Expert Mathematics & Science Tutoring

Introduction

Repeated percentage change is a crucial topic in GCSE Mathematics that involves finding the overall percentage change when a value undergoes multiple percentage changes. It's essential for real-world applications, such as calculating interest on savings or discounts on purchases.

Key Concepts and Definitions

• Percentage change: The change in a value expressed as a percentage.
• Repeated percentage change: The overall percentage change when a value undergoes multiple percentage changes.

Step-by-Step Explanations

1. Find the percentage change for each step: Calculate the percentage change of the new value compared to the original value.

2. Convert to decimals: Convert each percentage change to a decimal by dividing by 100.

3. Multiply the decimals: Multiply the decimals together to find the overall percentage change.

4. Convert back to percentage: Multiply the result by 100 to express it as a percentage.

Common Mistakes to Avoid

• Using the same percentage change multiple times: Each percentage change should be calculated compared to the original value.
• Forgetting to convert to decimals: The decimals must be multiplied together for accurate calculation.

Practice Problems

• Problem 1:

A shirt initially costs £20. It is then discounted by 20%, then there is an additional 10% discount. What is the overall percentage change?

• Solution:
• 20% discount: 20/100 £20 = £4 reduction
• New price: £20 £4 = £16
• 10% discount: 10/100 £16 = £1.60 reduction
• Final price: £16 £1.60 = £14.40
• Overall percentage change: [(£20 £14.40)/£20] 100 = 28% decrease

Conclusion

Repeated percentage change is a valuable concept with numerous applications. By understanding the key steps and avoiding common pitfalls, you can confidently tackle GCSE Mathematics questions on this topic. Remember to practice regularly and stay persistent in your studies.

FAQs

• Q: How do I know when to use repeated percentage change?
• A: It's used when a value undergoes multiple percentage changes, one after the other.
• Q: Can I check my answer by multiplying the individual percentages?
• A: No, the percentages must be converted to decimals before multiplying.
• Q: How can I prepare for exam questions on this topic?
• A: Practice problems, revise the steps, and check your understanding through online resources.