Out with the old and in with the new. Last year, the new Mathematics Extension 1 syllabus was examined in the HSC for the very first time. This new syllabus replaced a decades-old curriculum that had been in action at least since 1982.

As with any syllabus revamp, one of the biggest problems which students will face is the redundancy of past papers. This is especially true for a subject like Maths Ext 1, where past papers are by far the most effective way to study for the course.

Fear not, because past papers have not been rendered completely useless. In fact, there are many subject areas from days gone by which are still being examined under the new syllabus. By knowing which topics have changed and which topics have stayed the same across the syllabus switch, you can maximise the usefulness of past papers and make the most out of all the past HSC resources which NESA has provided.

Here’s a quick guide: Remember that maths is one of the few subjects in the HSC where the Year 11 course is explicitly tested in the final exam — so don’t neglect your Year 11 topics!

WHAT’S STAYED THE SAME

Functions (Yr 11)

The majority of the subtopics under this topic has stayed the same — including inequalities, polynomials, inverse functions and parametric representation.

Trigonometry (Yr 11)

The majority of this topic has not changed — inverse trigonometric functions, compound and angle formulae as well as the t-formulae were all tested in the old syllabus too.

Calculus (Yr 11)

The Year 11 calculus topic has been simplified but you can still find motion, exponential growth & decay and related rates of change questions in old syllabus past papers.

Combinatorics (Yr 11)

The permutations combinations subtopic is basically the same, with a few minor tweaks. The binomial theorem subtopic has been simplified quite a bit compared to the old syllabus but is still present.

Mathematical Induction (Yr 12)

Mathematical Induction used to be in the old syllabus as well. The new syllabus has simplified the topic and moved the harder content to Ext 2, but you can still do many of the old syllabus induction questions.

Projectile Motion (Yr 12)

The old syllabus still had projectile motion, although we didn’t formally use a vector approach to notate the equations of motion back then.

Trigonometry (Yr 12)

Has not changed. Auxiliary angle method, solving trigonometric equations using angle formulae and trigonometric identity proofs were all features of the old syllabus.

Calculus (Yr 12)

About half of the topic is the same. Integration by substitution, standard integrals that led to inverse trigonometric results, and the primitive of sin^2x and cos^2x were all tested in the old syllabus too.

WHAT’S GONE

Circle Geometry

Gone 🙁

Angles Between Two Lines

Gone 🙁

Internal and External Division of a Line

Gone 🙁

Harder Parametric Equations

Gone 🙁 New syllabus parametric equations should be much easier.

Velocity and Acceleration as a Function of x

Moved to the Mechanics topic in the new Maths Ext 2 syllabus.

Simple Harmonic Motion

Ditto.

Harder Mathematical Induction Proofs

Harder mathematical induction proofs (such as ones that featured inequalities, a starting integer that isn’t n = 1 , or integers that don’t increase by 1) have been moved to the new Maths Ext 2 course.

Iterative Methods of Approximating the Roots of a Polynomial Equation

Halving the interval? Newton’s method? Don’t need to know them anymore.

WHAT’S NEW

Graphical Relations (Yr 11 Functions)

Asked to graph y = |f (x)| or y = f(x) + g(x) etc.? This subtopic is new to Maths Ext 1. It was previously examined in the old Maths Ext 2 syllabus so you can still find past HSC questions by browsing the Extension 2 papers instead.

Product to Sums Formulae (Yr 11 Trigonometry)

The trigonometric product to sums/differences formulae were not formally in the old syllabus.

Pigeonhole Principle (Yr 11 Combinatorics)

The pigeonhole principle is new.

False Proofs by Mathematical Induction (Yr 12 Proof)

Recognising errors in false proofs is a new syllabus dot point under the mathematical induction topic.

Vectors (Yr 12)

This entire topic is new to the course and has never been tested before, except for the projectile motion subtopic. However, vector approach/model projectile motion questions have not been asked before.

Volumes of Solids of Revolution (Yr 12 Calculus)

Strangely enough, this topic used to be in both the Maths Advanced (2U) and the Maths Extension 2 (4U) paper, so peruse past papers for them instead. Be mindful that the old syllabus Ext 2 Volumes of Solids of Revolution questions may require techniques which you have not learnt (such as the method of cylindrical shells).

Differential Equations (Yr 12 Calculus)

Asked about slope fields, separation of variables or logistic equations? This subtopic is new.

Statistical Analysis (Yr 12)

This entire topic is new to the course and has never been tested before.