Worded problems are one of the main reasons students lose marks in GCSE maths — not because they can't do the maths, but because they can't find it. A question about a plumber's call-out charge or a train journey isn't harder maths than a straightforward algebra question; it just hides the maths inside a story. Once you learn to extract the numbers and translate the words, the calculation itself is usually quite familiar. AQA (8300), Edexcel (1MA1), and OCR (J560) all include context questions throughout their papers, but they're most common in the second half of Paper 2 and Paper 3, where they carry 3–5 marks each.
What You Need to Know First
Before you tackle worded problems, make sure you're comfortable with:
- Setting up equations from written descriptions — translating phrases like "five more than a number" into algebra
- Unit awareness — questions often mix cm and m, or pence and pounds; converting before calculating saves errors
- Reading tables and diagrams — worded problems often include additional information in a table, timetable, or graph
- Recognising common problem types — percentage change, ratio, proportion, speed/distance/time, and area/perimeter all appear regularly as worded contexts
- Checking whether your answer is sensible — a bag of flour that weighs 400 kg is a sign something went wrong
The more problem types you've seen, the faster you'll recognise what's really being asked.
The Four-Step Strategy for Worded Problems
When you first read a worded problem, the instinct is to start calculating straight away. Resist that. Rushing leads to using the wrong numbers or the wrong operation. Instead, use this four-step approach:
Step 1 — Read the whole question, then read it again. The first read gives you the general picture. The second read is where you gather information deliberately.
Step 2 — Underline every number and every unit. Circle or underline every numerical value in the question. Write the units next to each one. This forces you to notice everything that's been given.
Step 3 — Write down what you're being asked to find. At the top of your working, write: "Find: ..." and state what the answer should be — including its units. This keeps you on track.
Step 4 — Choose the method and calculate step by step. Identify which topic the question is testing (percentage, ratio, Pythagoras, etc.). Then work through it using that method, writing every step.
Worked Example 1 — Wages and Tax
Question: Ahmed works 37 hours a week and earns £11.50 per hour. He pays 20% income tax on everything he earns above £242 per week. How much does Ahmed take home each week after tax? [4 marks]
Step 1 — Read and understand: Ahmed earns a weekly wage. Some of it is taxed at 20%. We need his take-home pay.
Step 2 — Underline numbers: 37 hours, £11.50 per hour, 20% tax, £242 tax-free threshold.
Step 3 — Find: Ahmed's weekly take-home pay (£).
Step 4 — Calculate:
Weekly gross pay = 37 × 11.50 = £425.50
Taxable amount = 425.50 − 242 = £183.50
Tax paid = 20% of 183.50 = 0.20 × 183.50 = £36.70
Take-home pay = 425.50 − 36.70 = £388.80
Answer: Ahmed takes home £388.80 per week.
This question tests multiplication, subtraction, and percentage — nothing beyond Year 9 maths. The difficulty was entirely in reading and organising the information. The four-step approach separates that reading stage from the calculation stage, which is where most marks are lost.
Handling Multi-Step Worded Problems
Some worded problems have two or three parts that connect. Your answer from part (a) feeds into part (b). These questions test whether you can organise your working as much as whether you can do the arithmetic.
The key move is to label every result as you go. Write "weekly pay = £425.50" not just "= £425.50". When you come back to it in the next step, you'll know exactly what that number represents.
Worked Example 2 — Speed, Distance and Time
Question: A train leaves Manchester at 09:15 and arrives in London at 11:42. The distance between the two cities is 322 km.
(a) How long does the journey take? Give your answer in minutes. [1 mark]
(b) Calculate the average speed of the train in km/h. [2 marks]
(c) The return journey is 12% longer due to a diversion. How long does the return journey take if the train travels at the same average speed? Give your answer to the nearest minute. [3 marks]
Part (a):
Time from 09:15 to 11:42
= 2 hours 27 minutes
= 147 minutes
Part (b):
Speed = distance ÷ time
Time in hours = 147 ÷ 60 = 2.45 hours
Speed = 322 ÷ 2.45 = 131.4 km/h (to 1 d.p.)
Part (c):
Return distance = 322 × 1.12 = 360.64 km
Time = distance ÷ speed = 360.64 ÷ 131.4...
Use the unrounded speed from (b):
Time = 360.64 ÷ (322 ÷ 2.45) = 360.64 × (2.45 ÷ 322) = 2.744... hours
Convert to minutes = 2.744 × 60 = 164.7... minutes ≈ 165 minutes
Answer: The return journey takes 165 minutes.
Notice how part (c) asks you to use the result from part (b). Using the unrounded speed (131.428...) rather than the rounded answer (131.4) gives a more accurate final answer. This is a common mark scheme instruction: "use of a more exact value from (b)" earns the M mark even if the rounded version gives a slightly different result.
Common Mistakes Students Make
- Skipping the second read. Students read the question once, grab the first numbers they see, and start calculating. Key information — like "the remaining amount" or "after the discount" — gets missed.
- Ignoring units. A speed in km per minute is not the same as km per hour. Converting units correctly is worth marks in itself, and the wrong unit in the answer loses the A mark.
- Not labelling working clearly. Writing a string of calculations with no labels makes it impossible to follow — for you and the examiner. Write what each number represents.
- Rounding too early. Rounding a value in the middle of a multi-step calculation and carrying the rounded answer forward causes a compounding error by the end. Keep full precision until the final step.
- Not writing the answer in context. The question asks "how much does Ahmed take home?" — the answer should be "Ahmed takes home £388.80 per week", not just "388.80". The units and context matter for the final A mark on many questions.
Exam Tips for Worded Problems
- Annotate the question. Underline numbers, circle units, and write a brief note at the top of your working: "Find: weekly take-home pay (£)." This takes 20 seconds and prevents you going off in the wrong direction.
- Identify the topic type first. Ask yourself: is this percentages? Ratio? Speed? Simultaneous equations? Once you've named the topic, you know which method to use — even if the story around it is unfamiliar.
- Check your answer makes sense. A speed of 1,800 km/h for a train is wrong. A take-home pay of −£50 is wrong. A brief sanity check catches errors before you move on.
- Mark scheme insight — context questions often have marks for setting up. AQA and Edexcel frequently award M1 for correctly identifying the first operation, even if the rest of the calculation goes wrong. Write your setup clearly.
- If you're stuck, try a simpler version. Replace the numbers with easy ones (£100, 10%, etc.) to see what the question is really asking. Then go back and apply that same method to the real numbers.
Practise Now
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