2024 paper · worked-solution library
HSC Mathematics
Extension 1 answers
30 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 2024 NSW HSC Mathematics Extension 1 examination. The source examination material is © NESA.
Multiple choice · Questions 1–10
polynomial roots
1 markQuestion 2definite integrals areas
1 markQuestion 3pigeonhole principle
1 markQuestion 4inverse trigonometric functions
1 markQuestion 5inverse trigonometric functions
1 markQuestion 6advanced trig equations
1 markQuestion 7binomial distribution
1 markQuestion 8binomial distribution
1 markQuestion 9combinatorics
1 markQuestion 10advanced trig equations
1 markWritten response · Questions 11–14
vectors
2 marksQuestion 11(b)absolute value inequalities
2 marksQuestion 11(c)antidifferentiation
3 marksQuestion 11(d)differential equations
2 marksQuestion 11(e)inverse trigonometric functions
1 markQuestion 11(f)rates motion
2 marksQuestion 11(g)definite integrals areas
3 marksQuestion 12(a)vectors
3 marksQuestion 12(b)volumes of revolution
3 marksQuestion 12(c)binomial distribution
3 marksQuestion 12(d)mathematical induction
3 marksQuestion 12(e)absolute value inequalities
3 marksQuestion 13(a)differential equations
4 marksQuestion 13(b)advanced trig identities
5 marks · linked parts kept togetherQuestion 13(c)vectors
4 marksQuestion 13(d)antidifferentiation
3 marksQuestion 14(a)differential equations
4 marksQuestion 14(b)inverse functions
3 marksQuestion 14(c)inverse trigonometric functions
3 marks · linked parts kept togetherQuestion 14(d)vector motion
4 marksPaper composition
What the 2024 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 | Q11(d), Q13(a), Q14(a) | 10 | 14% |
| Vectors | Q11(a), Q12(a), Q13(c) | 9 | 13% |
| Antidifferentiation | Q11(c), Q13(d) | 6 | 9% |
| Inverse trigonometric functions | Q4, Q5, Q11(e), Q14(c) | 6 | 9% |
| Absolute value inequality | Q11(b), Q12(e) | 5 | 7% |
| Binomial distribution | Q7, Q8, Q12(c) | 5 | 7% |
| Trigonometric identity | Q13(b) | 5 | 7% |
| Definite integral | Q2, Q11(g) | 4 | 6% |
| Vector motion | Q14(d) | 4 | 6% |
| Inverse function | Q14(b) | 3 | 4% |
| Mathematical induction | Q12(d) | 3 | 4% |
| Volume of revolution | Q12(b) | 3 | 4% |
| Rates of change | Q11(f) | 2 | 3% |
| Trigonometric equation | Q6, Q10 | 2 | 3% |
| Combinatorics | Q9 | 1 | 1% |
| Pigeonhole principle | Q3 | 1 | 1% |
| Polynomial roots | 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 4 question groups identified as using a graph, chart, direction field or diagram, representing 11 marks.
| Question | Marks |
|---|---|
| Question 2 | 1 |
| Question 11(g) | 3 |
| Question 12(e) | 3 |
| Question 13(a) | 4 |
| Total | 11 |