How to best prepare for your QCAA Mathematics External Exams

Manoj Arachige -

Breaking down the assessment

General Mathematics

The external assessment consists of two papers. Paper 1 contains short responses and multiple choice simple familiar questions. In previous years there have been 15 multiple-choice questions with 4 options for each question. Paper 2 contains short responses to complex familiar and complex unfamiliar questions.  You are allowed to bring in a QCAA-approved scientific calculator and will be provided with the formula book for General Mathematics.

Mathematical Methods and Specialist Mathematics

This external assessment contains two papers. Paper 1 and Paper 2 have simple familiar, complex familiar and complex unfamiliar questions. For both papers, there are 10 multiple-choice questions each with 4 options for every question. For Paper 1 you are NOT allowed to bring a calculator in but will be provided the appropriate formula book. For Paper 2 you are permitted to bring a QCAA-approved graphics calculator and/or QCAA-approved scientific calculator. I strongly urge you to have a graphics calculator on hand and according to preference, you may bring in the scientific calculator if you feel more comfortable/quicker using it for simpler calculations/inputs.

For all three mathematics subjects simple familiar, complex familiar and complex unfamiliar questions are allocated marks in the exams as 60%, 20% and 20% respectively over Paper 1 and 2.

Simple familiar requires you to respond to situations where:

  • relationships and interactions are clear and have few elements.
  • all information to solve the question is identifiable.

Complex familiar involves responding to contexts where:

  • relationships and interactions have various elements with connections that are made with subject matter within and/or across the domain of mathematics.
  • all information to solve the problem is identifiable.

Complex unfamiliar includes answering questions where:

  • relationships and interactions have various elements with connections that are made with subject matter within and/or across the domain of mathematics.
  • all information to solve the questions is not immediately identifiable and students will have limited prior experience to them.

Multiple-choice questions

  • Relatively easier, require limited working out and are done relatively quickly compared to short-response questions.
  • This can include requiring calculations, analysing graphs, using formulas, point-blank definitions and more.
  • Each multiple-choice question is worth 1 mark.

Papers 1 and 2 allow for 5 minutes of perusal and 90 minutes of working time each. Each paper will have its own allocated session, and these sessions could occur either on the same day or the following day. The entire assessment (both papers) will test your understanding and knowledge of the Unit 3 and 4 syllabus for each respective mathematics.

Where to start?

Understanding the Content

For each mathematics subject, there is a syllabus/subject matter with dot points aligning with each mathematical concept explored. These dot-points demonstrate what you can be tested on in your external exam. The subject matter can be found on the QCAA education website for every senior subject conducted in Queensland.

I recommend having a copy of your math subject’s syllabus and reading through it for Units 3 and 4. Then employ a traffic light system of green, yellow and red.

Green represents content you understand well and can answer simple, complex familiar and complex unfamiliar questions relating to them. Yellow shows an “okay” understanding of a specific dot point and can answer simple familiar and some complex familiar questions. Red displays a limited understanding of the matter and difficulty in completing simple familiar questions.

For dot points that are in the “yellow zone” it demonstrates that you understand the topic to a certain degree and may just need to do more questions. Whereas content in the “red zone” shows that you may need extra support to understand a concept whether that comes from revisiting the topic in your mathematical book allocated by your school, asking your teacher for further assistance and/or browsing the web/YouTube to explain the content.

Going through the unit 3 and 4 syllabus highlight the dot points using this colour coding system to demonstrate to yourself how much of the content you understand. This will help target your revision and what subject matter you may need to “relearn” and/or revise.  Below is an example of what it may look like, I’ve taken the Mathematical Methods syllabus and went through a topic 1 of unit 3 with this colour coding system using the 2025 updated subject matter.

You can also pair questions to specific dot points from your mathematical book and/or question bank to help regularly revise concepts and types of questions you may encounter.

This colour coding system can be helpful for many people; however, it may not be the best fit for you. This is simply an example of a method to organise your thoughts and categorise what needs to be done to perform as well as you can for your external exam. If this system doesn’t fit your method of studying, search and try a different method that will help your revision be targeted and organised for you to achieve the best mark possible in your exam.  

But it is highly important to understand what the syllabus contains as that is all you can be asked for your final exam and is the best way to ensure you don’t miss any concepts no matter how small or difficult they may be. 

