"Hence" Is the Most Expensive Word in an NSC Maths Exam — Here's How to Use It

Here is the rule, stated as plainly as possible: when a question says "hence," you are required to use the result you just found in the previous part. Not a similar method. Not a faster method you happen to know. The specific value, expression, or equation you produced one line above. If you solve the new part from first principles instead — even if you land on the exact right answer — the marking memorandum typically awards zero for that sub-question, because the marks are allocated to the connection between the two parts, not to the final number.

Why This Rule Exists

NSC Mathematics questions are frequently built as a staircase: part (a) establishes a fact, and part (b) — the "hence" part — tests whether you can carry that fact forward and apply it somewhere new. This is a deliberate test of mathematical reasoning, not just computation. Examiners want to see that you understand *why* the first result is useful, not just that you can solve two separate problems that happen to appear next to each other on the page.

"Hence" Looks Different in Every Topic — But the Rule Never Changes

Students often recognise "hence" instantly in algebra but miss it completely in geometry or calculus, because the surface details change even though the underlying instruction is identical. A few examples of what "hence" typically demands, topic by topic:

• Algebra: "Hence, solve for x" after finding the roots of a related equation — substitute or transform using the value you already found, rather than re-deriving it.
• Sequences and series: "Hence, calculate the sum of the first 20 terms" after finding a general term Tn — plug your Tn formula into the sum formula rather than restarting from the pattern.
• Functions and graphs: "Hence, determine the coordinates of the turning point" after finding f'(x) = 0 — use the x-value you already solved for, don't re-differentiate and re-solve.
• Trigonometry: "Hence, solve the equation for x ∈ [0°, 360°]" after simplifying an expression — substitute your simplified form into the equation rather than working with the original, more complex expression.
• Euclidean geometry: "Hence, prove that..." after establishing an earlier angle or length relationship — your proof must explicitly reference that earlier result as a step, not just arrive at a similar conclusion independently.

"Hence or Otherwise" Is a Different Instruction

Don't confuse "hence" with its close cousin, "hence or otherwise." The second phrase gives you permission to use any valid method — including one that doesn't touch the previous part at all. In practice, the "hence" route using your previous answer is almost always faster, and NSC markers structure the marks so that route earns credit efficiently. But if you got the previous part wrong or can't see the connection, "hence or otherwise" is your safety net: a correct answer from a completely different method still earns full marks. "Hence" alone gives you no such safety net — the connection is mandatory.

A Two-Second Check Before You Answer a "Hence" Question

Before you write anything for a "hence" sub-question, ask yourself one question: what value, expression, or equation did I just produce in the part above, and where does it fit into what I'm being asked now? If you can't immediately answer that, go back and re-read the previous part — the connection is there, even if it isn't obvious at first glance. Writing down your previous answer at the top of your new working, before you do anything else, is a simple habit that makes the connection impossible to forget.