How Do I Answer GCSE Maths Problem-Solving Questions?

What is a problem-solving question in GCSE maths?

A problem-solving question in GCSE maths is a multi-step question where the method is not stated, so you have to decide which maths to use and in what order. LoveMaths Tutoring UK suggests treating them as their own skill to practise, because they often combine topics, such as area and money, or ratio and percentages, in one question.

Problem-solving questions appear on both the Foundation and Higher tier papers. They are usually worth several marks, so a clear method is worth practising.

What steps should I follow to answer a problem-solving question?

LoveMaths Tutoring UK recommends the same five steps for every problem-solving question, so you always know how to start:

1. Read it twice. Underline the numbers and circle exactly what the question asks for.
2. List what you know. Write down each piece of information, with units.
3. Draw a diagram. Even a rough sketch makes shapes, journeys and sharing problems clearer.
4. Take one small step. Ask "what can I work out from this information?" and do it, even if you cannot yet see the whole route.
5. Check it makes sense. Re-read the question and check the answer is the thing it asked for, in the right units.

What does a worked example look like?

This worked example from LoveMaths Tutoring UK shows the five steps on a typical multi-step question.

A rectangular garden measures 12m by 8m. A path 1m wide runs around the inside edge of the garden. The rest of the garden will be covered in grass seed. One box of grass seed covers 25m² and costs £12. How much will the grass seed cost?

1. The question asks for a cost in pounds, not an area.
2. The path takes 1m off each side, so the grass area is (12 - 2) by (8 - 2), which is 10m by 6m.
3. Grass area = 10 × 6 = 60m².
4. Boxes needed = 60 ÷ 25 = 2.4, but you cannot buy part of a box, so round up to 3 boxes.
5. Cost = 3 × £12 = £36.

The check step matters here: 2.4 boxes is not a sensible answer in context, and stopping at 60m² would answer the wrong question.

How do I get marks if I cannot finish the question?

GCSE maths mark schemes usually award method marks for correct working, even if the final answer is wrong or missing. LoveMaths Tutoring UK recommends these habits to collect every available mark:

• Write down every calculation, not just the result
• Label what each number is, for example "grass area = 60m²"
• Never leave a problem-solving question blank: work out anything you can from the information given
• If you get stuck, move on and come back, rather than losing time

What are the most common mistakes in problem-solving questions?

Many lost marks in problem-solving questions come from a small number of avoidable mistakes. LoveMaths Tutoring UK suggests watching out for these:

• Answering a different question from the one asked, such as giving an area when a cost was asked for
• Rounding too early, which makes later answers inaccurate
• Forgetting units, or mixing units such as centimetres and metres
• Not rounding sensibly in context, such as buying 2.4 boxes or hiring 3.5 buses
• Missing a piece of information given in an earlier part of the question

How should I practise problem-solving questions?

The best practice is mixed: problem-solving questions from different topics, so you get used to choosing the method yourself. LoveMaths Tutoring UK suggests:

• Doing two or three mixed problem-solving questions in each revision session
• Working through past papers for your tier, then marking with the mark scheme to see where method marks are given
• Keeping a log of questions you could not start, and retrying them a week later
• Trying maths brain teasers to practise thinking through unfamiliar problems

LoveMaths Tutoring UK also provides one to one online maths tutoring at GCSE, including GCSE resits, in one-hour sessions over Zoom planned around a prior assessment. Students can start with the free online assessment.