2026 HSC Prep Checklist (all booklets)

 The 2026 HSC Maths preparation cycle is underway for NSW Year 12 students. Whether you are sitting Extension 1, Extension 2, or both, a structured checklist beats random past paper grinding.

Extension 1 revision checklist

• ☐ Trigonometry — HSC Trigonometry
• ☐ Polynomials — HSC Polynomials Extension 1
• ☐ Induction — HSC Induction
• ☐ Vectors — HSC Vectors
• ☐ Probability — HSC Probability
• ☐ Distributions — HSC Distributions
• ☐ Integrals — HSC Integrals

Extension 2 revision checklist

• ☐ Complex numbers — HSC Complex Numbers
• ☐ Combinatorics — HSC Combinatorics
• ☐ Inequalities — HSC Inequalities
• ☐ Mechanics — HSC Mechanics
• ☐ Differential equations — HSC Differential Equations
• ☐ Polynomials — HSC Polynomials
• ☐ Proofs — HSC Proofs
• ☐ Hard problems — HSC Last Resorts

Shared resources

• HSC Sequences — Advanced and Extension 1
• HSC Functions — all courses
• HSC Collections — mixed past paper practice

Start here

Every booklet is free, NESA-aligned, and available at Vu's Maths Hub. Extension 1 past papers, Extension 2 worked solutions, HSC Maths revision notes, and a genuine tutoring alternative — all in one place for NSW students preparing for the 2026 HSC Mathematics exams.

Bookmark: https://vumaths.com/

Proof Techniques

 Proof is the language of higher mathematics — and a significant part of both HSC Maths Extension 1 and Extension 2. NESA expects clear, logical arguments: direct proof, proof by contradiction, proof by contrapositive, and mathematical induction.

Proof methods you must know

• Direct proof — assume P, derive Q step by step
• Proof by contradiction — assume ¬Q, derive a contradiction
• Proof by contrapositive — prove ¬Q → ¬P instead of P → Q
• Mathematical induction — base case, inductive assumption, inductive step
• Combinatorial proof — counting arguments (Extension 2)

Proof booklets

HSC Proofs on Vu's Maths Hub covers proof structure, rigour, and strategies with proof by contradiction examples for Extension 1 and 2.

For induction specifically: HSC Induction — HSC mathematical induction proofs for divisibility, inequalities, and summations.

Proof in context

Proof skills appear in HSC Combinatorics, HSC Inequalities, and HSC Polynomials. Harder proof questions: HSC Last Resorts.

Free NESA-aligned HSC Maths booklets — your tutoring alternative for NSW Year 12 proof revision at vumaths.com.

Inequalities Extension 2

 HSC inequalities Extension 2 is a topic where knowing the right technique makes the difference between a one-line proof and a dead end. AM-GM, Cauchy-Schwarz, and clever algebraic manipulation appear regularly in Extension 2 exams and in harder past paper questions.

Essential inequality tools

• AM-GM inequality — arithmetic mean ≥ geometric mean for non-negative reals
• Cauchy-Schwarz inequality — (Σaᵢbᵢ)² ≤ (Σaᵢ²)(Σbᵢ²)
• Triangle inequality for complex numbers and vectors
• Proof techniques for inequalities — substitution, homogenisation, convexity arguments
• Connection to induction — proving inequalities by mathematical induction

Inequalities booklet

HSC Inequalities on Vu's Maths Hub covers common techniques, classic results, and worked examples for Extension 2 preparation.

Related revision

• HSC Induction — inequality proofs by induction
• HSC Proofs — proof structure and rigour
• HSC Last Resorts — creative approaches to hard inequality problems

Extension 2 worked solutions, free HSC Maths revision notes — vumaths.com.

Integrals and Calculus

 HSC integrals and calculus applications are tested across Advanced, Extension 1, and Extension 2. Extension students face harder integration — substitution, integration by parts, partial fractions, and volumes of solids of revolution.

