Tackling GCSE Maths problem-solving questions means working through four steps: decode what the wordy question is actually asking, identify which topic and method it's hiding, show every step of working for method marks, and check the answer makes sense in context. This structured approach turns unfamiliar, multi-step questions into a sequence of smaller, manageable problems.
Why problem-solving questions feel harder than they are
Since the 2015 GCSE Maths reforms (first exams 2017), AQA, Edexcel and OCR papers all carry a significant share of marks for "problem-solving" and "reasoning" questions rather than pure recall or single-step calculation. These questions:
- Wrap a familiar skill (percentages, ratio, area, simultaneous equations) inside an unfamiliar real-world context — recipes, paint tins, phone contracts, journey times
- Rarely tell you which method to use — that's the skill being tested
- Often require two or more linked calculations before you reach the final answer
- Award most of their marks for method, not just the final number
Students who are technically fluent in isolated topics often still lose marks here — not because they can't do the maths, but because they don't recognise which maths is needed, or they don't lay out their working clearly enough to earn method marks.
The four-step technique
Step 1: decode the question
Read the question twice. First pass: get the general picture. Second pass: underline or circle every number, unit and instruction word ("total", "difference", "at least", "per", "each").
Ask three questions:
- What am I actually being asked to find? (Write it down in your own words if it helps.)
- What information have I been given, and in what units?
- What information is implied but not stated? (e.g. "a box of 12 eggs" implies you may need to divide or multiply by 12)
Step 2: identify the hidden topic
Multi-step GCSE questions almost always combine two or three topics. Common combinations include:
| Context clue | Likely topic(s) hidden inside |
|---|---|
| "% off", "increased by", "VAT" | Percentages, often compound |
| "for every", "mixed in the ratio" | Ratio and proportion |
| "per hour", "speed", "density" | Compound measures (distance/time/mass) |
| "similar shapes", "scale drawing" | Ratio, similarity, scale factors |
| Two unknowns, two conditions | Simultaneous equations |
| "the nth term", repeating pattern | Sequences |
Write the topic name in the margin before you start calculating — this alone reduces the chance of picking the wrong method under exam pressure.
Step 3: plan and show your working
Before reaching for a calculator, jot a mini-plan: "Step 1 — find cost per kg. Step 2 — find total cost. Step 3 — compare to budget." Multi-step questions on all three exam boards award marks at each stage (method marks, M1/M2), not only for the final answer (A1). A correct final answer with no working can score zero if the method isn't visible; an incorrect final answer with clear, sound working can still pick up most of the marks.
Write every stage down, including:
- The formula or relationship you're using, in words or symbols
- Intermediate values, clearly labelled (e.g. "cost per litre = £1.35")
- Units at every stage — dropping units is a common way to lose marks even with correct numbers
Step 4: check the answer against the question
Before moving on, re-read the original question and check three things:
- Does the answer answer the question asked? (If asked for a difference, have you given a difference, not one of the two original values?)
- Is the size sensible? A shop discount that makes an item cost more, or a journey time of 400 hours, signals an arithmetic slip.
- Are the units and rounding correct? Money to 2 decimal places, sensible significant figures, correct units stated.
A worked example
"A café buys coffee beans in 2 kg bags costing £14.50 each. Beans are sold in cups using 18 g per cup. The café sells each cup for £2.80. Work out the profit made from one bag of beans, ignoring other costs."
- Decode: find profit = revenue − cost, for one bag.
- Identify hidden topics: unit conversion (kg to g), division, multiplication, subtraction.
- Plan and work:
- Beans per bag: 2 kg = 2000 g
- Cups per bag: 2000 ÷ 18 = 111.1, so 111 whole cups (round down — you can't sell a partial cup)
- Revenue: 111 × £2.80 = £310.80
- Cost of one bag: £14.50
- Profit: £310.80 − £14.50 = £296.30
- Check: profit is positive and plausible for a bag that yields over 100 cups — passes the sense check. Rounding down cups (not to the nearest whole number) matches the real-world context, a detail examiners specifically reward.
Common mistakes to avoid
- Starting to calculate before deciding what's being asked. This wastes time and often answers the wrong question.
- Rounding too early. Keep full accuracy through intermediate steps and only round the final answer, unless the question specifies otherwise.
- Ignoring context-based rounding. Numbers of people, buses, boxes or cups must round to sensible whole numbers in the direction the context demands (usually rounding up for "enough to fit everyone", rounding down for "how many complete units").
- Not showing units. Even correct numbers can lose marks if units are missing or inconsistent.
- Giving up when the topic isn't obvious. Multi-step questions are deliberately unfamiliar in phrasing — the underlying maths is still GCSE content from the specification.
How to practise this skill
- Work through past papers from AQA, Edexcel and OCR specifically targeting the multi-step and problem-solving questions, not just single-skill ones — mark schemes show exactly where method marks are awarded.
- After every practice question, write a one-line note on which topics were hidden inside it — over time this builds a mental library of context clues.
- Time yourself loosely, but on early practice prioritise getting the method right over speed; speed comes with repetition.
- Revisit questions you got wrong a week later without looking at your previous working, to check the technique has actually transferred.
Frequently asked questions
What is the best technique for GCSE Maths problem-solving questions?
The most reliable technique is a four-step approach: decode exactly what's being asked, identify which topic or topics are hidden in the wording, plan and show full working step by step, then check the final answer against the original question for sense and units. This structure works across all exam boards because it targets how method marks are awarded, not just the final number.
Why do I understand the maths but still lose marks on wordy questions?
Most marks lost on multi-step questions come from misreading the question, not from lacking the maths skill itself. Students often calculate a correct value that doesn't actually answer what was asked, or skip showing working and lose method marks even when their final answer is right. Slowing down at the decoding stage and writing a short plan before calculating fixes most of this.
How many marks are multi-step problem-solving questions usually worth?
Multi-step and problem-solving questions typically carry more marks than single-step questions — often 4 to 6 marks each — because they combine several skills and test genuine reasoning rather than recall. Exact weighting varies by paper and exam board (AQA, Edexcel, OCR), so check the specification and past mark schemes for the board you're sitting.
Do I need a calculator for GCSE Maths problem-solving questions?
It depends on the paper. Each GCSE Maths specification includes both non-calculator and calculator papers, and problem-solving-style questions appear on both. The technique for decoding and planning the question is identical either way; on the non-calculator paper, keep working in fractions or simple decimals where possible to reduce arithmetic errors.
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