EDEXCEL GCSE HIGHER MATHS - What is Estimation and Money Calculations

Edexcel GCSE Higher Maths: Estimation and Money Calculations

Estimation

Estimation is a useful skill for quickly checking if your answers are reasonable and for solving problems where an exact answer isn't required. Here are some techniques:

Rounding:

• Round to the nearest whole number: This is useful for quick calculations. For example, to estimate 3.7 + 5.2, you could round to 4 + 5 = 9.
• Round to significant figures: This is useful when dealing with very large or small numbers. For example, to estimate 2345.6 x 0.0047, you could round both numbers to 2000 and 0.005 respectively, giving you 2000 x 0.005 = 10.

Using Compatible Numbers:

This involves changing numbers slightly to make calculations easier. For example, to estimate 19.8 / 3.2, you could change it to 20 / 3, giving you an estimate of 6.67.

Using Proportions:

This involves using known values to estimate unknown values. For example, if you know that 10 apples cost £2, you can estimate that 5 apples would cost £1.

Money Calculations

Percentage Calculations:

• Finding a percentage of an amount: To find 10% of an amount, divide by 10. To find other percentages, use the following:
  • 5% = 10% / 2
  • 20% = 10% x 2
  • 25% = 10% x 2.5
  • 50% = 100% / 2
• Increasing/decreasing an amount by a percentage:
  • To increase an amount by a percentage, add the percentage of the amount to the original amount.
  • To decrease an amount by a percentage, subtract the percentage of the amount from the original amount.

Simple Interest:

• Simple interest: This is a fixed percentage of the original amount that is earned or paid over a certain period of time.
• Formula: Simple Interest = (Principal x Rate x Time) / 100
  • Principal is the original amount invested or borrowed.
  • Rate is the interest rate per annum.
  • Time is the time period in years.

Compound Interest:

• Compound interest: This is interest calculated on both the original amount and any accumulated interest.
• Formula: Amount = Principal x (1 + (Rate/100))^Time

Currency Conversion:

• Exchange Rates: These are used to convert one currency to another.
• Conversion: Multiply the amount in the original currency by the exchange rate to get the amount in the new currency.

Example Problem:

A shop sells a dress for £45. The shop offers a 20% discount on all items. What is the discount amount?

Solution:

1. Calculate 10% of the original price: £45 / 10 = £4.50
2. Calculate 20% of the original price: £4.50 x 2 = £9.00

Therefore, the discount amount is £9.00

Practice Problems

1. Estimate the value of 78.3 x 0.49 using rounding.
2. Calculate the simple interest on a loan of £1000 at a rate of 5% per annum for 3 years.
3. Convert £500 to Euros using an exchange rate of 1 Euro = £0.85.

Remember to always show your working clearly and use appropriate units.