Integration techniques to master

• Standard integrals and reverse chain rule
• Trigonometric integrals — double angle, t-substitution
• Integration by parts — LIATE rule for choosing u and dv
• Partial fractions for rational functions
• Definite integrals — areas, volumes of revolution, arc length
• Improper integrals (Extension 2)

Integrals booklet

HSC Integrals on Vu's Maths Hub covers integration techniques and applications with full Extension 1 and Extension 2 worked solutions.

Calculus across the course

Integration connects to:

• HSC Differential Equations — solving ODEs by integration
• HSC Mechanics — displacement from velocity, velocity from acceleration
• HSC Trigonometry — trig integrals
• HSC Functions — areas between curves

Free NESA-aligned HSC Maths booklets — past paper practice and tutoring alternative at vumaths.com.

Sequences and Series

 HSC sequences and series form a foundation for both Mathematics Advanced and Extension 1. Students work with arithmetic and geometric sequences, sigma notation, recurrence relations, and convergence — skills that also support mathematical induction proofs.

Key concepts

• Arithmetic sequences — common difference, nth term, sum of n terms
• Geometric sequences — common ratio, nth term, sum to n terms and infinity
• Sigma (Σ) notation — manipulating sums and splitting series
• Recurrence relations — defining terms recursively
• Financial mathematics applications (Advanced course overlap)

Sequences booklet

HSC Sequences on Vu's Maths Hub covers arithmetic and geometric series, sigma notation, and recurrence relations with worked examples.

Connected topics

Sequences link directly to HSC Induction (proving summation formulas), HSC Functions (sequences as functions on ℕ), and HSC Combinatorics (binomial series).

For mixed revision: HSC Collections. Free HSC Maths revision notes for NSW Year 12 at vumaths.com.

Differential Equations Extension 2

 HSC differential equations Extension 2 asks you to model real-world situations with first-order ordinary differential equations, then solve them using separation of variables, integrating factors, or substitution techniques.

What Extension 2 expects

• Formulating differential equations from word problems
• Separation of variables — dy/dx = f(x)g(y)
• First-order linear ODEs and integrating factors
• Direction fields and qualitative behaviour of solutions
• Applications: growth and decay, cooling, mixing, resisted motion

Differential equations booklet

HSC Differential Equations on Vu's Maths Hub provides methods, modelling examples, and step-by-step Extension 2 worked solutions.

Study alongside

• HSC Mechanics — many mechanics problems reduce to ODEs
• HSC Integrals — integration techniques for solving ODEs
• HSC Functions — understanding solution curves

Free NESA-aligned HSC Maths booklets for NSW Year 12 — Extension 2 past paper practice and revision at vumaths.com.

Trigonometry Extension 1

 HSC trigonometry Extension 1 goes well beyond SOHCAHTOA. Students must master compound angle formulas, double angle identities, trig equations over specified domains, and inverse trigonometric functions — often in multi-step exam questions.

Key trig topics for Extension 1

• Compound angle identities: sin(A ± B), cos(A ± B), tan(A ± B)
• Double angle formulas and t-formulae
• Solving trig equations — general solutions and restricted domains
• Inverse trig functions — domain, range, and compositions
• Trig graphs and transformations

Free trigonometry booklet

HSC Trigonometry on Vu's Maths Hub covers identities, equations, graphs, and inverse trig with worked examples for Extension 1 and Extension 2.

Trig connects everywhere

Trigonometry links to HSC Complex Numbers (Euler's formula), HSC Integrals (trig integration), and HSC Mechanics (projectile motion angles).

For mixed practice: HSC Collections. For past paper style revision across all topics, visit vumaths.com.

Extension 1 worked solutions, NESA-aligned HSC Maths revision notes — free for NSW students.

Polynomials Extension 1

 HSC polynomials Extension 1 builds algebraic fluency that underpins much of the Extension 1 and 2 courses. You need confident factorisation, remainder and factor theorem applications, and the ability to sketch polynomial graphs from their roots.

