Growth Formula: Error Analysis & Misconceptions
Mathematics
GCSE Higher
12 questions
~24 mins
1 views0 downloads
About This Worksheet
This worksheet explores common errors and misconceptions related to the Growth Formula in compound interest. It includes procedural questions, real-world scenarios, and challenges to deepen understanding.
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Growth Formula: Error Analysis & Misconceptions
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Introduction
Read the key concept carefully before attempting the questions.
1.
The growth formula for compound interest is A = P(1 + r)^t, where A is the amount, P is the principal, r is the annual growth rate (as a decimal), and t is the time in years. Understanding this formula correctly is essential to avoid errors in calculations.
[2 marks]B
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the amount after 3 years if £1000 is invested at an annual growth rate of 5%.
[3 marks]2.
Find the principal if the amount after 4 years is £1500 at an annual growth rate of 4%.
[3 marks]3.
What is the growth rate if £2000 grows to £2420 in 2 years?
[3 marks]C
Problem Solving & Reasoning
Answer the following multi-step questions clearly, explaining your reasoning.
1.
A sum of £5000 is invested at 3% annual growth. How long will it take for the investment to double? Show all your working.
[4 marks]2.
A student mistakenly applies the growth formula using r = 3% as 0.3 instead of 0.03. If they calculate the amount after 5 years with a principal of £200, what error do they make? Correct their mistake and find the accurate amount.
[4 marks]D
Real-world Applications
Tackle these contextual problems involving growth calculations.
1.
A savings account offers 2.5% annual interest, compounded yearly. If you deposited £1500, how much will you have after 10 years?
[3 marks]2.
An investment of £2000 grew to £3000 in 5 years. What was the approximate annual growth rate? Round to two decimal places.
[3 marks]E
Challenge & Extension
Attempt these more difficult problems to extend your understanding.
1.
A population of 10,000 grows at an annual rate of 4%. How many years will it take for the population to reach at least 20,000?
[4 marks]2.
If £8000 is invested at an annual growth rate of 7%, what amount will it be worth after 12 years? Use the growth formula and show your calculations.
[4 marks]F
Mixed Review & Error Analysis
Review these questions to test your understanding and identify common mistakes.
1.
A student applies the growth formula with r = 0.05 but forgets to convert it to decimal form, using r = 5 instead. Calculate the amount after 3 years for a principal of £1000 and identify the mistake.
[4 marks]2.
A common misconception is to add the growth rate directly as a percentage without converting to a decimal in the formula. Explain why this leads to errors and correct the calculation for £1000 at 10% over 2 years.
[4 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet