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LearnEdexcelYMA012018 specificationWMA11 · Pure Mathematics 1Algebra and functions

WMA11 · Module

Algebra and functions

Quadratic functions, discriminant and completing the square

3 subtopics≈ 110 min in total

Start the module: Indices and surds Open graphing calculator

Indices and surds
$a^{\frac mn}$ means "take the $n$ th root, then raise to the power $m$ ", and $a^{-n}=\dfrac1{a^n}$ . Surds are roots left exact: simplify them by pulling out square factors, and remove them from denominators by multiplying by the conjugate.
≈ 30 min
Quadratics, simultaneous equations and inequalities
Completing the square finds the turning point of a quadratic; the discriminant $b^2-4ac$ tells you how many roots it has. Solve a line and a curve together by substitution, and solve quadratic inequalities by sketching the parabola and reading off where it is above or below the axis.
≈ 40 min
Curve sketching and transformations
A factorised cubic crosses the $x$ -axis at each factor's root and touches it at a repeated root. Reciprocal graphs have asymptotes. Changes outside the bracket act vertically and do what you expect; changes inside act horizontally and do the opposite.
≈ 40 min