Maths Advanced or Extension 1: how to choose

If you are choosing between Maths Advanced and Extension 1, you are usually deciding whether to take Advanced on its own or add Extension 1. Advanced is a two-unit course; Extension 1 adds one unit and develops further mathematical arguments, proofs and models. NESA Extension 1 course requirements

Look at the work you enjoy and the feedback on recent attempts, then consider how much time you have and what you want to study later. Your working will usually tell you more about a difficulty than the test mark alone.

This guide covers the new courses examined from 2027. If you are considering a change within the 2026 cohort, check the rules for your current course with your school.

How the courses fit together

These descriptions and hours come from NESA's Advanced course information and Extension 1 course information. The hours describe the courses; the amount of homework you need will vary.

In Year 12, Extension 1 students sit its exam alongside Advanced or Extension 2, depending on their enrolment. Taking Extension 2 changes the combination. This article considers Advanced with or without Extension 1. NESA examination requirements

Two examples of the work

These original Plume exercises show some of the reasoning involved in each course. They are not NESA questions or entry tests, and two examples cannot establish the relative difficulty of the courses. Both include questions that require substantial reasoning.

Advanced: find the largest possible area

A rectangle has a perimeter of 28 cm. Find its largest possible area.

If one side is $x$ cm, the other is $14-x$ cm. The area is therefore

$$A(x)=x(14-x)=14x-x^2,\qquad 0<x<14.$$

Differentiating the area function gives

$$A'(x)=14-2x.$$

The derivative is zero at $x=7$. It is positive before 7 and negative after 7, so the area increases and then decreases. Its maximum is

$$A(7)=49\text{ cm}^2.$$

Both sides are 7 cm, making the rectangle a square. Substituting those dimensions into the perimeter gives 28 cm, which agrees with the question.

If you found the exercise difficult, identify the first step you could not complete. You may need practice expressing the second side in terms of $x$, forming the area function or explaining why the stationary point is a maximum. Optimisation is part of the new Advanced calculus outcomes.

Extension 1: prove a pattern by induction

Prove that the sum of the first $n$ positive odd integers is $n^2$ for every positive integer $n$.

First check $n=1$: the sum is $1=1^2$.

Next, assume the statement holds for an arbitrary positive integer $k$:

$$1+3+\cdots+(2k-1)=k^2.$$

Adding the next odd integer, $2k+1$, to both sides gives

$$1+3+\cdots+(2k-1)+(2k+1) =k^2+2k+1=(k+1)^2.$$

We have shown that if the statement holds for $k$, it also holds for $k+1$. Since it holds for 1, the argument applies successively to every positive integer.

Trying a few values of $n$ lets you notice the pattern. Induction explains why it continues beyond those examples. The method is part of the new Extension 1 Year 12 course, so it may be unfamiliar if you have not studied the topic. Consider whether the explanation makes sense to you and whether you want to understand why it works.

Discuss your recent work with your teacher

Bring two or three pieces of work, including an unfinished question and a correction you made after feedback. Ask your teacher where you need more practice with earlier content and where you are still learning a new method. Repeated algebra errors may affect both courses, while a slow first attempt at a proof may mean you need more guided practice with proof.

Agree on what you will try over the next few weeks. You might aim to solve a particular type of equation without help, explain each step in a proof or finish a mixed set in the available time. Those attempts will give you more to discuss than a mark on its own.

Your school's entry and continuation rules will also affect your options, so ask how they apply to you.

Compare the courses with your circumstances

Use the questions below to prepare for that conversation.

Check university prerequisites and assumed knowledge on the institution's own website. They describe different expectations, so record the exact wording for the course you are considering. A friend's choice of subjects may not meet your course's requirements.

You can use our HSC study timetable to see where regular practice would fit. Include assessments and other commitments before adding the extra sessions.

If you are considering dropping Extension 1

Identify the problem you hope the change will solve. You may need more time on Advanced content, help with one Extension topic, or a reduction in maths work so you can keep up with other subjects.

Discuss that problem with your teacher before changing your enrolment. Ask whether particular support or practice would help, when you need to decide, and how dropping the course would affect your remaining units and eligibility.

An extra unit does not guarantee a higher ATAR. Your performance still matters, as UAC explains in its scaling guidance. When weighing an expected scaling advantage, consider how well you are likely to learn the course.

Our 2027 Maths guide explains the syllabus changes in more detail. Plume's Maths Advanced and Extension 1 course pages describe the teaching available. Bring recent working if you would like to discuss which course you need help with.