Work out
Do the calculation and show the working.
Example. Work out 15% of 40.
Show answer
6 10% is 4, so 5% is 2, and 4 + 2 = 6.
GCSE Maths command words
What “show that”, “write down”, “give a reason” and “prove” mean in GCSE Maths, with an example of each and how the marks are earned.
Used on AQA-style and Edexcel-style papers. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.
Calculate
Same job as work out. A calculator is usually allowed.
Example. Calculate 7.5².
Show answer
56.25 7.5 × 7.5 = 56.25.
Find
Get the value the question asks for.
Example. Find x when 3x = 12.
Show answer
x = 4 Divide both sides by 3.
Write down
The mark is for the answer. Little or no working is expected.
Example. Write down the value of 10².
Show answer
100
Simplify
Make it shorter, and finish the simplifying.
Example. Simplify 8x + 3x.
Show answer
11x 8 + 3 = 11.
Solve
Find the value of the letter.
Example. Solve 2x − 1 = 9.
Show answer
x = 5 2x = 10, so x = 5.
Expand
Multiply out the brackets.
Example. Expand 4(x − 2).
Show answer
4x − 8 4 × x and 4 × −2.
Factorise
Put the expression into brackets.
Example. Factorise 6x + 9.
Show answer
3(2x + 3) 3 is the highest common factor.
Show that
The answer is given. The marks are for the steps that reach it.
Example. Show that 3/4 of 20 is 15.
Show answer
15, from the working 20 ÷ 4 = 5 and 5 × 3 = 15.
Prove
A chain of reasons that works for every case, not one example.
Example. Prove the sum of two odd numbers is even.
Show answer
2(m + n + 1), which is even Odd numbers are 2m + 1 and 2n + 1. Their sum is 2m + 2n + 2.
Explain
Give a reason in words, with a number if it helps.
Example. Explain why 2/3 is bigger than 3/5.
Show answer
10/15 is bigger than 9/15 2/3 = 10/15 and 3/5 = 9/15.
Give a reason
Name the angle fact or rule you used.
Example. A triangle has angles 40° and 60°. Give a reason why the third is 80°.
Show answer
Angles in a triangle sum to 180° 180 − 40 − 60 = 80.
Estimate
Round to 1 significant figure first, then calculate.
Example. Estimate 19.6 × 5.1.
Show answer
100 20 × 5 = 100. The exact product is 99.96.
Compare
Say which is bigger, or how they differ, using a number.
Example. Compare the mean and the median of 1, 2 and 9.
Show answer
Mean 4, median 2 The mean is pulled up by 9.
Printable poster
Print this page for a classroom poster of the short meanings.
Work out
Do the calculation and show the working.
Calculate
Same job as work out. A calculator is usually allowed.
Find
Get the value the question asks for.
Write down
The mark is for the answer. Little or no working is expected.
Simplify
Make it shorter, and finish the simplifying.
Solve
Find the value of the letter.
Expand
Multiply out the brackets.
Factorise
Put the expression into brackets.
Show that
The answer is given. The marks are for the steps that reach it.
Prove
A chain of reasons that works for every case, not one example.
Explain
Give a reason in words, with a number if it helps.
Give a reason
Name the angle fact or rule you used.
Estimate
Round to 1 significant figure first, then calculate.
Compare
Say which is bigger, or how they differ, using a number.