Why Algebra Costs the Most Marks
Across typical Cambridge IGCSE 0580 question banks, algebra topics — including expressions, equations, factorisation, functions, and sequences — account for roughly 220 out of 1,176 marks available across the full paper set. That is more concentrated topic risk than any other strand. It is also the area where presentation errors are most costly, because algebra questions almost always separate method marks from accuracy marks. A student who knows the method but presents it carelessly can lose accuracy marks on every single algebra question on the paper, adding up to 10 or more lost marks purely from presentation. The good news: these are fixable with specific habits.
Factorisation — What Gets Full Marks
When a question asks you to factorise an expression, full marks require two things: both brackets correct, and the factorised form shown as the answer. For example, factorising x² + 7x + 12 means writing (x + 3)(x + 4) as your answer — not just identifying that 3 and 4 multiply to 12 and add to 7. The intermediate step should be visible. For quadratics with a coefficient on x² — such as 2x² + 7x + 3 — the mark scheme expects to see the decomposition of the middle term or an equivalent method before the final factorised form. Writing the answer without working on a question worth three marks means the examiner cannot award any method marks if the factorisation is wrong. For difference of two squares, such as 4x² - 9, the answer is (2x + 3)(2x - 3). Writing 4x² - 9 = (2x)² - 3² and stopping is not a complete answer.
Solving Equations — Show Every Step
The instruction 'solve' means find the value(s) of the unknown. Mark schemes for solving questions award marks at specific steps, not just for the final answer. For a linear equation like 3x - 7 = 2x + 5, the mark scheme typically has one M mark for correctly rearranging to isolate x and one A mark for the correct value. If you jump from the original equation to x = 12 in one mental step, the examiner cannot award the M mark if your answer is wrong. The rule: one operation per line. Start a new line for each transformation of the equation. Label your final answer clearly — write x = 12, not just 12. On multi-step equations involving fractions, the method mark is almost always awarded for the correct algebraic step of clearing the fraction, before any collection of terms. Missing that step means missing a mark.
Simultaneous Equations — Method Choice Matters
For linear simultaneous equations, both elimination and substitution earn full marks if applied correctly. However, the mark scheme is written around the most efficient method for the numbers given. If the coefficients are already matched — for example, 3x + 2y = 11 and 3x - y = 5 — elimination by subtraction is the intended route. If one equation has a single variable isolated — such as y = 2x + 1 and 3x + 4y = 18 — substitution is expected. Choosing the right method matters because a wrong method on the first step loses the method mark, even if subsequent algebra is correct. For non-linear simultaneous equations — one linear, one quadratic — substitution is almost always required. You substitute the linear equation into the quadratic to produce a single quadratic in one variable, solve that, then substitute back to find both coordinate pairs. Both pairs must be stated for full marks.
Quadratics — The Common Pitfalls
Three specific errors appear in IGCSE examiner reports on quadratic questions every year. First: not rearranging to ax² + bx + c = 0 before factorising or applying the quadratic formula. If the equation is given as x² + 3x = 10, the first step is always x² + 3x - 10 = 0. Attempting to factorise or apply the formula without rearranging produces nonsense. Second: applying the quadratic formula without writing the full substitution. The mark scheme expects to see the formula written with your values substituted — for example, x = (-3 ± √(9 + 40)) / 2. Writing only the final numerical answers without the substitution loses the method mark if either answer is wrong. Third: stating only one solution. The quadratic formula always produces two solutions unless the discriminant is zero. Both solutions must be stated.
Functions — What Core vs Extended Students Need
Core tier students need to substitute values into functions and evaluate expressions. For f(x) = 3x - 2, finding f(5) means substituting: 3(5) - 2 = 13. The mark is for the correct evaluation, and the working should show the substitution explicitly. Extended tier students need three additional skills. Composite functions: for f(x) = 2x + 1 and g(x) = x², finding fg(x) means f applied after g, giving f(x²) = 2x² + 1. The notation fg means g first, then f — many students get this backwards. Inverse functions: to find f⁻¹(x) for f(x) = 3x - 2, replace f(x) with y, rearrange for x, then swap x and y. The answer is f⁻¹(x) = (x + 2) / 3. The mark scheme requires the rearrangement to be shown. Domain restrictions: if a function has a restricted domain, values outside it are not valid substitutions. The mark scheme may specifically ask you to state the domain of an inverse function.
Sequences — nth Term vs Next Term
IGCSE sequence questions use two distinct command words that require completely different responses. 'Find the next term' asks for one number — the value that continues the pattern. 'Find an expression for the nth term' or 'find a formula for the nth term' asks for an algebraic expression in terms of n. Answering the second type with a number earns zero marks. For linear sequences, the nth term is an + b, where a is the common difference and b is found by checking the formula against the first term. For the sequence 5, 8, 11, 14, the difference is 3, giving 3n + b. Substituting n = 1: 3(1) + b = 5, so b = 2. The nth term is 3n + 2. For quadratic sequences, the second difference is constant, and the nth term involves n². Examiners are explicit in reports: many students who correctly find the pattern write the next few terms instead of the algebraic expression, earning no marks on a question they clearly understood.
Apply This in Practice
The most effective revision for algebra is mark-scheme-led. Attempt a question without looking at the mark scheme, then compare your working step-by-step with what the scheme awards marks for. Identify precisely where your working would — and would not — earn marks. The free diagnostic quiz covers all the algebra topics above with exam-style questions and pinpoints the specific areas where your marks are currently being lost.