2021 paper · worked-solution library
HSC Mathematics
Extension 1 answers
31 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 2021 NSW HSC Mathematics Extension 1 examination. The source examination material is © NESA.
Multiple choice · Questions 1–10
vectors
1 markQuestion 2advanced trig identities
1 markQuestion 3polynomial roots
1 markQuestion 4differential equations
1 markQuestion 5vectors
1 markQuestion 6binomial distribution
1 markQuestion 7advanced trig equations
1 markQuestion 8coordinate geometry
1 markQuestion 9inverse trigonometric functions
1 markQuestion 10pigeonhole principle
1 markWritten response · Questions 11–14
vectors
1 markQuestion 11(b)combinatorics
2 marksQuestion 11(c)antidifferentiation
3 marksQuestion 11(d)combinatorics
1 markQuestion 11(e)rates motion
2 marksQuestion 11(f)inverse trigonometric functions
2 marksQuestion 11(g)advanced trig equations
3 marksQuestion 11(h)polynomial roots
2 marksQuestion 12(a)differential equations
1 markQuestion 12(b)differential equations
4 marksQuestion 12(c)mathematical induction
3 marksQuestion 12(d)graph transformations
6 marks · linked parts kept togetherQuestion 13(a)volumes of revolution
3 marksQuestion 13(b)vector motion
4 marksQuestion 13(c)definite integrals areas
3 marksQuestion 13(d)advanced trig identities
4 marks · linked parts kept togetherQuestion 14(a)vectors
3 marksQuestion 14(b)differential equations
4 marksQuestion 14(c)vectors
4 marks · linked parts kept togetherQuestion 14(d)normal distribution
3 marksQuestion 14(e)inverse functions
2 marksPaper composition
What the 2021 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 |
|---|---|---|---|
| Differential equation | Q4, Q12(a), Q12(b), Q14(b) | 10 | 14% |
| Vectors | Q1, Q5, Q11(a), Q14(a), Q14(c) | 10 | 14% |
| Graph transformations | Q12(d) | 6 | 9% |
| Trigonometric identity | Q2, Q13(d) | 5 | 7% |
| Trigonometric equation | Q7, Q11(g) | 4 | 6% |
| Vector motion | Q13(b) | 4 | 6% |
| Antidifferentiation | Q11(c) | 3 | 4% |
| Combinatorics | Q11(b), Q11(d) | 3 | 4% |
| Definite integral | Q13(c) | 3 | 4% |
| Inverse trigonometric functions | Q9, Q11(f) | 3 | 4% |
| Mathematical induction | Q12(c) | 3 | 4% |
| Normal distribution | Q14(d) | 3 | 4% |
| Polynomial roots | Q3, Q11(h) | 3 | 4% |
| Volume of revolution | Q13(a) | 3 | 4% |
| Inverse function | Q14(e) | 2 | 3% |
| Rates of change | Q11(e) | 2 | 3% |
| Binomial distribution | Q6 | 1 | 1% |
| Coordinate geometry | Q8 | 1 | 1% |
| Pigeonhole principle | Q10 | 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 9 question groups identified as using a graph, chart, direction field or diagram, representing 24 marks.
| Question | Marks |
|---|---|
| Question 7 | 1 |
| Question 8 | 1 |
| Question 9 | 1 |
| Question 12(a) | 1 |
| Question 12(b) | 4 |
| Question 12(d) | 6 |
| Question 13(a) | 3 |
| Question 13(c) | 3 |
| Question 14(c) | 4 |
| Total | 24 |