SACE 2023: Expert guide to specialist maths exam

A maths whiz who got an ATAR of 99.5 offers expert advice on how to achieve the best results in specialist mathematics – including what to write down and bring in.

Westminster School Year 12 maths students Zoe Sibbons and Harry Gregg prepare for their exams. Picture: Brenton Edwards

Highly experienced Stage 2 Specialist Mathematics, Mathematical Methods and Physics tutor at TutorsSA, the leading tutoring institute in Adelaide, established over 10 years ago, Ryan Clarke has identified the best steps to maximise student potential in the critical Specialist Mathematics exam.

YOUR EXPERT GUIDE TO THE 2023 SACE EXAMS

In the Specialist Mathematics examination students will be allowed to bring in two A4 double sided sheets of handwritten notes.

These notes are a crucial component to completing an exam successfully and should contain all necessary formulas from throughout the year.

As the students get to write these sheets themselves it is key the sheets are made to be organised and easily readable.

Grouping formulas for each topic allows for easy retrieval upon reading an exam question and identifying its topic.

When writing the formula sheets, it is recommended to write the formulas using small text and to do so very neatly.

Two A4 double-sided sheets are a considerable amount of room so if all formulas are written to a small size this will then leave space for examples and diagrams.

Examples and diagrams take up a lot more space than formulas, however they can also provide a lot more detail.

For these reasons it is important to only include diagrams of what the student finds to be the most difficult concepts and for when the formulas must be used in conjunction with a diagram, or they would not make sense.

Three common mistakes of past years have been:

ROUNDING and using approximation when an exact answer is required. When a question in the exam requires an exact answer, the answer must be given in rational or irrational form.

When finding an exact answer there cannot be any rounding of values. This is true for all working steps and the final answer.

To ensure working steps are kept in exact form it is also best to write these values in rational or irrational form.

Tutors SA tutor Ryan Clarke. Picture: Supplied

When substituting working values into equations the whole value must be given, preferably in brackets to keep the order of operations and substitutions clear.

Most graphics calculators will have an option to convert values to exact form, but it may not work for more complicated solutions.

If the calculator is unable to convert an answer to exact form, the answer can still be double checked by typing it into the calculator.

The calculator will convert the exact value to a decimal which can then be compared with the working out done on the calculator.

If these values match to all decimal places, then this is likely the correct exact answer.

Be aware that most calculators will struggle to find the exact answer when calculating integrals.

In these cases, the calculator’s answer may only tend towards the exact solution.

NOT showing working out. Generally, the answer is only worth one mark, meaning a four-mark question requires the answer along with three steps of working out.

Each working mark is often when a key change is made during working out, for example fully expanding brackets or cancelling a variable.

This does not mean to only include the same number of working lines as the question is worth marks, but it does mean multiple lines together may still only be worth a single mark.

Two question types where working out is even more essential are ‘show that’ type questions and questions where the answer has already been provided.

Westminster School Year 12 maths students Zoe Sibbons and Harry Gregg prepare for their exams. Picture: Brenton Edwards

In ‘show that’ questions working out is worth majority of the marks and all working must be shown.

In some cases, the working out may be assisted by diagrams and written statements but this must be assessed on a question-by-question basis.

In questions where the answer has been given the marks are all for working out and remember each mark is a critical working step.

If the question provides a substitute answer, but not the correct final answer then the final answer is still worth a mark.

This may look like ‘If you were unable to find the answer for part (a) instead use 5.’ Do not confuse this for the correct final answer.

NOT using brackets. In the exam there will be many complicated working steps, making use of many operations.

While BEDMAS is still to be followed, it can often become easier to include brackets for more complex situations or where order would otherwise be ambiguous.

Some examples of where it would be important to use brackets are to show when the sum notation stops or which division to complete first when there are multiple divisions on top of one another.

These additional brackets are often just as important for written working out as they are to include when using the calculator.

As a final word of advice, get familiar with the calculator as it is a powerful tool that can do a lot more than many students may initially realise.

It is not required to clear the memory of the graphics calculator for the specialist exam, meaning additional information may be stored on the calculator for the exam.

Additionally pay close attention to conversion between radians and degrees, it is an easy mistake to use the wrong mode but is just as easy to avoid if kept in mind.

Most importantly good luck for the exam!

Ryan Clarke was advanced in mathematical subjects by a year at secondary school, allowing him to complete both specialist and methods studies at a Stage 2 level in year 11 before being accepted into a Head Start Scholarship with Adelaide University. Ryan achieved a raw ATAR of 98.4, selection rank of 99.95 was runner-up dux at his school with a high distinction in his scholarship studies. Ryan is a mathematics and physics tutor with Tutors SA, an Adelaide-based leading institute that provides private tuition from Reception to Year 12, including tuition for all core SACE subjects.