Core Extension 1 polynomial skills

• Factorisation — common factors, grouping, sum and difference of cubes
• Remainder theorem and factor theorem
• Division of polynomials — long division and equating coefficients
• Graph sketching — turning points, inflection, multiplicity of roots
• Solving polynomial equations and inequalities

Dedicated Extension 1 booklet

HSC Polynomials Extension 1 on Vu's Maths Hub covers factorisation, remainder theorem, and polynomial graphs with worked examples.

Extension 2 polynomials

When you move to Extension 2, the algebra gets harder — complex roots, conjugate pairs, and relationships between coefficients and roots. See HSC Polynomials and HSC Complex Numbers.

Also useful: HSC Functions for transformations and HSC Induction for polynomial identities proved by induction.

NESA-aligned, free HSC Maths booklets — your tutoring alternative for NSW Year 12.

Vectors Extension 1 & 2

 HSC vectors appear in both Extension 1 and Extension 2, with increasing depth. Extension 1 introduces 2D vectors and basic applications; Extension 2 extends to 3D geometry, lines and planes, and the cross product.

Extension 1 vs Extension 2 vectors

Extension 1: Vector addition, scalar multiplication, dot product, projections, and geometric applications in 2D.

Extension 2: 3D vectors, cross product, equations of lines and planes, intersections, distances, and angles between lines and planes.

Vectors booklet

HSC Vectors on Vu's Maths Hub covers geometric and algebraic methods with worked solutions for both Extension 1 and Extension 2 level problems.

Vectors in other topics

Vectors are essential for HSC Mechanics (forces and motion) and connect to HSC Complex Numbers (complex numbers as 2D vectors).

Also review HSC Trigonometry for angle calculations and HSC Collections for mixed exam-style vector questions.

Free HSC Maths revision notes and Extension 1 & 2 worked solutions at vumaths.com.

Mechanics Extension 2

 HSC mechanics Extension 2 applies calculus and vectors to physical situations — motion under gravity, resisted motion, forces on inclined planes, and projectile trajectories. It is one of the most applied topics in the Extension 2 course.

What to master

• Vector kinematics — displacement, velocity, acceleration as vectors
• Newton's laws applied to particles and connected systems
• Projectile motion — parametric equations, range, maximum height
• Resisted motion — exponential decay models, terminal velocity
• Setting up and solving differential equations from physical models

Free mechanics booklet

HSC Mechanics on Vu's Maths Hub covers vectors, motion, forces, and modelling with projectile motion worked examples and resisted motion HSC questions.

Related booklets

Mechanics relies heavily on:

• HSC Vectors — dot product, cross product, 3D geometry
• HSC Differential Equations — first-order ODEs from physical models
• HSC Integrals — integration techniques for motion problems

Extension 2 past paper practice with NESA-aligned worked solutions — free at vumaths.com.

Complex Numbers Extension 2

 HSC complex numbers Extension 2 introduces a number system beyond the real line. Students work with z = a + bi, plot points on the Argand diagram, convert between Cartesian and modulus-argument form, and apply De Moivre's theorem to powers and roots.

Topics covered in the HSC

• Arithmetic of complex numbers — addition, multiplication, conjugates
• Modulus and argument; modulus-argument (polar) form
• Argand diagram geometry — loci, regions, and transformations
• De Moivre's theorem — finding powers and nth roots of complex numbers
• Connection to polynomials — complex roots and conjugate pairs

Revision resources

The HSC Complex Numbers booklet at Vu's Maths Hub provides algebra, geometry, and application problems with full worked solutions.

Complex numbers link directly to HSC Polynomials (roots in ℂ) and HSC Trigonometry (Euler's formula connections).

Exam tips

Always sketch the Argand diagram. Convert to modulus-argument form before applying De Moivre. Check that your roots are evenly spaced around a circle.

Extension 2 worked solutions, NESA-aligned content, and free HSC Maths booklets — everything at vumaths.com.

Combinatorics Extension 2

 HSC combinatorics Extension 2 tests your ability to count arrangements, selections, and partitions — often under exam pressure. One miscount in a combinatorial argument can invalidate an entire proof, so systematic methods matter.

