Edexcel 1MA1 GCSE Maths · 3 Worked Solutions

Edexcel GCSE Maths: Percentages Worked Solutions

Real mark-scheme-derived worked solutions for Edexcel GCSE Maths Percentages questions. Every solution includes step-by-step working, the correct final answer, marks awarded, and a common mistake callout — with question-level AO breakdown from the official 1MA1 spec.

Q1 Higher 4 marks

Edexcel 1MA1 · 2024

Question

A company has 25,000 workers. The number of workers increases at a rate of 6% per year for 3 years. Calculate the total number of workers at the end of the 3 years.

Worked Solution

A 6% increase each year means multiplying by 1.06 each year (the multiplier for a 6% increase).
After 1 year: 25 000 × 1.06 = 26 500 workers.
After 2 years: 26 500 × 1.06 = 28 090 workers.
After 3 years: 28 090 × 1.06 = 29 775.4 ≈ 29 775 workers (round to a whole number).
Equivalently, use the compact formula: 25 000 × 1.06³ = 25 000 × 1.191016 = 29 775.4 ≈ 29 775.

Final Answer

29 775

Common Mistake

Calculating simple interest instead of compound interest — adding 6% of 25 000 (= 1500) three times gives 29 500, which is wrong. Compound interest is applied to the running total each year.

Assessment Objectives (question level, Edexcel 1MA1 spec — not per step)

AO1 Use standard techniques — 40%

AO2 Reason and communicate — 30%

AO3 Solve problems — 30%

Q2 Higher 4 marks

Edexcel 1MA1 · 2023

Question

Tamsin buys a house with a value of £150 000. The value of Tamsin's house increases by 4% each year. Rachel buys a house with a value of £160 000. The value of Rachel's house increases by 1.5% each year. At the end of 2 years, whose house has the greater value? You must show how you get your answer.

Worked Solution

Calculate the value of Tamsin's house after 2 years at 4% per year: 150 000 × 1.04² = 150 000 × 1.0816 = 162 240.
Calculate the value of Rachel's house after 2 years at 1.5% per year: 160 000 × 1.015² = 160 000 × 1.030225 = 164 836.
Compare: Rachel's house is worth £164 836, Tamsin's is worth £162 240. Rachel's house has the greater value.

Final Answer

Rachel's house, with a value of £164 836 compared to Tamsin's £162 240

Common Mistake

Using the original values to compare without doing the compound interest calculation, or using simple interest (e.g. 4% × 2 = 8% total for Tamsin) — always apply the percentage to the value at the start of each year.

Assessment Objectives (question level, Edexcel 1MA1 spec — not per step)

AO1 Use standard techniques — 40%

AO2 Reason and communicate — 30%

AO3 Solve problems — 30%

Q3 Higher 2 marks

Edexcel 1MA1 · 2022

Question

The value of Michelle's car has decreased by 15%. The car now has a value of £13,600. Work out the value of Michelle's car before the decrease.

Worked Solution

A 15% decrease means the car is now worth 100% – 15% = 85% of its original value.
Write the equation: 85% of original value = £13 600, so 0.85 × original = 13 600.
Divide both sides by 0.85: original value = 13 600 ÷ 0.85 = £16 000.

Final Answer

16000

Common Mistake

Adding 15% to £13 600 (= £15 640) instead of dividing by 0.85 — that gives the wrong answer because 15% of £13 600 is not the same as 15% of the original price.

Assessment Objectives (question level, Edexcel 1MA1 spec — not per step)

AO1 Use standard techniques — 40%

AO2 Reason and communicate — 30%

AO3 Solve problems — 30%

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Edexcel GCSE Maths: Percentages Worked Solutions

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