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Hence

Afrikaans: Gevolglik / Dus

You must build directly on the result you obtained in the previous part of the question. The previous answer is not just useful context, it is the required starting point for your working. If you reach the correct final answer by a completely different method, you will still lose the marks assigned to the 'hence' instruction, because those marks are awarded specifically for using the connection between the two parts.

Common mistake

The most common error is ignoring the previous answer and solving the next part from scratch. Students often do this because they are not confident in their previous answer and don't want to carry an error forward. But 'hence' does not allow you to choose your own method, you must start from the previous result, even if you suspect it is wrong. If your previous answer was incorrect, you can still earn method marks in the 'hence' part by applying the correct process to your (wrong) value, as long as your approach is right.

Signal phrases

These are the words that tell you this instruction is being used.

  • Hence determine...: you must use the result from the previous part as your starting point, not re-derive it.
  • Hence, calculate...: the comma after 'hence' is common but does not change the meaning; the link to the previous answer is still compulsory.
  • Hence solve for x, use the factorised or rearranged form from the previous part, then apply the zero-product rule or the quadratic formula to that result.
  • Hence, or otherwise, determine..., the 'or otherwise' gives you an alternative route if you could not complete the previous part, but using the previous result is always the faster and intended method.
  • Hence write down...: if the next part says both 'hence' AND 'write down', you must use the previous result AND you don't need to show additional working beyond reading off the answer from it.
  • Hence find the gradient of the tangent, this signals that you must use the derivative you found in the previous part; substituting the x-value into a freshly differentiated function will cost you the 'hence' marks.
  • Hence, or otherwise, show that..., even for a 'show that' part linked by 'hence', start from the previous result rather than working from first principles.

Past paper examples

Hence, determine the values of x for which f(x) ≥ g(x), using the graph in 5.2.

Source: DBE Mathematics Paper 1, November 2023, Question 5.3

Test yourself

Before you read the answer, what is this question asking you to do?

3.1 Solve for x: x² − 5x + 6 = 0 3.2 Hence, determine the values of x for which x² − 5x + 6 ≥ 0.

Practice question: not from a past paper

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