2023 paper · worked-solution library
HSC Mathematics
Extension 1 answers
26 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 2023 NSW HSC Mathematics Extension 1 examination. The source examination material is © NESA.
Multiple choice · Questions 1–10
rates motion
1 markQuestion 2binomial distribution
1 markQuestion 3differential equations
1 markQuestion 4definite integrals areas
1 markQuestion 5inverse trigonometric functions
1 markQuestion 6vectors
1 markQuestion 7inverse trigonometric functions
1 markQuestion 8graph transformations
1 markQuestion 9inverse functions
1 markQuestion 10combinatorics
1 markWritten response · Questions 11–14
coordinate geometry
2 marksQuestion 11(b)combinatorics
2 marksQuestion 11(c)polynomial roots
3 marksQuestion 11(d)inverse trigonometric functions
2 marksQuestion 11(e)advanced trig equations
3 marksQuestion 11(f)binomial distribution
4 marks · linked parts kept togetherQuestion 12(a)antidifferentiation
3 marksQuestion 12(b)mathematical induction
3 marksQuestion 12(c)binomial distribution
3 marks · linked parts kept togetherQuestion 12(d)combinatorics
2 marksQuestion 12(e)volumes of revolution
4 marksQuestion 13(a)rates motion
7 marks · linked parts kept togetherQuestion 13(b)vector motion
8 marks · linked parts kept togetherQuestion 14(a)inverse functions
3 marksQuestion 14(b)polynomial roots
4 marks · linked parts kept togetherQuestion 14(c)vectors
7 marks · linked parts kept togetherPaper composition
What the 2023 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 |
|---|---|---|---|
| Binomial distribution | Q2, Q11(f), Q12(c) | 8 | 11% |
| Rates of change | Q1, Q13(a) | 8 | 11% |
| Vector motion | Q13(b) | 8 | 11% |
| Vectors | Q6, Q14(c) | 8 | 11% |
| Polynomial roots | Q11(c), Q14(b) | 7 | 10% |
| Combinatorics | Q10, Q11(b), Q12(d) | 5 | 7% |
| Inverse function | Q9, Q14(a) | 4 | 6% |
| Inverse trigonometric functions | Q5, Q7, Q11(d) | 4 | 6% |
| Volume of revolution | Q12(e) | 4 | 6% |
| Antidifferentiation | Q12(a) | 3 | 4% |
| Mathematical induction | Q12(b) | 3 | 4% |
| Trigonometric equation | Q11(e) | 3 | 4% |
| Coordinate geometry | Q11(a) | 2 | 3% |
| Definite integral | Q4 | 1 | 1% |
| Differential equation | Q3 | 1 | 1% |
| Graph transformations | Q8 | 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 34 marks.
| Question | Marks |
|---|---|
| Question 3 | 1 |
| Question 4 | 1 |
| Question 8 | 1 |
| Question 9 | 1 |
| Question 12(e) | 4 |
| Question 13(a) | 7 |
| Question 13(b) | 8 |
| Question 14(b) | 4 |
| Question 14(c) | 7 |
| Total | 34 |