HSC Mathematics Extension 1 is the step up from Maths Advanced in New South Wales. It is a new course for students finishing Year 12 in 2027: a new syllabus starts in Term 4, 2026. This guide explains the exam, the Year 12 focus areas, worked examples and a calm plan for the year.
Key takeaways
- The HSC Extension 1 exam is 2 hours plus 10 minutes reading time, worth 70 marks.
- Section I has 10 marks of objective-response questions. Section II has 60 marks across 23 to 28 items.
- The 2024 syllabus is taught to Year 12 from Term 4, 2026. The first HSC exam on it is in 2027.
- Year 12 focus areas: proof by induction, vectors, inverse trig functions, further calculus skills, further applications of calculus, and the binomial distribution.
- Extension 1 students also sit the Advanced paper (or the Extension 2 paper).
What is HSC Maths Extension 1?
Quick answer: Mathematics Extension 1 is an extra NSW HSC maths course taken on top of Mathematics Advanced. It goes deeper into proof, calculus, vectors and probability. The HSC exam is 2 hours plus 10 minutes reading time and is worth 70 marks. From 2027 it is examined on the new 2024 syllabus set by NESA.
Extension 1 suits students who enjoy maths and want a stronger base for university courses in engineering, science, economics, maths or computing. It assumes everything in Mathematics Advanced. So a student who is shaky in Advanced should fix that first. Our HSC Maths Advanced guide covers that course and its new syllabus.
What is the HSC Extension 1 exam format?
NESA's exam specifications for the 2024 syllabus are:
| Part | Marks | What it looks like |
|---|---|---|
| Section I | 10 | Objective-response questions |
| Section II | 60 | 23 to 28 items; questions may have parts; at least one item worth 4 or 5 marks |
| Total | 70 | 2 hours + 10 minutes reading time |
A reference sheet is provided. NESA-approved calculators may be used.
A few points parents often miss:
- Advanced content is assumed. The exam focuses on Year 12 Extension 1 outcomes, but questions can use anything from Advanced and the Year 11 Extension 1 course.
- Questions can mix topics. NESA says questions may draw on knowledge from across the course. A single question might combine calculus and vectors, for example.
- Extension 1 students sit two maths papers. They take the Extension 1 paper and the Advanced paper. Extension 2 students take the Extension 1 and Extension 2 papers instead.
As with other HSC courses, the final HSC mark combines the school-based assessment mark and the exam mark.
What changes with the new 2024 syllabus?
The Mathematics Extension 1 11-12 Syllabus (2024) replaces the 2017 syllabus. The timeline is:
| Date | What happens |
|---|---|
| Term 4, 2026 | Year 12 teaching on the new syllabus begins |
| HSC 2027 | First HSC exam on the new syllabus |
This matters for practice. Past HSC papers are still very useful, but some older questions may test content that has moved or changed. Ask the teacher which past questions still match the new syllabus.
What are the Year 12 Extension 1 focus areas?
NESA lists six Year 12 focus areas:
- Proof by mathematical induction. Proving results about sums and divisibility, and spotting errors in false "proofs".
- Introduction to vectors. Vector notation, operations and their uses.
- Inverse trigonometric functions. Now placed in Year 12.
- Further calculus skills. Building on the calculus from Advanced.
- Further applications of calculus. Using calculus to model and solve problems.
- The binomial distribution and the sampling distribution of the mean.
For the detailed dot points in each area, read the syllabus on the NSW Curriculum website. Teachers follow it closely when they write school assessments.
Worked examples in the Extension 1 style
Example 1: Proof by induction
Prove that 1 + 3 + 5 + ... + (2n − 1) = n² for all integers n ≥ 1.
- Base case (n = 1): LHS = 1. RHS = 1² = 1. So the statement is true for n = 1.
- Assume the statement is true for n = k: 1 + 3 + ... + (2k − 1) = k².
- Prove for n = k + 1. Add the next term, 2(k + 1) − 1 = 2k + 1, to both sides.
- LHS = k² + (2k + 1) = k² + 2k + 1 = (k + 1)².
- This is the RHS for n = k + 1. So if it is true for n = k, it is true for n = k + 1.
- Conclusion: Since it is true for n = 1, by mathematical induction it is true for all integers n ≥ 1.
