2025 paper · worked-solution library
HSC Mathematics
Extension 1 answers
32 dependency-safe solution groups, each followed by three fresh practice challenges and separate answer guides.
The question descriptions here are TestMum paraphrases of questions from the 2025 NSW HSC Mathematics Extension 1 examination. The source examination material is © NESA.
Multiple choice · Questions 1–10
absolute value inequalities
1 markQuestion 2vectors
1 markQuestion 3trigonometric substitution
1 markQuestion 4binomial distribution
1 markQuestion 5advanced trig equations
1 markQuestion 6inverse trigonometric functions
1 markQuestion 7differential equations
1 markQuestion 8vectors
1 markQuestion 9vectors
1 markQuestion 10inverse functions
1 markWritten response · Questions 11–14
inverse functions
2 marksQuestion 11(b)advanced trig equations
3 marksQuestion 11(c)advanced trig identities
2 marksQuestion 11(d)inverse trigonometric functions
2 marksQuestion 11(e)vectors
1 markQuestion 11(f)polynomial roots
2 marksQuestion 11(g)definite integrals areas
3 marksQuestion 12(a)rates motion
3 marksQuestion 12(b)volumes of revolution
2 marksQuestion 12(c)mathematical induction
3 marksQuestion 12(d)differential equations
3 marksQuestion 12(e)advanced trig equations
3 marks · linked parts kept togetherQuestion 13(a)differential equations
3 marksQuestion 13(b)combinatorics
2 marksQuestion 13(c)vector motion
4 marksQuestion 13(d)binomial distribution
4 marksQuestion 13(e)combinatorics
3 marks · linked parts kept togetherQuestion 14(a)pigeonhole principle
2 marksQuestion 14(b)vector motion
4 marksQuestion 14(c)vectors
3 marksQuestion 14(d)inverse trigonometric functions
3 marksQuestion 14(e)polynomial roots
3 marksPaper composition
What the 2025 paper tested
The paper contains 70 marks. This breakdown groups each dependency-safe question or linked part by its main mathematical idea, so students can see which areas received the greatest weighting.
| Question type | Where it appeared | Marks | Share |
|---|---|---|---|
| Vector motion | Q13(c), Q14(b) | 8 | 11% |
| Differential equation | Q7, Q12(d), Q13(a) | 7 | 10% |
| Trigonometric equation | Q5, Q11(b), Q12(e) | 7 | 10% |
| Vectors | Q2, Q8, Q9, Q11(e), Q14(c) | 7 | 10% |
| Inverse trigonometric functions | Q6, Q11(d), Q14(d) | 6 | 9% |
| Binomial distribution | Q4, Q13(d) | 5 | 7% |
| Combinatorics | Q13(b), Q13(e) | 5 | 7% |
| Polynomial roots | Q11(f), Q14(e) | 5 | 7% |
| Definite integral | Q11(g) | 3 | 4% |
| Inverse function | Q10, Q11(a) | 3 | 4% |
| Mathematical induction | Q12(c) | 3 | 4% |
| Rates of change | Q12(a) | 3 | 4% |
| Pigeonhole principle | Q14(a) | 2 | 3% |
| Trigonometric identity | Q11(c) | 2 | 3% |
| Volume of revolution | Q12(b) | 2 | 3% |
| Absolute value inequality | Q1 | 1 | 1% |
| Trigonometric substitution | Q3 | 1 | 1% |
| Total | 70 | 100% | |
Marks are counted once only. Linked “hence” parts remain together and are assigned to the shared main question type.
Visual-stimulus reconciliation
Questions containing visual material
This paper contains 5 question groups identified as using a graph, chart, direction field or diagram, representing 11 marks.
| Question | Marks |
|---|---|
| Question 7 | 1 |
| Question 9 | 1 |
| Question 11(d) | 2 |
| Question 12(a) | 3 |
| Question 14(b) | 4 |
| Total | 11 |