2022 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 2022 NSW HSC Mathematics Extension 1 examination. The source examination material is © NESA.
Multiple choice · Questions 1–10
inverse trigonometric functions
1 markQuestion 2graph transformations
1 markQuestion 3polynomial roots
1 markQuestion 4graph transformations
1 markQuestion 5coordinate geometry
1 markQuestion 6vectors
1 markQuestion 7combinatorics
1 markQuestion 8vectors
1 markQuestion 9inverse functions
1 markQuestion 10differential equations
1 markWritten response · Questions 11–14
vectors
2 marksQuestion 11(b)antidifferentiation
3 marksQuestion 11(c)combinatorics
2 marksQuestion 11(d)vectors
2 marksQuestion 11(e)advanced trig equations
3 marksQuestion 11(f)absolute value inequalities
3 marksQuestion 12(a)differential equations
2 marksQuestion 12(b)pigeonhole principle
2 marksQuestion 12(c)tangents gradients
3 marksQuestion 12(d)differential equations
4 marks · linked parts kept togetherQuestion 12(e)binomial distribution
2 marksQuestion 12(f)mathematical induction
3 marksQuestion 13(a)vectors
3 marksQuestion 13(b)volumes of revolution
3 marksQuestion 13(c)inverse functions
2 marksQuestion 13(d)polynomial roots
3 marksQuestion 13(e)binomial distribution
3 marks · linked parts kept togetherQuestion 14(a)differential equations
4 marksQuestion 14(b)vectors
3 marksQuestion 14(c)vector motion
4 marksQuestion 14(d)binomial distribution
4 marksPaper composition
What the 2022 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 |
|---|---|---|---|
| Vectors | Q6, Q8, Q11(a), Q11(d), Q13(a), Q14(b) | 12 | 17% |
| Differential equation | Q10, Q12(a), Q12(d), Q14(a) | 11 | 16% |
| Binomial distribution | Q12(e), Q13(e), Q14(d) | 9 | 13% |
| Polynomial roots | Q3, Q13(d) | 4 | 6% |
| Vector motion | Q14(c) | 4 | 6% |
| Absolute value inequality | Q11(f) | 3 | 4% |
| Antidifferentiation | Q11(b) | 3 | 4% |
| Combinatorics | Q7, Q11(c) | 3 | 4% |
| Inverse function | Q9, Q13(c) | 3 | 4% |
| Mathematical induction | Q12(f) | 3 | 4% |
| Tangents and gradients | Q12(c) | 3 | 4% |
| Trigonometric equation | Q11(e) | 3 | 4% |
| Volume of revolution | Q13(b) | 3 | 4% |
| Graph transformations | Q2, Q4 | 2 | 3% |
| Pigeonhole principle | Q12(b) | 2 | 3% |
| Coordinate geometry | Q5 | 1 | 1% |
| Inverse trigonometric functions | Q1 | 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 10 question groups identified as using a graph, chart, direction field or diagram, representing 18 marks.
| Question | Marks |
|---|---|
| Question 2 | 1 |
| Question 4 | 1 |
| Question 5 | 1 |
| Question 6 | 1 |
| Question 7 | 1 |
| Question 10 | 1 |
| Question 12(a) | 2 |
| Question 13(a) | 3 |
| Question 13(b) | 3 |
| Question 14(c) | 4 |
| Total | 18 |