HSC Mathematics Extension 1 2027 Practice Pack 1
Year 12 · Comprehensive Practice Pack
Packs 1–4 follow the same course scope and learning structure, with different questions in each pack. Choose any pack to start.
90 practice questions
Worked solutions and marking guidance
294 practice marks · 2 PDF booklets
Learn as you go through Year 12
2027 Practice Packs are designed to support your learning from the start of your Year 12 course. Follow the topics you’re learning at school, work through the examples and practise at your own pace. You don’t need to finish the whole course before you start. Use the solutions and review guidance to understand mistakes, then return to mixed revision and course checks as you cover more topics.
Six Year 12 topic chapters, six additional worked examples, ninety independent questions, two selected-skill checks, mixed revision and a review sheet.
2027 edition · Year 12
Syllabus alignment: NESA Mathematics Extension 1 11–12 Syllabus (2024), Year 12; first HSC 2027
Topic practice across 6 chapter groups in the Year 12 course.
Syllabus baseline checked .Materials and format: Untimed practice using a NESA-approved scientific calculator and the Extension 1 2024 reference sheet. Required tables and digital-workshop instructions are supplied.
What is inside Pack 1?
Build your skills one topic at a time across the Year 12 HSC Mathematics Extension 1 course, then bring them together in checks and mixed revision.
- 6 topic sets with worked support, independent practice and self-checks.
- Two course checks and mixed revision, with the actual chapter counts listed below.
- Course-specific resource conditions stated in the question booklet.
- A printable skill review sheet to record what to revisit.
- Worked solutions, marking criteria, common errors and suggested next steps.
The 90-question total includes topic self-checks, course checks and mixed revision. The 6 worked examples are additional learning support.
Two PDFs in the pack
The question booklet and separate solutions booklet use matching question references.
Questions and learning activities
90 practice questions · 294 practice marks
Year 12 learning in one student booklet: worked examples, topic questions, two course checks, mixed revision and the review sheet.
Solutions and marking guidance
Worked solutions and marking criteria for every practice question, with common errors and suggestions for what to practise next.
Use this separate booklet to check your method after attempting the questions.
What Pack 1 covers
The contents below follow the order in the question booklet. Each topic set includes its final self-check.
- Check 1 — test the conditions1 question
- Proof by mathematical induction8 questions
- Introduction to vectors and two-dimensional motion20 questions
- Inverse trigonometric functions12 questions
- Further calculus skills16 questions
- Further applications of calculus20 questions
- Binomial laws and sampling distributions of the mean10 questions
- Mixed revision — connect and defend2 questions
- Check 2 — justify a new conclusion1 question
Total: 90 questions · 294 practice marks
How to use this resource
- Start with a topic you are learning at school. You do not need to finish the whole course first.
- Review the topic prerequisites and worked example. Attempt its practice questions, then the final self-check independently.
- Use the separate solutions and marking guidance to check your reasoning and record a next step on your review sheet.
- If you want a starting check, try Check 1 on topics you have already studied before viewing its solutions. Record untaught material as “Not yet studied”.
- Return to mixed revision and Check 2 as you cover more topics and complete directed practice. Compare your independent work on the selected topics.
This is self-marked topic practice for Year 12 HSC Mathematics Extension 1. Use it alongside your school materials. Practice marks are a review aid and do not predict an assessment grade or ATAR.
Start with the free sample
Pack 0 provides an independent topic-sized learning sequence with the same self-marking approach. Open its page to check current sample availability.
View Pack 0 — Free sample →Independent practice resource
Original Skill Align topic practice for the course and edition shown above. Skill Align is an independent publisher and is not affiliated with or endorsed by NESA. The course checks support self-review; they do not predict an external examination grade or provide a validated diagnostic score.