Algebra & functions
A-level Maths (9MA0) · exam-style practice, examiner-report intelligence and the tools that drill it.
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 ≠ 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) > … or f(x) ≥ …, not x > …
- 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
On calculator-restricted algebra questions ('solutions relying entirely on calculator technology are not acceptable') the scheme awards nothing for unsupported roots — the factorisation or division must be on the page.
June 2023 Paper 1 question paper + mark scheme (Q02)
Factor-theorem method marks need f(a) evaluated and set against 0 explicitly — quoting the factor without the shown substitution loses the M mark.
June 2024 Paper 1 mark scheme (Q01)
In range/domain answers the scheme distinguishes f(x) from x: a correct interval written with the wrong variable ('x ≥ 3' for a range) is not condoned.
June 2023 Paper 1 mark scheme (Q07)
Try it — exam-style
f(x) = 2x3 - x2 - 25x - 12. Show that (x - 4) is a factor of f(x), and hence factorise f(x) completely.
The function f is defined by f(x) = 2 + √(x - 1) for x ≥ 1. (i) State the range of f. (ii) Find f−1(x) and state its domain.
Solve |2x - 5| = x + 1.
f(x) = 2x - 3 and g(x) = x2 + 1. Find (i) fg(2) and (ii) gf(x), simplifying your answer.
Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.
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Stuck on algebra & functions?
Functions questions are won on notation — range vs domain, f(x) vs x. I make the distinctions stick, and your first lesson is free.