Key combinatorics concepts

• Fundamental counting principle and multiplication rule
• Permutations and combinations — when order matters vs when it does not
• Binomial coefficients and Pascal's triangle identities
• Binomial theorem and expansion exercises
• Classic Extension 2 counting problems — circular arrangements, restrictions, inclusion-exclusion

Free combinatorics booklet

HSC Combinatorics on Vu's Maths Hub covers counting principles, permutations, combinations, and HSC Extension 2 counting problems with step-by-step worked solutions.

Combinatorics in context

Combinatorics often appears alongside proof questions. Review HSC Proofs and HSC Induction for Extension 1 proof skills that transfer to Extension 2.

For mixed past paper practice, try HSC Collections or the harder problems in HSC Last Resorts.

NESA-aligned, free, and built for NSW Year 12 Mathematics students — your HSC tutoring alternative for Extension 2 combinatorics revision.

Mathematical Induction

 HSC mathematical induction is one of the most distinctive Extension 1 topics — and one of the most feared. Students must prove statements about natural numbers using a base case, an inductive assumption, and an inductive step. Get the structure wrong and you lose marks even if the maths is correct.

What induction questions look like

Extension 1 induction problems typically involve:

• Proving divisibility (e.g. "show that 7ⁿ − 1 is divisible by 6")
• Proving inequalities (e.g. "show that 2ⁿ > n² for n ≥ 5")
• Proving summation formulas (e.g. sums of squares or cubes)
• Strong induction variants for harder questions

Dedicated induction booklet

The HSC Induction booklet on Vu's Maths Hub walks through patterns, inequalities, and divisibility proofs with full worked examples — exactly the kind of HSC mathematical induction proofs NESA assesses.

Pair it with HSC Proofs for broader proof techniques including direct proof and proof by contradiction.

Related Extension 1 topics

Induction connects to HSC Sequences (summation and series) and HSC Polynomials Extension 1 (algebraic manipulation in inductive steps).

Free Extension 1 worked solutions, NESA-aligned revision, and past paper practice — all at vumaths.com.

Year 12 Maths NSW Study Plan

 Year 12 Maths NSW is intense — especially if you are taking Extension 1, Extension 2, or both alongside other HSC subjects. A structured study plan beats last-minute cramming every time.

Term-by-term revision plan

Term 4 (Year 11 → 12 transition): Review Advanced foundations. Read HSC Functions and HSC Sequences.

Term 1 Year 12: Focus on Extension 1 core topics — HSC Trigonometry, HSC Polynomials Extension 1, and HSC Induction.

Term 2: Extension 2 topics if applicable — HSC Complex Numbers, HSC Combinatorics, HSC Vectors.

Term 3: Mixed revision with HSC Collections and past paper practice.

Pre-exam: Target weak areas. Use HSC Last Resorts for Extension 2 hard problems.

Free resources for every NSW student

All booklets are free at Vu's Maths Hub — read in your browser, download for offline study, or print for class. No account needed.

Whether you are in Sydney, Newcastle, Wollongong, or anywhere in regional NSW, Year 12 Maths preparation starts with quality HSC Maths revision notes and Extension 1 & 2 worked solutions.

NESA Syllabus Alignment

 The NESA HSC Mathematics syllabus defines exactly what Extension 1 and Extension 2 students must know for the NSW HSC exam. Smart revision starts with the syllabus — then fills in depth with worked examples and past paper practice.

