My approach to QCE Maths problem solving

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Rishi is a 2020 QCE graduate, achieving an ATAR of 99.90. In this article, Rishi reflects on a potential technique to use through QCE Maths problem solving, based on their own experiences.

For QCE Maths Q&A, check out our dedicated sections of the ATAR Notes Forums:
QCE General Maths | QCE Maths Methods | QCE Specialist Maths.

The time will come in every student’s life when they open a maths test, 5 minutes of perusal counting down on the timer in front of them, and they scan the paper, only to read a question that makes a grand total of 0 sense. It might say something about a derivative, something about logarithms, something about a THICCC (yes, thick with 3 Cs) tree – that last one is right from the 2020 QCE Methods paper.

Regardless, whatever it may say, it may as well be written in Latin. You have no idea where to begin. Unfortunately, I am positive that a time like this will happen to everyone and trust me, it’s a terrible feeling. So, the question is: what am I meant to do? Well, below is a mnemonic that helped to me to tackle tricky questions, and get a 98% for the external Specialist Maths test.

So what’s the secret? Here it is: Don’t Fork With The Apple Crumble. An innocent saying at first glance, but hidden in the depths of the first letters of every word is the key to how I did well on the external.

So let’s go through these step by step, and then I’ll explain when to use the saying.

1. Data/diagram

This essentially refers to first writing out all the data you are given in a question and creating an accompanying diagram if necessary. This should always be your first step if you’re ever stuck as (1) it can result in easy marks,  and (2) it’ll help you to better understand what to do next.

2. Formula

This is where you should whip out your trusty formula and data book, and begin to write down all the formulas that you think are important for this question. Just write them ALL down. Markers can see ‘evidence of thinking/working’, and so may award you marks even if you don’t finish the question. This will also help you to narrow down your focus and target your approach with your working.

3. What do you need to find?

Particularly necessary in Specialist Maths where the questions all feel like they’re trying to trick you, this step is one of the most common and yet, one of the most forgotten. Make sure you actually write down what the question is asking you to find and the potential things you will need to find to get there.

4. Test/theory

Write down a possible theory for what you are thinking the solution path will look like. Even if you don’t get time or you can’t actually do it, you can get marks for showing you knew what to actually do. This can be as simple as finding the 2^nd derivative, or you can write a whole list of steps to actually go through.

5. Actually try something

This is the most difficult step for most people. You have an idea of what to do, but you don’t know how to get there. The solution? Just try something. Even if it seems stupid or pointless, it may help you to understand the real way to finish the question – or maybe once you start you’ll naturally flow into the answer.

6. Check/compare

When I say compare, I don’t mean with other students (although when you do practice questions, working together is a great idea). Instead, I mean compare to what you already – and definitely – know.

For example, if the question is asking you to find a length and you get a negative answer, you automatically know something went wrong. If the question asks you to find the speed of a tennis ball and you get an answer faster than the speed of light, you know that something went wrong. This is what I mean by check/compare. Check to see if your answer seems reasonable and, if not, check your working.

Now, if all your working seems to be correct but your answer is wrong, go back to step 4 and test another theory. If your answer seems right, then great, move on and be confident with yourself. Lastly, if the question actually asks you to show your answer is reasonable, write a few sentences to explain why you think it’s fine, and if you know it’s wrong, write why you know it’s.

It should be noted that with these steps, sometimes not all are necessary, and you can maybe skip a few of them – so make your own judgement based on the question and see if each step is required.

Now that we know what the steps are, when should we use them? Well, it’s pretty simple really. I used these steps whenever I didn’t automatically know what to do or how to approach a problem solving question. And most of the time, it helped to get me a few marks or even make it possible for me to complete the entire question. Now it should be noted that in your exam, this will take a little bit of time, so finish all the questions you know first and then come back to the harder ones and try applying this method.

That being said, I know this method may not work for everyone, so I would recommend trying it out on a complex question (it works best for maths and sciences, but can be applicable to some humanities and social sciences), and see how you find it. If you find that it helps, continue using it!

Good luck with your Year 12 studies and I wish you all the best with your year! 😊

– Rishi Goel

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