How to Revise for GCSE Maths

What does the GCSE Maths exam look like?

Using AQA GCSE Mathematics (8300) as the example, you sit three papers at the same tier. Each lasts 1 hour 30 minutes and is worth 80 marks and a third of the GCSE. Paper 1 is non-calculator and Papers 2 and 3 allow a calculator. Foundation tier awards grades 1 to 5 and Higher tier awards grades 4 to 9. Any topic can appear on any paper, and the questions get harder as each paper goes on. AQA's specification also sets out how the marks are shared between topic areas, and notes that these weightings are prescribed by Ofqual and are the same for every exam board. On Foundation tier, number and ratio carry about 25 per cent each, algebra 20 per cent, and geometry and probability with statistics 15 per cent each. On Higher tier, algebra is the largest area at about 30 per cent, with ratio and geometry at 20 per cent each and number and probability with statistics at 15 per cent each. That tells you where to spend time. A Foundation student who is weak on ratio and proportion is giving up a quarter of the exam. A Higher student who avoids algebra is avoiding nearly a third of it.

How do you find out what to revise?

Do not start at chapter one. Sit a full paper under timed conditions, mark it, and list every topic where you dropped marks. That list is your revision plan. It will be shorter and more specific than you expect: not “algebra” but “expanding double brackets”, “rearranging formulae where the subject appears twice” and “solving quadratics by factorising”. Sort the list into quick wins, which are topics you half know and can fix in a session, and bigger jobs that need teaching from scratch. Do the quick wins first. Early progress keeps you going, and on a maths paper every mark is worth the same whether it came from an easy topic or a hard one.

How should you practise a topic?

Use a three-step routine. First, study one clear worked example and make sure you can say why each line follows from the one before. Second, cover it and reproduce it on a blank page. Third, do a set of similar questions without looking back, and mark them. If you need to look back, you have not learned it yet. That is fine, but be honest with yourself about it. Explaining each step to yourself as you go is a technique researchers call self-explanation. The psychologist John Dunlosky, reviewing the evidence, lists it among the strategies that show real promise, particularly for problem solving. In practice it just means muttering “I am multiplying both sides by x because I want it out of the denominator” rather than copying the pattern.

Why should you mix topics together?

If you do twenty Pythagoras questions in a row, you never have to decide to use Pythagoras. In the exam, that decision is the hard part. Dunlosky describes interleaved practice, where different problem types are mixed within a session, as a way of practising exactly that decision, and notes that it feels slower while producing better results later. So once a topic is no longer brand new, stop practising it alone. Use mixed question sets, the first half of past papers, or five-a-day style sheets that jump between number, algebra, geometry and statistics. Come back to each topic after a gap of days, not minutes.

How do you pick up marks on problem-solving questions?

On AQA's Higher tier, 40 per cent of marks are for using standard techniques, 30 per cent for reasoning and communicating mathematically, and 30 per cent for solving problems. On Foundation it is 50, 25 and 25. So a large share of the paper is wordy, multi-step questions where the method is not given to you. Students lose these marks by leaving them blank. Mark schemes award method marks for correct steps, so a partial attempt is almost always worth something.

• Read the question twice and underline the numbers and what you are asked to find.
• Write down what you know: label the diagram, write a relevant formula, define a letter for the unknown.
• Ask what topic this is in disguise. Ratio? Simultaneous equations? Similar shapes?
• Do the first thing you can do, even if you cannot see the end. The next step often appears once the first is on paper.
• Show every line of working, including on the calculator papers. An unsupported wrong answer scores nothing; a wrong answer with a correct method can still score most of the marks.
• Check the answer against the question. Is it sensible, in the right units, rounded as asked?

What do you need to memorise?

Less than in other subjects, but not nothing. Make flashcards for the formulae and facts your board expects you to know, such as area and volume formulae, circle facts, angle rules, the quadratic formula on Higher tier, exact trigonometric values, and conversions between fractions, decimals and percentages. Check your own board's current guidance on which formulae are given in the exam, because this has changed in recent years and you should not rely on an older student's advice. For Paper 1, keep non-calculator skills sharp: long multiplication and division, fraction arithmetic, working with negative numbers, and estimating. Five minutes a day is enough. These skills fade quickly if you reach for the calculator all year.

What does a good maths week look like?

Little and often beats a weekly marathon. Aim for three or four sessions of 30 to 40 minutes. In each, spend five minutes redoing an old mistake, twenty minutes on a target topic, and ten minutes on mixed questions. Once a fortnight, and weekly as exams approach, sit a timed paper and rebuild your list from it. Keep a mistakes book. For each error write the question, what went wrong and the corrected method. Redo those questions from scratch a week later. Most students make the same five or six types of mistake again and again. Once you can see yours written down, you can fix them.

Sources

AQA GCSE Mathematics 8300: specification at a glance: Three papers, calculator rules, timings, marks, tiers and the grades available on each tier. AQA GCSE Mathematics 8300: subject content: Topic-area weightings by tier, which Ofqual prescribes for every exam board. AQA GCSE Mathematics 8300: scheme of assessment: Assessment objectives and their weightings on Foundation and Higher tier. John Dunlosky, “Strengthening the Student Toolbox”, American Educator (2013): A cognitive psychologist's review of which study strategies work: practice testing, distributed practice and interleaving, and why rereading and highlighting do less than students expect.