The Finale: always exploit the "Show that..." Questions | Top 7 GCSE Maths Mistakes

Part 7 of 7 in our series "Top 7 Mistakes which GCSE Maths students make".

---

Invest three minutes of your time now to avoid heartbreak on Results Day!

For those of you in Year 11, or with children in that same year, you'll be acutely aware that GCSE exam season is little more than six weeks away now! The Easter holidays, during which you might have done lots of revision - or conversely, none at all (I won't tell if you don't) - are fast drawing to a close. This timely blog series by Gill Learning highlights seven common GCSE Maths mistakes and HOW to resolve them before the day of your exam rolls around! And whichever exam board your school or academic institution opts for, these common mistakes will apply to yours.

Any fair round of negotiations usually ends up with both parties meeting in the middle; it doesn't matter too much exactly who makes the first offer and counter-offer. Imagine, though, if you could read the other person's mind while you were bartering. What if you knew in advance the best price that they'd give you? You'd be guaranteed to get the best deal available, every time! You'd still have to play along, of course, pretending that you were being squeezed and having to compromise.

Well, whether many students realise it or not, the age-old "Show that..." format of an exam question empowers students with a similar "omniscient upper hand" of sorts. And that power affords you multiple options. "Don't look a gift horse in the mouth" is sometimes over-used, but given that almost every GCSE Maths exam includes at least one "Show that..." question, on this occasion I think it's rather apt! So read on to learn the "rules of engagement" and the best techniques when it comes to tackling (and exploiting the weakness of) "Show that..." questions in your Maths exams.

---

It's your good friend the "show that" question. These questions literally give you the answer from the very beginning! So, instead of marks being awarded for your final answer, all of the credit belongs to your "showing" of why something else must be true.

Students often take the approach of "pretending" that they haven't been given the answer, and instead work from first principles. For example, if the question says "Show that x = 74 degrees", they treat the question simply as if it said "Find the value of x." If you're confident on how to solve the problem regardless of it being a "show that", then this is a perfectly good method!

However, it's when a student is on the precipice of a solution, but not quite 100% there, that their exam technique sometimes fails them. If you're feeling touch-and-go on a "show that" question, remember that you can work "backwards" as well as forwards (or both), and oftentimes your solution will meet in the middle. In other words, you can use the same fact that you're trying to "show" is true to infer other values relevant to the problem.

Back to our angle-finding example from above; it's actually a Circle Theorem question. Imagine that only two angles are labelled in the diagram: one is known to be 53 degrees, and the other is labelled as x. You're asked to "show that x = 74 degrees". At this point, you're just as entitled to assume that 74 degrees is correct and hence use it to prove that the known angle must indeed be 53 degrees as labelled - what I'd call "working backwards" - as you are to work forwards. Spoilers: 180 - 53 * 2 = 74 degrees, or (180 - 74)/2 = 53 degrees, by the way.

There are two layers to this revelation. Firstly, it just doesn't occur to some students that working in either direction, as such, is a legit technique; well, you heard it here first, it is perfectly valid. Secondly, though, the point is that sometimes, for no good reason at all, one order of things will "pop out of the page" at you more clearly than the other does. You should feel empowered to go with the flow, to roll with the punches, or any other proverb that you so desire!

Bear in mind that "show that" questions are often part (a) of a larger question; so even if all else fails, and you can't adequately solve part (a), you can of course still continue with part (b) of the question onwards, because you were literally told the answer to part (a)! It reminds me of that TV show hosted by Jimmy Carr, "I literally just told you", it's called. (Has anyone else seen it?)

Lastly, remember that if your "show that" solution is looking "close but no cigar", you can always employ a degree of creative licence! The examiner would probably have to give you the benefit of the doubt if you'd omitted the last "intended" line of working from the mark scheme, and had just written your (predetermined) final answer of "x = 74 degrees". Returning to my bartering analogy from the beginning, this is what you might refer to as the "playing along" part. Haha!

---

And just like that, this week-long, seven-part blog series draws to a close. Thanks to everyone who reads it, in part or in full; I do hope that you found the hints and tips I've conveyed helpful, and perhaps that I even made you chuckle along the way. We've encountered everything from how to revise effectively and how to use your calculator, through to making a plan and the importance of sanity-checking your exam answers.

None of what we've explored constitutes a silver-bullet, but nevertheless, if you avoid repeating any of the Top 7 GCSE Maths Mistakes, then you'll already be one-up on your peers. Every mark counts, and steering clear of the most common pitfalls might just make the different between you getting a high grade-5, or you sneaking up into a grade-6 come August.

Please be sure to subscribe to our mailing list to be the first to know whenever new blogs, topic learning resources, or tutorial availability go live on the Gill Learning website. You can sign up at the bottom of this webpage.

All that leaves for me to say is: GOOD LUCK with all your GCSE Maths and Science exams throughout May and June!