What’s the point of two exams? What should I revise? And what even is a bound reference? All your questions will be answered here by a high achiever in VCE maths methods!

VCE Mathematical methods (maths methods) is one of the most popular STEM subjects, with many students completing it as a university course prerequisite, or even just out of interest. This subject is highly competitive despite its large cohort and can also be very challenging. In this blog, I will be explaining the course and its assessments, the exam, and tips and tricks for you to get the scores you’re aiming for!

**Assessments**

The VCE maths methods course is more condensed than other VCE maths courses such as specialist maths, as it doesn’t actually cover many topics but rather looks at all of the topics in depth. The topics studied (for the study design in 2023 onwards) are as follows:

- Functions, relations and graphs
- Polynomial, power, exponential, logarithmic and circular functions
- Properties of difference functions
- Transformation of functions

- Algebra, number and structure
- Inverses and composite functions
- Solving equations

- Calculus
- Differentiation and integration
- Optimisation and finding local maxima/minima
- Properties of derivatives, anti-derivatives and integrals

- Data analysis, probability, and statistics
- Discrete random variables
- Continuous random variables
- Statistical inference

Assessments will usually be a typical test-style SAC which focus on a certain area of study. Typically, the first and second areas of study are combined into a single SAC as a lot of the content will overlap (sometimes this may be divided into a two or three part SAC), whilst the other two areas of study are in two separate SACs. These SACs are often all tech-active, however, the use of technology depends on your teacher and class.

**The Exam**

The maths methods exam will consist of two parts; a 40 mark tech-free exam, and a 80 mark tech-active exam. The reason for this is to test your ability to do maths by hand, but also with the assistance of technology. The tech-free exam (exam 1) does not permit notes in the exam, however, a formula sheet will be provided. There are around 8 to 11 short answer questions, each testing a different concept. These questions often increase in difficulty, with the last question typically being the most difficult (and is typically a functions, algebra or calculus-based question).

The tech-active exam allows you to bring a “bound reference” (more information about this will be provided below), and you will also be provided with a formula sheet. Also, depending on your school, you will either bring a CAS calculator or be provided with a computer with the Mathematica program (version 12.0). This exam consists of 20 multiple choice questions, as well as 5 short answer questions with multiple parts. Multiple-choice questions will often test a certain concept and are often straightforward. On the other hand, short answer questions may test multiple skills and are much more challenging.

Typical short-answer questions will often require you to complete calculations, but in some cases, you may be asked to give reasoning for a solution or a concept. For example, in question 5 of the 2021 exam, you are required to perform various calculations with respect to the graph f(x) = sin(x/2)+cos(2x), where a graph of the function is provided. These different types of questions can be found within this question: firstly, questions 5a, b and c for example test simple concepts, and can be simply solved by examining the graph, performing a substitution (using a CAS or Mathematica) and using graph transformations. Next, question e is more complicated, and requires you to find the area under the graph of a similar function g(x) = sin(x/a) + cos(ax) which contains an unknown constant a. The aim of this is for you to recognise patterns within the first three questions in the function f(x), then apply this to a more general case g(x).

Question 5f will require you to give reasoning as to why the graph of g(x) cannot have a value of g which is greater than 2 or less than -2. Firstly, it would be helpful to see a general pattern for this when we change values of a. From the function itself, there are also some things that we can determine: first, the function g(x) is the addition of two functions sin(x/a) and cos(ax). We know that when we add functions, the values of the function when we substitute different values of x are added to give the resulting value g(x). For the graph of sin(x/a), the maximum y value is 1 and the minimum y value is -1 since the graph has an amplitude of 1. This is the same for cos(ax) which has a maximum y value of 1 and the minimum y value of -1. Note that the different periods of the functions do not affect their maximum and minimum values. Hence, if we added the maximum and minimum values of the functions sin(x/a) and cos(ax) respectively, we would get 2 and -2, which corresponds to the maximum and minimum values of g(x).