Question Banks and Past External Exams

There are many different “methods” to begin your preparations for your external exam. Another tactic is collating all the resources that are available to you; revision papers/questions given by your school, questions available in the allocated book your school uses and past external exam papers from 2020 onwards. For further practice, you can turn to other states (e.g. Victoria) for final past papers and complete questions/exams that fit the QCAA syllabus.

After collating your resources create a week-by-week timetable of the question banks and exams you will complete leading up to your externals. This way you have organized resources and a timetable to stick to that will greatly help you revise without feeling overwhelmed and that there are a million things to do before your externals.

Question banks will act as revision resources to the different types of questions you can be asked on different topics. When sitting past exams it’s vital to try and replicate the “in-exam experience” with a timer, print-out of the appropriate formula sheet, writing on paper and in a silent room where you won’t be disturbed during your exam. By doing so you can identify which exam techniques you may need to work on (timing, being able to stay calm when unsure how to do a question at first glance, skipping questions you may not be able to complete, minimising silly mistakes, etc).

Breaking down your mock exam results

This section assumes that you’ve received your mock exam results and looking to best use that experience to enhance your results for the external exam.

The actual mark you receive doesn’t matter and comparing to others won’t help either. In most cases, you had little to no time to prepare for them and it’s just seeing how much math content has been stored in your long-term memory. Further, the mock exam is also an example of what your teachers think may be on your external exam and will not contain all the content you could be tested on.

However, it does allow you to practice with:

  1. The exam format
  2. Timing
  3. The pressure of sitting in a hall
  4. Getting comfortable with seeing a question you don’t know how to solve straight away.

After receiving your mock exam papers, it’s important to try and identify what topics you had trouble with and what topics you understood better. The mock exams are a great tool to use to practice your exam techniques and see what you “know” and what you don’t “know” in the syllabus. This will then help you with potentially filling out the traffic light system explored before and targeting your revision to do the best you can in your exams.

It’s almost guaranteed that you will do far better in your actual exams than your mock exams if you do targeted revision and take on feedback from your mocks.

Final Tips and Tricks

  •  Always have a printout of your formula sheet with you.

This applies whether you are doing a question bank or timed exams. It’s important to be very familiar with your formula book, especially what formulas/content isn’t on it.

  • Learn all the permittable tricks you can do with your calculator.

Especially for Specialist Mathematics and Mathematical methods, your graphics calculator will save you lots of time and get rid of silly mistakes from working out in your technology-active paper. This includes utilising tables, graphs, equation solver and more features to complete questions. For example, if you are doing simultaneous equations, it may be more efficient to graph both equations and find the intercept of the two.

  • Try to snag some extra marks even if you don’t know how to complete a question.

This could involve drawing a diagram, writing down the appropriate formula and completing certain calculations. You are more likely to face this in complex unfamiliar questions that may also be worth a substantial number of marks (6 to 10) and if you are able to attain some marks these will help boost your overall score. This also includes guessing or conditionally guessing (between two or three options) if you are stuck on a multiple-choice question.

FAQs

How much is the QCE Maths external exam worth?

For all mathematics subjects the external exams, Paper 1 and Paper 2 are worth a combined 50% of your score for that subject. For General Mathematics Paper 1 is worth 30% and Paper 2 is worth 20% of your overall grade in the subject. Whereas, for Specialist Mathematics and Mathematical Methods Paper 1 and 2 are equally weighted at 25% each of your overall grade in the respective subject.

What should I do on the night before my Math exam?

It’s important to take it easy and stay in a “relaxed” state of mind. The night before you may do some questions just to keep you on your toes and look over a topic that you may not feel overly confident on, but it’s recommended to do an activity that isn’t stressful and relaxes you (e.g an episode of a tv show, watch some TV, have a chat with friends/family, etc). Try and go to sleep at an appropriate time, achieving a full 8 hours.

What do I do if I come across a question I can’t do straight away?

The best thing to do is mark the question/page and skip it to a question you are able to do, especially if this occurs earlier on in your exam. It’s important to stay as relaxed as possible and not to panic, you may need to take some deep breaths and then resume. This ensures you’re in the right headspace to answer questions as accurately as possible. 

Want more personalized study guidance to help drastically improve your marks? A private tutor can make the biggest difference!

Written by KIS Academics Tutor for QCE Specialist Mathematics and Mathematical Methods, Ragulan Gnanavel. He also provides assistance for Physics, English and Modern History assignments. Ragulan is currently pursuing a Bachelor of Actuarial Studies and a Bachelor of Commerce at UNSW. He has outstanding credentials as a tutor, and you can view Ragulan’s profile here and request him as a tutor.