Three courses, one progression

NSW Year 12 Mathematics follows a clear pathway:

• Mathematics Advanced — core calculus, functions, statistics
• Extension 1 — adds induction, polynomials, vectors, distributions
• Extension 2 — adds complex numbers, combinatorics, mechanics, differential equations

NESA-aligned booklets for every syllabus topic

Vu's Maths Hub organises free HSC Maths booklets by topic, each mapped to the NESA syllabus outcomes. Key resources include:

• HSC Functions — Advanced, Extension 1, and Extension 2
• HSC Sequences — series and recurrence relations
• HSC Proofs — proof structure for Extension 1 and 2
• HSC Collections — mixed syllabus coverage for exam prep

Why alignment matters for SEO and study

When you search for "HSC Maths revision notes" or "Extension 2 worked solutions," you want material that matches what NESA actually assesses — not generic maths content from overseas curricula. Every booklet at vumaths.com is written specifically for NSW HSC Mathematics students.

Teachers can share a single link with their class; students get NESA-aligned past paper practice without paying for a tutoring alternative.

Extension 2 Past Papers & Worked Solutions

 Extension 2 exams are unforgiving. HSC Extension 2 past papers reveal the standard NESA expects, but the jump from Advanced to Extension 2 means many questions combine multiple topics — complex numbers with polynomials, combinatorics with proof, mechanics with differential equations.

Build topic depth before past papers

Do not rush into full papers until you have solid foundations in each Extension 2 strand. Revise with these NESA-aligned booklets:

• HSC Complex Numbers — Argand diagrams, modulus-argument form, De Moivre's theorem
• HSC Combinatorics — permutations, combinations, counting problems
• HSC Inequalities — AM-GM, Cauchy-Schwarz
• HSC Mechanics — projectile and resisted motion
• HSC Differential Equations — first-order ODEs and modelling
• HSC Polynomials — roots and complex conjugates

When standard methods fail

Extension 2 often rewards creative thinking. HSC Last Resorts covers harder problems where usual techniques stall — exactly the kind of questions that appear in the final questions of past papers.

Mixed revision for exam readiness

Combine topic booklets with HSC Collections for cross-topic Extension 2 practice. All resources are free at Vu's Maths Hub — your HSC tutoring alternative for NSW Year 12 Mathematics.

Extension 2 worked solutions, past paper practice, and NESA-aligned revision notes — everything you need for 2026 HSC Maths preparation in one place.

Extension 1 Past Papers & Worked Solutions

 HSC Extension 1 past papers are the gold standard for exam preparation — but doing a paper without checking your working is only half the job. The students who improve fastest pair past paper practice with topic revision and detailed worked solutions.

How to use past papers effectively

1. Revise the topic first. Before attempting a past paper question on induction or vectors, review the theory.
2. Time yourself. Simulate exam conditions for at least one paper per fortnight.
3. Mark harshly. Partial marks matter — show working for every step.
4. Fill gaps immediately. If you stumble on a topic, go straight to a focused booklet.

Topic booklets for Extension 1 gaps

When a past paper exposes a weak area, use these free resources on Vu's Maths Hub:

• Stuck on trig? → HSC Trigonometry
• Polynomial questions? → HSC Polynomials Extension 1
• Induction proofs? → HSC Induction
• Integration? → HSC Integrals
• Probability? → HSC Probability and HSC Distributions

Mixed Extension 1 practice

HSC Collections curates mixed-topic problems across Advanced and Extension 1 — a useful HSC Maths past papers alternative when you want exam-style variety without hunting through years of NESA papers.

Extension 1 worked solutions should explain why each step works, not just what the answer is. That is the standard across every booklet at vumaths.com.

Free HSC Maths Booklets (all 18 linked)

Looking for free HSC Maths booklets with worked solutions? Textbooks and tutoring can be expensive, but NSW Year 12 students deserve quality revision material without a paywall. That is why Vu's Maths Hub exists — a free online library of HSC Mathematics Extension 1 and Extension 2 booklets.

