Subject content — AQA GCSE Further Mathematics
Teaching note based on the AQA specification.
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Subject content explained
This statement sets an expectation that you can recognise and use numbers and the number system in six named areas: fractions, decimals, percentages, ratio, proportion and order of operations.
Read the full explanation
It is not a single technique but a foundation used throughout the qualification, so practise moving fluently between forms. Work in one consistent representation at a time. For example, 0.35 = 35/100 = 7/20, and 7/20 as a percentage is 35%. For ratio and proportion, find the value of one part first: to share £60 in the ratio 2:3, add 2 + 3 = 5 parts, so each part is £60 ÷ 5 = £12, giving £24 and £36. For order of operations, apply brackets, indices, division and multiplication before addition and subtraction, so 3 + 4 × 2 = 11, not 14. Check each answer for sense before you finish.
Your focus
- Convert a value between a fraction, a decimal and a percentage, showing each equivalent form.
- Share a quantity in a given ratio by finding the value of one part.
- Evaluate a calculation with mixed operations in the correct order.
Subject content exam tips
Marking Points
- Converts between fractions, decimals and percentages accurately and shows the equivalent form for each value.
- Simplifies a fraction to its lowest terms, for example reducing 35/100 to 7/20.
- Finds a percentage of an amount by converting to a decimal, for example 15% of 240 as 0.15 × 240 = 36.
- Calculates the total number of parts in a ratio and finds the value of one part before scaling.
- Applies order of operations by performing multiplication before addition, for example 3 + 4 × 2 = 11.
- Checks answers for reasonableness, such as confirming that shared amounts add back to the original total.
Examiner Tips
- 💡Write the equivalent fraction, decimal or percentage on your working so each step can be followed and credited.
- 💡Identify the total number of ratio parts before you divide, and state the value of one part.
- 💡Estimate a rough answer before a multi-step calculation, then compare it with your final result.
Common Mistakes
- Adds the ratio parts to the total amount instead of dividing; correct by dividing the total by the sum of the ratio parts first.
- Works strictly left to right in 3 + 4 × 2 and gets 14; correct by performing the multiplication before the addition.
- Divides by 15 to find 15% of an amount; correct by writing 15% as 0.15 and multiplying by the amount.
- Reads 0.5 as one fifth by misplacing the digit; correct by reading 0.5 as 5/10, which simplifies to 1/2.