**Preparing the bound reference**

A bound reference is essentially a book containing all your notes that you will be allowed to bring into the tech-active exam. There are a few rules regarding your bound reference:

- It needs to be A4 size or smaller when closed (e.g. an A4 notebook or textbook of A4 size)
- Pages need to be permanently bound together on either the horizontal or vertical side
- Cannot have any fold-out pages or removable pages with perforations.

However, your bound reference can have as many pages as you want!

Most students will create their own bound reference with a notebook, and write their own notes about different concepts or how to utilise certain functions in CAS or Mathematica, and exemplar questions in the book. However, some will bind their own book containing practice exams, or bring a textbook. Note that if you choose to bring more than one notebook, they must be bound together into a “single” bound reference (using glue, tape or staples). More details regarding the bound reference can be found here on the VCAA website.

The bound reference is not meant to be used during reading time, however, it can be openly consulted during the rest of the time in the tech-active exam.

For those who are completing the CBE exam with Mathematica instead of CAS, you will be allowed to bring an additional digital bound reference if you would like. The digital bound reference must be a Mathematica nb file, and be contained on a USB, as you will not be using your own device, but rather a school device to complete your exam. Creating a digital bound reference is optional, however, many students find this helpful when recalling commands and functions. However, you may want to keep in mind that the larger you make your bound reference file, your calculation file for the exam may begin to lag.

**Exam preparation and advice**

Just like with all your other VCE subjects, exam preparation will begin from the very start of the year. For practice, I would always recommend past VCAA exams and the Excel Academics website, which will help consolidate your knowledge and provide you with valuable exam-style revision. Maths Methods is often considered to be “easier” than Specialist Maths since the study design contains fewer concepts, however, it is still a very challenging subject since it deeply tests your understanding of these concepts. Hence, if you are struggling to understand a certain concept, it is important to seek help from your friends, teachers and tutors until you do understand that concept. Since you will be heavily relying on technology in the tech-active exam, it is also important to be familiar with where to locate and how to use the different functions. You may find it helpful to write down this information in your bound reference.

Once you start approaching the end of the year, you can begin completing practice exams to get a feel of what the exam will be like. As there are two different exams, it is important to familiarise yourself with what may appear in the tech-free and tech-active exams. Additionally, since the probability topic is often more “straightforward” in the exam, you may also want to have a greater focus on the other areas of study. Probability questions in the exam require a good understanding of the concepts, however, they often will ask similar questions in each exam. Hence, you may find it helpful to do additional questions on the other topics on top of practice exams.

**Additional tips and tricks!**

As mentioned above, the methods exam does not contain much course content, but this actually makes a lot of the questions much harder since VCAA will expect a deeper understanding of the topics. Hence, make sure you completely familiarise yourself with the topics and ask for help if you are struggling to do so.

Also, when completing tech-free exam questions throughout the year as revision, attempt these questions with tech-free methods. Sometimes, it is very easy to think that you understand the question well and can quickly solve it with technology instead, however, this will slowly affect your ability to complete tech-free questions. Hence, even though the two exams are weighted differently, make sure that you are not only focusing on the tech-active side of the exam but also the tech-free exam.

Lastly, make sure that you are familiar with the commands and functions in your CAS or Mathematica. CAS and Mathematica contain many useful functions and commands aside from solely solving equations, graphing and doing probability calculations. Also, it is important to be familiar with these commands and functions as you will need to perform them quickly during the exam. As time is very limited and you will need to copy down certain calculations, spending too much time on your device can hinder your ability to complete the exam.

Hopefully, this guide has familiarized you with what to expect from the maths methods course and exam. Best of luck with your methods studies!

**Credits**

This blog was written by our tutor, Leonie. You can find her profile here.

*“My name is Leonie and I’m currently studying a Bachelor of Engineering and Arts at Monash University. Having recently completed VCE, I currently tutor physics, chemistry, maths and Japanese SL, with the hopes to help students make the most out of their studies and achieve the marks they are aiming for.”*