'Show That': How to Answer Without Giving Away the Method

A 'show that' question gives you the target result directly in the question text, 'show that a = 3 and b = 2', 'show that the price of the cellphone is R4 779,13'. The marks are not for stating that number. You already have it. The marks are for the working that gets a stranger, starting from nothing but what the question gave you, to that exact number by a valid method. If your working doesn't genuinely produce the given value, adjusting a step so the arithmetic lands where you already know it should, you haven't shown anything. You've copied the answer into your own script and dressed it up as a derivation.

Why Examiners Give You the Answer at All

This isn't a kindness. 'Show that' sub-questions usually sit inside a larger, multi-part question, and the value they hand you is often needed for the next part. If you got the earlier part wrong, or skipped it, a 'show that' step lets you recover: you're handed the correct number so you can keep working on the rest of the question without your first mistake following you through every subsequent part. That only works, though, if you treat the given value as a target to prove, not a shortcut to write down.

A Real 'Show That' Question, Worked Backwards From an Answer

The Grade 10 November 2018 Paper 1 exam, question 7.2, described a cellphone advertised at R229 per month for 24 months with no deposit, financed by a hire purchase agreement charging 7.5% per annum simple interest on the cash price. It then asked candidates to show that the cash price of the phone was R4 779,13.

The number is already sitting right there in the question. What earns the marks is the method: recognising that the total of the monthly instalments (24 × R229 = R5 496) is the accumulated amount A in the simple interest formula A = P(1 + in), then substituting n = 2 years and i = 0,075, and solving the equation for P. Do that correctly and P comes out to R4 779,13, matching the given figure. A student who just writes 'P = R4 779,13' because the question already said so, with no formula and no substitution shown, earns nothing, because there's no method on the page to mark.

A Real 'Show That' Question From Functions

The November 2019 Paper 1 exam, question 4.1 to 4.2, gave the graphs of f(x) = x² + bx − 3 and g(x) = a/(x + p), sharing a y-intercept and intersecting at two points, with the vertical asymptote of g passing through the x-intercept of f. After finding p in 4.1, question 4.2 asked candidates to show that a = 3 and b = 2.

Again, both values are already stated. The mark allocation sits entirely in the method: using the shared y-intercept and the known x-intercept of f to build two equations, one from each graph, and solving them as a simultaneous system. A student who writes 'a = 3, b = 2, confirmed' without setting up and solving those equations has stated a fact the examiner already gave away for free. Nothing has been shown.

The One Move That Costs You Everything

The single most damaging habit in a 'show that' answer is adjusting your working partway through so it lands on the given number. It usually happens under pressure: you substitute, calculate, and get something close to the target but not exact, so you quietly change a sign or round differently a few lines up so the final line matches. A marker reading a 'show that' answer is checking the logic of every line against the one before it, not just glancing at the final answer, so an inconsistency between your method and your own working stands out immediately, and it reads as exactly what it is.

If your working doesn't land on the given value, the honest move is to go back and find your actual error, a sign mistake, a wrong substitution, an incorrect formula, not to force the last line to agree with the question. Examiners' reports consistently flag this kind of 'fudging' as one of the clearest tells that a student didn't genuinely work the problem.

What This Is Not: A Licence to Skip Steps

Because the destination is already known, it's tempting to treat a 'show that' question as needing less working than a 'calculate' or 'determine' question asking for the same value. The opposite is true. Since there's no uncertainty about the final line, the mark allocation shifts almost entirely onto the intermediate steps, so skipping them costs you a larger share of the available marks than it would on a question where the final answer itself still carried weight.

• Write down the formula or relationship you're using before you substitute anything.
• Show every substitution explicitly, with the actual numbers from the question, not just the result of the substitution.
• If you reach the given value, say so explicitly on the final line, don't just stop and assume it's obvious.
• If you don't reach it, look for your own error rather than adjusting the arithmetic to match.

Treat the Given Value as a Checkpoint, Not a Shortcut

Used properly, a 'show that' question is one of the few places in an NSC paper where you get to check your own work as you go, if your method produces the stated value, you know your approach and your arithmetic are both correct, and you can move into the next part of the question with real confidence. That's a genuine advantage. It only exists, though, if the working you write down is the working that actually got you there.