Algebra & functions

The topic on one screen

• Factor theorem: if $f(a) = 0$ then $(x - a)$ is a factor. Show the substitution AND the zero — then divide or compare coefficients for the quotient.
• Composite functions work inside-out: $fg(x)$ means $g$ first. $fg \ne gf$ almost always.
• Inverse functions: swap $x$ and $y$, rearrange. Domain of $f^{-1}$ = range of $f$, and vice versa — state both when asked.
• Range questions: sketch or reason from the shape; write ranges as $f(x) > \ldots$ or $f(x) \ge \ldots$, not $x > \ldots$
• Modulus equations: split into the two linear cases, solve both, then CHECK each solution in the original equation.
• Partial fractions and algebraic division feed later calculus questions — sloppy algebra here costs marks two questions later.

Where students actually lose marks

Try it — exam-style

Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.

Drill it properly