Algebra and functions
Includes quadratic functions and completing the square
Modulus graphs and equations
What means, how to sketch by reflecting the negative part, and two reliable ways to solve modulus equations: squaring both sides, or splitting into cases and checking.
≈ 40 minCompleting the square and the vertex
Rewrite as , read off the vertex, line of symmetry and least or greatest value, and use it to sketch parabolas and solve real problems about maximum height or area.
≈ 45 minSolving quadratic equations
Three ways to solve (factorising, completing the square and the formula), choosing the quickest, giving exact answers, and spotting quadratics in disguise such as .
≈ 45 minModulus inequalities
Solving inequalities with moduli: the "between" and "outside" patterns, squaring when both sides are moduli, and using a sketch when a modulus is compared with a line.
≈ 40 minThe discriminant and the nature of roots
How tells you whether a quadratic has two, one or no real roots without solving it, how to find unknown constants from that, and how to show an expression is always positive.
≈ 40 minPolynomials: division, factor and remainder theorems
Long division for polynomials, why the remainder on dividing by is just , and how the factor theorem lets you factorise cubics and find unknown coefficients.
≈ 45 minPartial fractions
Splitting a complicated fraction into simpler ones, which you need for integrating and for binomial expansions: the right form for each kind of denominator, and quick ways to find the constants.
≈ 45 minLinear and quadratic inequalities
Solve linear inequalities, then quadratic ones using critical values and a sketch, write the answer correctly (and, or, set notation), and combine two conditions.
≈ 35 minSimultaneous equations and lines meeting curves
Solve one linear and one quadratic equation together by substitution, find the points where a line meets a curve, and use the discriminant to decide whether a line crosses, touches or misses a curve.
≈ 40 min