Markers want all three parts written clearly: base case, assumption, and the inductive step, plus a conclusion. Skipping the conclusion is a common way to lose a mark.
Example 2: Vectors
Question: Let a = (3, 4) and b = (2, −1). Find |a| and a · b.
- |a| = √(3² + 4²) = √25 = 5.
- a · b = (3)(2) + (4)(−1) = 6 − 4 = 2.
Since a · b is not 0, the vectors are not perpendicular. Many questions ask students to test for perpendicular vectors this way.
Example 3: Binomial probability
Question: A fair coin is tossed 5 times. Find the probability of exactly 2 heads.
- X ~ Bin(5, 0.5). Use P(X = r) = ⁿCᵣ pʳ (1 − p)ⁿ⁻ʳ.
- P(X = 2) = ⁵C₂ (0.5)² (0.5)³.
- ⁵C₂ = 10, and (0.5)⁵ = 1/32.
- P(X = 2) = 10/32 = 5/16 = 0.3125.
Students often forget the ⁿCᵣ part. Without it, the answer only counts one order of heads and tails.
What are the most common Extension 1 mistakes?
- Weak Advanced skills. Algebra, trig and calculus slips from Advanced cost marks in Extension 1.
- Incomplete induction proofs. No clear assumption, or no conclusion.
- Losing signs in vectors. Write each component on its own line.
- Not showing reasoning in the longer Section II items, where marks are given for each step.
- Rushing Section I. Ten marks of objective questions still need careful checking.
- Practising only one paper. Extension 1 students need to do well on both the Extension 1 and the Advanced papers.
A Year 12 Extension 1 study plan
| When | Focus |
|---|---|
| Term 4 (Year 12 starts) | Induction and vectors. Write one full proof each week. |
| Term 1 | Inverse trig functions, further calculus skills and applications. |
| Term 2 | Binomial distribution and sampling. First timed practice papers. |
| Term 3 | Trial HSC. Fix the topics that lost the most marks. |
| Final 6 weeks | Mixed Extension 1 and Advanced papers under exam time. |
| Last week | Reference sheet drills, mistake log review and good sleep. |
Keep a mistake log from the first week. Write the question, the mark lost and why. It becomes the best revision list for the trial and the HSC.
For students in Victoria, our VCE Maths Methods exam guide covers the closest Victorian course.
Want to know where your child stands before Year 12? Talk to an advisor and book a free demo class.
How 1-on-1 tutoring helps with HSC Maths Extension 1
At Asymptode, every class is live, online and 1-on-1. One mentor works with one student and follows the school's own syllabus and assessment dates. Here is how that helps with Extension 1:
- We fix Advanced first. The mentor checks the Advanced skills underneath each Extension 1 topic, so new content has a solid base.
- We teach how to write proofs. Induction and "show that" questions need clear, logical writing. The mentor reads each line and shows how to set it out.
- We watch every step. Many Extension 1 marks are lost to small method slips. A mentor sees them as they happen.
- Homework fits the gap. Worksheets are on the focus areas your child needs, checked by the same mentor.
- Parents see progress. You get short updates on what improved and what still needs practice.
- Every class is recorded, so your child can revise a method before an assessment task or the HSC.
We teach students across Australia online, at times that suit the family. See our fees or talk to an advisor to book a free demo class.
FAQ
How long is the HSC Maths Extension 1 exam?
The exam is 2 hours plus 10 minutes reading time. It is worth 70 marks.
How many marks is Section I in Extension 1?
Section I is worth 10 marks of objective-response questions. Section II is worth 60 marks.
When does the new Extension 1 syllabus start?
Year 12 teaching on the 2024 syllabus starts in Term 4, 2026. The first HSC exam on it is in 2027.
Do Extension 1 students also sit the Advanced exam?
Yes. Students enrolled in Extension 1 sit the Advanced paper as well. Students in Extension 2 sit the Extension 1 and Extension 2 papers instead.
Is a calculator allowed in HSC Extension 1?
Yes. NESA-approved calculators may be used, and a reference sheet is provided.
What topics are in Year 12 Extension 1?
The six Year 12 focus areas are proof by induction, introduction to vectors, inverse trigonometric functions, further calculus skills, further applications of calculus, and the binomial distribution and sampling distribution of the mean.