1.5 Calculations
Calculations
Everything on calculations that can come up in the WJEC GCSE Mathematics and Numeracy, in Unit 2 and Unit 3. Each skill below has the method, the mistake that costs the most marks, a worked example, and free practice marked the way WJEC marks it.
A worked example
Order of operations · [1 mark]
Work out 30 − 2².
- B126
The exam skills (6)
Order of operations
- Brackets first.
- Then powers (indices).
- Then × and ÷, then + and −, working left to right.
Watch out: Working left to right from the start. 5 + 2 × 2 is 9, not 14.
Reciprocals
- The reciprocal of a number is 1 ÷ the number.
- For a fraction, flip it upside down: 3/4 becomes 4/3.
- For a decimal, write it as a fraction first, then flip it.
Watch out: Changing the sign. The reciprocal of 2 is 1/2, not −2.
Multiplying
- Split the calculation into easy parts, e.g. 121 × 30 = 121 × 3 × 10.
- Use a written method you trust: column, grid or bus stop.
- Check with an estimate.
Watch out: No working on a non-calculator question. The method mark needs a complete method shown.
Number machines
- Forwards: do the steps in order.
- Backwards: start with the output and do the inverse of each step, last step first.
- Check by putting your answer back through the machine.
Watch out: Undoing the steps in the wrong order.
Using a calculator
- Type the whole calculation in one go, using brackets for the top and bottom.
- Write down the full display: there is a mark for it.
- Then round as the question asks.
Watch out: Rounding in the middle of the calculation. Only round at the very end.
Fractions
- Work out the brackets first: use a common denominator to add or subtract.
- To divide by a whole number, multiply the denominator by it.
- Simplify your answer fully.
Watch out: Leaving the answer unsimplified when the question says simplest form.
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