2020 paper · worked-solution library
HSC Mathematics
Extension 1 answers
25 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 2020 NSW HSC Mathematics Extension 1 examination. The source examination material is © NESA.
Multiple choice · Questions 1–10
quadratic inequalities
1 markQuestion 2inverse functions
1 markQuestion 3inverse trigonometric functions
1 markQuestion 4vectors
1 markQuestion 5polynomial graphs
1 markQuestion 6vectors
1 markQuestion 7differential equations
1 markQuestion 8combinatorics
1 markQuestion 9vectors
1 markQuestion 10rates motion
1 markWritten response · Questions 11–14
polynomial roots
3 marks · linked parts kept togetherQuestion 11(b)vectors
3 marksQuestion 11(c)graph transformations
3 marksQuestion 11(d)advanced trig equations
4 marksQuestion 11(e)differential equations
2 marksQuestion 12(a)mathematical induction
3 marksQuestion 12(b)binomial distribution
3 marks · linked parts kept togetherQuestion 12(c)pigeonhole principle
2 marksQuestion 12(d)advanced trig identities
3 marksQuestion 12(e)differential equations
3 marksQuestion 13(a)differentiation techniques
5 marks · linked parts kept togetherQuestion 13(b)volumes of revolution
4 marksQuestion 13(c)inverse trigonometric functions
7 marks · linked parts kept togetherQuestion 14(a)combinatorics
8 marks · linked parts kept togetherQuestion 14(b)advanced trig identities
7 marks · linked parts kept togetherPaper composition
What the 2020 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 |
|---|---|---|---|
| Trigonometric identity | Q12(d), Q14(b) | 10 | 14% |
| Combinatorics | Q8, Q14(a) | 9 | 13% |
| Inverse trigonometric functions | Q3, Q13(c) | 8 | 11% |
| Differential equation | Q7, Q11(e), Q12(e) | 6 | 9% |
| Vectors | Q4, Q6, Q9, Q11(b) | 6 | 9% |
| Differentiation techniques | Q13(a) | 5 | 7% |
| Trigonometric equation | Q11(d) | 4 | 6% |
| Volume of revolution | Q13(b) | 4 | 6% |
| Binomial distribution | Q12(b) | 3 | 4% |
| Graph transformations | Q11(c) | 3 | 4% |
| Mathematical induction | Q12(a) | 3 | 4% |
| Polynomial roots | Q11(a) | 3 | 4% |
| Pigeonhole principle | Q12(c) | 2 | 3% |
| Inverse function | Q2 | 1 | 1% |
| Polynomial graphs | Q5 | 1 | 1% |
| Quadratic inequality | Q1 | 1 | 1% |
| Rates of change | 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 7 question groups identified as using a graph, chart, direction field or diagram, representing 18 marks.
| Question | Marks |
|---|---|
| Question 1 | 1 |
| Question 5 | 1 |
| Question 6 | 1 |
| Question 7 | 1 |
| Question 11(c) | 3 |
| Question 13(b) | 4 |
| Question 13(c) | 7 |
| Total | 18 |