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Free Year 12 HSC Mathematics Extension 1 practice exams

12 free practice exams in the style of the real HSC test, each about 30 questions in 120 minutes, plus 10 minutes reading time, in 2 sections, calculator allowed.

954 free practice exams.

Practise Year 12 Mathematics Extension 1 now

The practice exams

  1. HSC Mathematics Extension 1 (Year 12) · Practice exam 1 (32 questions, 120 minutes)
  2. HSC Mathematics Extension 1 (Year 12) · Practice exam 2 (33 questions, 120 minutes)
  3. HSC Mathematics Extension 1 (Year 12) · Practice exam 3 (32 questions, 120 minutes)
  4. HSC Mathematics Extension 1 (Year 12) · Practice exam 4 (30 questions, 120 minutes)
  5. HSC Mathematics Extension 1 (Year 12) · Practice exam 5 (30 questions, 120 minutes)
  6. HSC Mathematics Extension 1 (Year 12) · Practice exam 6 (29 questions, 120 minutes)
  7. HSC Mathematics Extension 1 (Year 12) · Practice exam 7 (33 questions, 120 minutes)
  8. HSC Mathematics Extension 1 (Year 12) · Practice exam 8 (33 questions, 120 minutes)
  9. HSC Mathematics Extension 1 (Year 12) · Practice exam 9 (32 questions, 120 minutes)
  10. HSC Mathematics Extension 1 (Year 12) · Practice exam 10 (30 questions, 120 minutes)
  11. HSC Mathematics Extension 1 (Year 12) · Practice exam 11 (30 questions, 120 minutes)
  12. HSC Mathematics Extension 1 (Year 12) · Practice exam 12 (29 questions, 120 minutes)

Try a question

How many distinct solutions does sin(7x) + sin(3x) = 0 have for 0 ≤ x ≤ 3π/2?

  1. 8
  2. 10
  3. 11
  4. 14
Answer

C. 11. Using the sum-to-product identity gives 2sin(5x)cos(2x) = 0. The equation sin(5x) = 0 gives x = kπ/5 for k = 0, 1, …, 7: eight solutions. The equation cos(2x) = 0 gives x = π/4, 3π/4, 5π/4: three solutions. The two sets do not overlap, so there are 11 distinct solutions.

What the real test covers

The Higher School Certificate is the Year 12 qualification in New South Wales, awarded by NESA. The written HSC exams are held in October and November.

Each practice exam: about 30 questions in 120 minutes, plus 10 minutes reading time, in 2 sections, calculator allowed.

Kinds of question: 32% multiple choice, 18% short answer, 49% longer written answers.

Topics in these practice exams

How to prepare with ExamUp

  1. Warm up by topic. Do 10 Mathematics Extension 1 questions at a time in Quick practice: each answer is checked straight away, with no timer and no sign-up.
  2. Sit one whole paper. Do a full practice exam in one go, timed like the real HSC paper, so the day itself holds no surprises.
  3. Fix what you missed. Your results show where the marks went, topic by topic. Practise just the questions you got wrong, with an explanation for each.
  4. Go again a week later. Do another paper and compare. A free account keeps every result, and a parent can follow along live.

Quick questions

Are these Year 12 HSC Mathematics Extension 1 practice exams free?
Yes. All 12 practice exams here are free, with no plan, trial or card. You can try a question on this page and practise by topic without an account; a free account keeps your results.
How long is each practice exam?
Each one is about 30 questions in 120 minutes, plus 10 minutes reading time, in 2 sections, calculator allowed.
Are these the real HSC papers?
No. ExamUp is independent and is not connected with NESA (the NSW Education Standards Authority). Every question is written new in the style of the real HSC papers. Links to the official past papers are on our Past papers page.
What topics do the questions cover?
Most often: Vectors, The Binomial Distribution, Further Integration, Differential Equations, Working with Functions. That is from the questions in these practice exams.
How are the answers marked?
Multiple-choice and short answers are marked the moment you finish, each with an explanation. Longer written answers are marked by the ExamUp team against a marking guide.

More practice

All HSC practice · Every exam · Official past papers