Edexcel GCSE Maths: Percentages and Percentage Change

Edexcel GCSE Maths: Percentages and Percentage Change

This tutorial covers calculating percentage increases, decreases, profit, loss, and compound and simple interest. We'll explore their applications in financial contexts like sales, budgeting, and interpreting statistical data.

1. Basic Percentages

• Understanding Percentages: A percentage is a fraction out of 100. The symbol "%" represents "out of one hundred." For example, 50% is the same as 50/100.
• Converting Fractions and Decimals to Percentages:
  • To convert a fraction to a percentage, multiply by 100.
  • To convert a decimal to a percentage, multiply by 100.
• Calculating a Percentage of a Number:
  • Divide the number by 100 to find 1%.
  • Multiply the result by the desired percentage.

Example: Find 20% of 150.

1. 1% of 150 is 150/100 = 1.5
2. 20% of 150 is 1.5 x 20 = 30

2. Percentage Increase and Decrease

• Percentage Increase:

  • Calculate the difference between the original value and the new value.
  • Divide the difference by the original value.
  • Multiply the result by 100.

• Percentage Decrease:

  • Calculate the difference between the original value and the new value.
  • Divide the difference by the original value.
  • Multiply the result by 100.

Example: A price increases from £50 to £60. Calculate the percentage increase.

1. The difference is £60 - £50 = £10.
2. Divide the difference by the original value: £10 / £50 = 0.2
3. Multiply by 100: 0.2 x 100 = 20% Therefore, the price increased by 20%.

3. Profit and Loss

• Profit: Profit is the difference between the selling price and the cost price of an item, if the selling price is higher.
• Loss: Loss is the difference between the selling price and the cost price of an item, if the cost price is higher.

Example: A shopkeeper buys a product for £20 and sells it for £25. Calculate the profit.

1. Profit = Selling Price - Cost Price
2. Profit = £25 - £20 = £5

4. Simple Interest

• Simple Interest: Interest calculated only on the principal amount.
• Formula: Simple Interest = (Principal x Rate x Time) / 100

Example: Calculate the simple interest on a principal of £1000 at a rate of 5% per annum for 3 years.

1. Simple Interest = (1000 x 5 x 3) / 100 = £150

5. Compound Interest

• Compound Interest: Interest calculated on both the principal amount and the accumulated interest from previous periods.
• Formula: Amount = Principal (1 + Rate/100)^Time

Example: Calculate the compound interest on a principal of £1000 at a rate of 5% per annum for 3 years.

1. Amount = 1000 (1 + 5/100)^3 = £1157.63
2. Compound Interest = Amount - Principal = £1157.63 - £1000 = £157.63

6. Real-World Applications

• Sales: Calculating discounts and sale prices.
• Budgeting: Planning and managing expenses.
• Statistics: Interpreting data and drawing conclusions.

Example: A store offers a 20% discount on a product priced at £100. Calculate the sale price.

1. Discount = 20% of £100 = £20
2. Sale Price = Original Price - Discount = £100 - £20 = £80

7. Tips for Success

• Practice regularly: Solve as many problems as possible to reinforce your understanding.
• Use a calculator: This will make calculations faster and reduce errors.
• Understand the concepts: Focus on understanding the underlying principles rather than just memorizing formulas.
• Apply the concepts in different contexts: Use real-world examples to relate percentages and percentage change to your everyday life.

By mastering percentages and percentage change, you'll gain valuable skills for everyday life and be well-prepared for your Edexcel GCSE Maths exam.