How to answer "Hence" questions in GCSE Maths

What it means

When a question says "Hence", it is a direct instruction: use a result from earlier in the same question to answer this part. The connection is usually visible — a factorisation you found in part (a), a formula you derived in part (b). Recognising and using that result is the whole point.

What examiners want

• Reference your earlier answer explicitly (e.g. "Using my factorisation from part (a)...")
• Use the previous result as the entry point, not as a check at the end
• Show one or two new lines that build on the previous answer
• Reach the final answer in a small number of additional steps

Worked example

Part (a): Factorise x² − 5x + 6. Part (b): Hence solve x² − 5x + 6 = 0.

From part (a), x² − 5x + 6 = (x − 2)(x − 3). Hence (x − 2)(x − 3) = 0. So x − 2 = 0 or x − 3 = 0, giving x = 2 or x = 3.

Common mistakes

• Ignoring the previous part and using the quadratic formula from scratch (loses all marks even with correct answer)
• Not writing the link sentence — "Hence" implies you should reference part (a) explicitly
• Re-doing the previous work instead of just using the answer

Marks tip

If the previous part produced a factorised form, a derivative, or a substitution, those are almost always the intended starting points. Look for the connection before you compute.

Related command words