.webp)
The 2024 HSC Mathematics Extension 2 exam was a rigorous assessment designed to challenge students’ mathematical reasoning, problem-solving abilities, and conceptual understanding. The exam covered key areas such as proof, vectors, complex numbers, calculus, and mechanics. With a mix of structured and unstructured problems, it required students to demonstrate fluency in mathematical techniques, logical reasoning, and application of abstract concepts to real-world scenarios.
Structure of the Exam
The exam was divided into two sections:
- Section I (10 marks) – A multiple-choice section assessing fundamental knowledge and quick problem-solving skills.
- Section II (90 marks) – A range of extended-response questions requiring detailed reasoning, calculations, and proofs.
Students had three hours to complete the paper, with an additional 10-minute reading time. The reference sheet provided standard formulae, but successful candidates needed strong algebraic manipulation and problem-solving strategies beyond basic formula application.
Easiest Question of the Exam
While difficulty is subjective, Question 11(b)(i), which required adding two complex numbers using their conjugates, was among the more straightforward questions. The marking feedback highlighted that high-achieving students efficiently applied the definition of conjugates, demonstrating an understanding of basic complex number operations. However, some students made transcription errors, indicating the importance of careful working.
Hardest Question of the Exam
One of the most challenging questions was Question 16(c), which involved modelling motion with resistance proportional to velocity. This problem required applying differential equations, a deep understanding of mechanics, and careful algebraic manipulation. The complexity arose from the need to solve a non-trivial first-order differential equation, interpret the physical scenario correctly, and apply appropriate boundary conditions. Even top students struggled with linking the motion equations to time-dependent solutions, reinforcing the need for a strong grasp of calculus and mechanics.
💡Maths Extension 2 is an advanced HSC math course for NSW students who have completed Extension 1. It further builds Math skills and knowledge. Read on for tips to succeed in this highly challenging course!
Key Skills and Common Mistakes in the 2024 HSC Mathematics Extension 2 Exam
Success in HSC Mathematics Extension 2 requires more than just memorising formulas—it demands a deep understanding of mathematical concepts, logical reasoning, and the ability to communicate solutions effectively. The 2024 examination report provides key insights into what distinguishes strong responses, the most common pitfalls, and critical advice for future students.
What Do Strong Responses Look Like?
Students who performed well in the 2024 exam demonstrated:
- Clear mathematical reasoning – Every step in a solution was logically justified, with well-structured working and correct notation.
- Precise algebraic manipulation – Strong candidates could efficiently simplify expressions, work with complex numbers, and handle intricate calculus problems.
- Understanding of the syllabus' depth – Rather than relying on memorisation, they showcased a conceptual grasp of vectors, proofs, and mechanics, applying knowledge flexibly.
- Effective use of the Reference Sheet – High-achieving students knew when and how to apply standard results, reducing unnecessary derivations.
- Accuracy in calculator use – While technology was helpful, successful students manually verified results and avoided over-reliance on calculators for algebraic manipulation.
💡Discover valuable insights into how ATARs are calculated and how subject scaling affects their final rank here!
Key Advice for Future Students
The examination report highlighted several areas where students can improve their performance:
- Read the Question Carefully – Many students missed crucial details in multi-step problems, leading to incomplete or incorrect solutions.
- Show All Relevant Working – Partial credit was awarded for valid reasoning, even if the final answer was incorrect.
- Understand Key Terminology – Words such as show, prove, evaluate, and hence require different response structures.
- Use the Correct Mode (Degrees vs Radians) – Several students lost marks in trigonometry and vector questions due to incorrect mode selection.
- Graphing and Sketching – Where required, responses should be neat, precise, and properly labelled, especially for modulus and argument inequalities.
- Practice with Unstructured Problems – The hardest questions often required creative problem-solving rather than routine application of methods.
💡Understand how HSC scaling works and discover which subjects get scaled the most and the least.
Common Mistakes in the 2024 Exam
The most frequent errors varied across different topics, with some being specific to certain questions:
- Algebraic Errors – Mistakes in expanding brackets, handling fractions, and simplifying expressions were common in calculus and complex number problems.
- Vector Misinterpretations – Many students struggled with dot products, projections, and direction vectors, leading to incorrect vector equations.
- Misuse of Complex Number Properties – Some students forgot that i2=−1 or incorrectly applied modulus-argument conversions.
- Errors in Proofs – Common missteps included incomplete induction steps and failure to justify logical statements when proving inequalities.
- Integration Mistakes – Some students applied incorrect techniques for substitution and integration by parts, often forgetting to include constants of integration.
- Incorrect Application of Mechanics – Motion problems involving resistive forces were particularly challenging, with misuse of differential equations being a recurring issue.
- Graphing Missteps – Some students neglected key details like dotted vs solid lines in modulus inequalities or failed to consider boundary conditions.
💡Check out why past papers are the best way to study for exams!
Question-Specific Observations
The examiner’s feedback on individual questions provides valuable insights into where students lost marks:
- Question 11 (Integration & Complex Numbers) – Many students incorrectly applied integration by parts and made algebraic errors in complex number calculations.
- Question 12 (Vectors & Partial Fractions) – Errors included sign mistakes in vector projections and incorrect algebraic decomposition in partial fractions.
- Question 13 (Simple Harmonic Motion & Resistive Forces) – Some struggled with setting up correct differential equations and interpreting velocity-time relationships.
- Question 14 (Proof & Mathematical Induction) – Many students did not justify their final steps properly, leading to incomplete or incorrect proofs.
- Question 15 (Vector Geometry & Integration by Parts) – Mistakes arose in finding midpoints in vector geometry and incorrect substitution in integral problems.
- Question 16 (Advanced Mechanics & Complex Number Roots) – The hardest question, with many struggling to link differential equations to time-based solutions.
Final Thoughts
The Mathematics Extension 2 exam remains one of the most challenging HSC papers, but the 2024 feedback highlights clear areas for improvement. Students aiming for high marks should focus on structured reasoning, careful algebraic manipulation, and developing flexibility in problem-solving. By addressing common mistakes and following the examiner’s advice, future candidates can significantly enhance their performance.
