How to answer "Hence or otherwise" questions in GCSE Maths

What it means

You have a choice. "Hence" usually offers the shortest path to the answer using the previous part. "Otherwise" allows any valid method. Both routes earn the same marks if the answer is correct, but "hence" is normally faster.

What examiners want

• A clearly chosen method — do not start with "hence" then switch midway
• If using "hence", reference the previous answer as the entry point
• If using "otherwise", a coherent alternative method that still earns method marks
• Show all working either way — mark schemes credit both paths equally

Worked example

Part (a): Show that x² + 4x − 5 = (x + 5)(x − 1). Part (b): Hence or otherwise solve x² + 4x − 5 < 0.

Hence: (x + 5)(x − 1) < 0. The roots of the quadratic are x = −5 and x = 1. The quadratic opens upwards, so it is negative between the roots. Solution: −5 < x < 1.

Common mistakes

• Believing "otherwise" forbids using the previous answer — it does not, it just permits a different method
• Switching halfway through a method
• Not noticing the easier path that "hence" gives you

Marks tip

Read part (a) carefully before starting part (b). The "hence" path is usually deliberately set up.

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