Problem solving and multi-step exam questions — Edexcel GCSE Maths revision

Reading and planning

• Underline the numbers and what the question actually asks for before calculating.
• Break a wordy question into smaller steps — write down what each step finds.
• Draw a quick diagram for shape, distance or ratio problems.

Working with multiple topics together

• Multi-step questions often combine percentages, ratio and area/volume in one problem.
• Write intermediate answers clearly with units so you can use them in the next step.
• Check units are consistent throughout (e.g. convert cm to m before using in a formula).

Key terms

Show that

A question type requiring full working to prove a given result.

Multi-step

A problem needing more than one calculation or topic to reach the answer.

Estimate

A rough calculation using rounded values to check an answer is sensible.

Best buy

Comparing value for money using unit price.

Compound measure

A measure made of two units, e.g. speed (distance/time) or density (mass/volume).

Bounds

The upper and lower limits a rounded value could actually be.

Common exam traps

• Answering only part of a multi-step question and stopping too early.
• Not writing a concluding sentence for a comparison question.
• Mixing units (e.g. cm and m) without converting.

Practice questions with answers

1. 1. A shop sells 3 pens for £2.10 or 5 pens for £3.50. Which is better value per pen?

   Answer: 5 pens for £3.50 (70p each vs 70p each — equal value)

   3 pens: 210÷3=70p each. 5 pens: 350÷5=70p each. Both are equal value.

2. 2. A car travels 150 miles in 3 hours. Find its average speed.

   Answer: 50 mph

   Speed = distance ÷ time = 150 ÷ 3 = 50 mph.

3. 3. A tank holds 40 litres. Water is added at 2.5 litres per minute for 6 minutes, then removed at 1 litre per minute for 4 minutes. How much water is now in the tank if it started empty?

   Answer: 11 litres

   Added: 2.5×6=15 litres. Removed: 1×4=4 litres. Total: 15-4=11 litres.

4. 4. A recipe for 4 people needs 300g of flour. How much flour is needed for 10 people?

   Answer: 750g

   Per person: 300÷4=75g. For 10: 75×10=750g.

5. 5. A rectangular garden is 8m by 5m. A path 1m wide is built all round the inside edge. Find the area of the path.

   Answer: 22 m^2

   Whole garden = 8×5=40. Inner area = 6×3=18. Path = 40-18=22 m^2.

More free Maths revision

• All Edexcel Maths revision pages
• All GCSE Maths topics
• Edexcel Maths: Fractions, percentages and standard form
• Edexcel Maths: Solving equations, rearranging and sequences
• Edexcel Maths: Ratio, proportion and rates of change
• Edexcel Maths: Angles, Pythagoras and trigonometry
• Edexcel Maths: Probability: trees, Venn diagrams and conditional probability
• Edexcel Maths: Statistics: averages, spread and diagrams
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