Revision notes.

Try this with Mathematics Methods – Foundation

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 Mathematics Methods – Foundation resources on ATARMAXXING ↗

Topics in the resource inventory

• Substitution, rearranging formulae and function notation y = f(x)
• Expanding, factorising, completing the square, the quadratic formula and the discriminant
• Pascal's triangle and binomial expansions; factor theorem and sum/difference of cubes for cubics
• Index laws, rational indices, surds, scientific notation and solving index equations
• Gradient, equations of lines, parallel and perpendicular lines
• Turning-point, factorised and general forms; sketching from the signs of a, b, c and Δ
• Sketching cubics, repeated zeros, end behaviour and finding a cubic's equation from its graph
• Translations, dilations and reflections; functions versus relations; domain and range
• Graphs of y = a × bˣ + k, exponential equations and growth, decay and finance applications
• Logarithms as indices, log laws, logarithmic equations and graphs of y = a log_n(x − h) + k
• Radians, arc length, the unit circle, exact values, symmetry properties and the sine and cosine rules
• Graphs of y = a sin bx, y = a cos bx and y = tan bx: amplitude, period, dilations and reflections
• Average versus instantaneous rates of change; gradients of chords and tangents
• Evaluating limits, the difference quotient and differentiating xⁿ from first principles
• The power rule, rational and negative powers, and equations of tangents and normals
• Local maxima and minima, sketching f′(x) from f(x), and displacement–time graphs
• Sample spaces, events, set notation, Venn diagrams, complements and the addition rule
• P(A|B), the multiplication rule and testing for independence from tables and data
• nCr, factorial notation and counting selections to compute probabilities
• Tree diagrams for independent three-stage and non-independent two-stage events; simulations and relative frequency estimates