx, y = a cos bx and y = tan bx: amplitude, period, dilations and reflectionsArea of study 3 · Exponential, logarithmic and circular (trigonometric) functions and graphs

    Circular (trigonometric) functions: graphs

13. Average versus instantaneous rates of change; gradients of chords and tangentsArea of study 4 · Calculus

    Rates of change

14. Evaluating limits, the difference quotient and differentiating xⁿ from first principlesArea of study 4 · Calculus

    Limits and first principles

15. The power rule, rational and negative powers, and equations of tangents and normalsArea of study 4 · Calculus

    Differentiation by rule and its applications

16. Local maxima and minima, sketching f′(x) from f(x), and displacement–time graphsArea of study 4 · Calculus

    Stationary points, curve sketching and motion

17. Sample spaces, events, set notation, Venn diagrams, complements and the addition ruleArea of study 5 · Probability and statistics

    Fundamentals of probability

18. P(A|B), the multiplication rule and testing for independence from tables and dataArea of study 5 · Probability and statistics

    Conditional probability and independence

19. nCr, factorial notation and counting selections to compute probabilitiesArea of study 5 · Probability and statistics

    Combinations

20. Tree diagrams for independent three-stage and non-independent two-stage events; simulations and relative frequency estimatesArea of study 5 · Probability and statistics

    Multi-stage events, experiments and relative frequency