Where can I download free repeated change PDF worksheets with answers?

On this MathsLinks page you can download free printable repeated change PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Maths Genie, Naiker Maths, Dr Austin, Maths4EveryOne, plus a printable one-page repeated change revision guide.

What GCSE grade is repeated change (6D)?

Repeated change (topic code 6D) is a Grade 6 ratio & proportion topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Repeated change Worksheets (PDF) with Answers — GCSE Maths

Free Repeated change PDF Worksheets & Answers

Grade 6 • Topic 6D

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Naiker Maths Exam question booklet & solutions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
Maths4EveryOne GCSE 9–1 practice booklet & solutions	Qs	Ans
E Classroom GCSE topic booklet & answers	Qs	Ans
PMT (Edxl) Edexcel GCSE topic questions & solutions	Qs	Ans
PMT (AQA) AQA GCSE topic questions & solutions	Qs	Ans
PMT (IGCSE) Edexcel IGCSE topic questions & solutions	Qs	Ans
The Maths Room Online topic notes & examples	Page

Grade 6 topics
6A - Recurring decimals	6B - Harder indices
6C - The product rule	6D - Repeated change
6E - Triple brackets	6F - Parallel and perpendicular
6G - Inequalities on graphs	6H - Similar shapes (area and vol)
6J - Negative scale factors	6K - Circle theorems
6L - Cumulative frequency	6M - Box plots
6N - Combined transformations	6P - Capture recapture

Explanation:

For repeated percentage change (compound interest or depreciation) over n years, use the multiplier formula: Final Amount = Initial Amount × (multiplier)ⁿ.

For an increase of r%, the multiplier is 1 + r100 (e.g. +3.2% → 1.032). For a decrease of r%, the multiplier is 1 − r100 (e.g. −12% → 0.88). If the percentage rate changes from year to year, multiply by each year's multiplier in turn.

Example 1: £4500 is invested at 3.2% compound interest per year for 4 years. Work out the value of the investment after 4 years.

Solution:

Multiplier for +3.2% = 1 + 0.032 = 1.032

Value = 4500 × 1.032⁴

Value = £5104.243...

Answer: £5104.24 (to the nearest penny)

Example 2: A car bought for £18,000 depreciates by 20% in Year 1, then by 12% per year for the next 2 years. Find its value after 3 years.

Solution:

Year 1 multiplier = 0.80; Years 2 & 3 multiplier = 0.88

Value = 18,000 × 0.80 × 0.88²

Value = 14,400 × 0.7744 = £11,151.36

Answer: £11,151.36

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Repeated change Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 OCR Jun 2022 3F Q24 6 marks

Full Paper (PDF) • Mark Scheme (PDF)

1600 fish are released into a new lake which has no fish.
The number of fish is expected to increase by 5% each year.

(a) The table shows the expected number of fish in the lake at the end of 1 year and at the end of 2 years.
Complete the table.
Round your answers to the nearest integer.
@@TABULAR₀@@ [3 marks]

(b) Use the table to draw a suitable graph to show the expected number of fish in the lake. [3 marks]

Worked Solution & Mark Scheme (6 marks)

Part (a) Solution:

Year 3: 1764 × 1.05 = 1852.2 ≈ 1852 M2
Year 4: 1852.2 × 1.05 = 1944.81 ≈ 1945. A1

Answer (a): 1852 and 1945

Part (b) Solution:

Plot all 5 points accurately and connect them. M2 A1

Answer (b): Points plotted at (0, 1600), (1, 1680), (2, 1764), (3, 1852), (4, 1945) and joined with a curve/line segments

Past Paper Example 2 IGCSE Jun 2022 1F Q21 / 1H Q6 6 marks

Full Paper (PDF) • Mark Scheme (PDF)

Asha bought an apartment.
The table gives information about the value of apartments, in euros, and the annual service charge band.

In 2021, the value of Asha’s apartment was 634 400 euros.
The value of Asha’s apartment had increased by 4% from its value in 2020

(a) Has the annual service charge band changed for Asha’s apartment?
Show your working clearly. [3 marks]

(b) Work out the total percentage by which the value of the boat had depreciated by the end of the second year after Pam bought the boat. [3 marks]

Worked Solution & Mark Scheme (6 marks)

Part (a) Solution:

634 400 ÷ 1.04 = 610 000 euros (600 000 ≤ x < 700 000, still Band B) M2 A1

Answer (a): No, in 2020 the value was 610 000 euros so it stayed in Band B

Part (b) Solution:

1 – 0.85² = 1 – 0.7225 = 0.2775 = 27.75% M2 A1

Answer (b): 27.75 %

Past Paper Example 3 OCR Jun 2024 5H Q12 5 marks

Full Paper (PDF) • Mark Scheme (PDF)

(a) Sasha invests £1000 at a rate of 5% per year compound interest.
Sasha says:
"After one year, my investment will get £50 in interest and will be worth £1050.
Therefore, after two years, my investment will get another £50 in interest and will be worth £1100."
Is Sasha correct?
Give a reason for your answer.
(b) Sasha buys a car.
The value, £V, of the car after n years is given by the formula
V = a × bⁿ.
The graph shows some information about the value of the car.

(b) Sasha buys a car.
The value, £V, of the car after n years is given by the formula
V = a × bⁿ.
The graph shows some information about the value of the car. [4 marks]

Find the value of a and the value of b.

Worked Solution & Mark Scheme (5 marks)

Part (a) Solution:

Compound interest is calculated on the new amount (£1050) in year 2, not the original £1000. C1

Answer (a): No, because in the second year the 5% interest is calculated on £1050 (giving £52.50 interest, total £1102.50).

Part (b) Solution:

When n = 0, V = 8000 ⇒ a = 8000 M3
When n = 1, V = 6400 ⇒ 8000 × b = 6400 ⇒ b = 6400 ÷ 8000 = 0.8. A1

Answer (b): a = 8000, b = 0.8

← 6C The product rule

Back to GCSE questions by topic

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Repeated change

Free Repeated change PDF Worksheets & Answers

Guide to Repeated change: Explanation, Diagrams & Worked Examples

GCSE Past Paper Repeated change Questions & Answers