What you get

Every booklet on Vu's Maths Hub includes:

• Topic-focused write-ups aligned with the NESA HSC Mathematics syllabus
• Step-by-step worked examples and exam-style problems
• An in-browser PDF viewer — read online, download, or print
• Creative Commons licensing for teachers and students

All 18 booklets at a glance

• HSC Sequences
• HSC Trigonometry
• HSC Combinatorics
• HSC Differential Equations
• HSC Functions
• HSC Distributions
• HSC Polynomials Extension 1
• HSC Probability
• HSC Proofs
• HSC Polynomials
• HSC Induction
• HSC Inequalities
• HSC Complex Numbers
• HSC Integrals
• HSC Mechanics
• HSC Vectors
• HSC Collections
• HSC Last Resorts

A genuine HSC tutoring alternative

Whether you need Extension 1 worked solutions, Extension 2 past paper practice, or HSC Maths revision notes for the 2026 exam cycle, start at https://vumaths.com/. No sign-up required — just open a booklet and start studying.

HSC Maths Extension 2: Revision Roadmap

 HSC Maths Extension 2 is the most demanding mathematics course in the NSW Year 12 curriculum. Students tackling Extension 2 need strong algebra, calculus, and proof skills — plus access to quality worked solutions when usual methods fail.

Core Extension 2 topics

The NESA Extension 2 syllabus covers advanced material including:

• Complex numbers — Argand diagrams, De Moivre's theorem, loci
• Advanced polynomials — roots, complex conjugates, graph features
• Combinatorics — permutations, combinations, binomial identities
• Inequalities — AM-GM, Cauchy-Schwarz, and algebraic techniques
• Mechanics — projectile motion, resisted motion, forces
• Differential equations — first-order ODEs and mathematical modelling
• Harder integration and proof techniques

Free Extension 2 booklets on Vu's Maths Hub

Vu's Maths Hub publishes free HSC Maths booklets with comprehensive worked examples. Browse the full Extension 2 library:

• HSC Complex Numbers
• HSC Combinatorics
• HSC Inequalities
• HSC Mechanics
• HSC Differential Equations
• HSC Polynomials
• HSC Last Resorts — creative techniques for harder problems

Extension 2 past papers and mixed revision

Practise with HSC Collections for mixed-topic Extension 2 questions, or cross-reference shared topics like HSC Integrals, HSC Vectors, and HSC Trigonometry.

Extension 2 worked solutions should show every step — not just the final answer. That is exactly what these NESA-aligned booklets deliver for NSW HSC Mathematics students preparing for 2026.

HSC Maths Extension 1: Complete Study Guide

If you are studying HSC Maths Extension 1 in New South Wales, you already know the course moves fast. Extension 1 builds on Mathematics Advanced and introduces topics such as trigonometry, polynomials, mathematical induction, vectors, and probability distributions. The key to a strong result is not just doing more questions — it is revising topic by topic with clear worked solutions.

What Extension 1 covers

The NESA HSC Mathematics syllabus for Extension 1 includes:

• Further trigonometry — identities, equations, and inverse functions
• Polynomials — factorisation, remainder theorem, and graph sketching
• Mathematical induction — divisibility, inequalities, and summation proofs
• Vectors — 2D and introductory 3D geometry
• Probability and statistics — distributions, conditional probability
• Calculus — integration techniques and applications

Free Extension 1 revision booklets

Vu's Maths Hub offers free, NESA-aligned HSC Maths booklets you can read online or download. Each booklet focuses on one topic with step-by-step worked examples — a practical HSC tutoring alternative for NSW Year 12 students.

Start with these Extension 1 resources:

• HSC Trigonometry — identities, trig equations, and inverse functions
• HSC Polynomials Extension 1 — factorisation, remainder theorem, polynomial graphs
• HSC Mathematical Induction — proof by induction for inequalities and divisibility
• HSC Vectors — dot product, cross product, and 3D geometry
• HSC Distributions — binomial and normal distributions
• HSC Integrals — integration by parts and volumes of revolution
• HSC Probability — conditional probability and independence

Past paper practice without the paywall

Extension 1 past papers are essential, but worked solutions are not always easy to find. Use HSC Collections for mixed-topic exam-style problems across Advanced and Extension 1, or browse the full library at vumaths.com.

Whether you are in Sydney, regional NSW, or studying remotely, these free HSC Maths revision notes help you prepare for the 2026 HSC and beyond.