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The 2024 HSC Mathematics Standard exam assessed students’ ability to apply mathematical concepts to real-world scenarios. The exam was designed to test numeracy skills, problem-solving abilities, and mathematical reasoning across a range of familiar and unfamiliar contexts. It was structured into two sections:
- Section I: A multiple-choice section testing fundamental skills and concepts.
- Section II: A mix of short-answer and extended-response questions requiring mathematical reasoning, calculations, and interpretation of results.
The exam covered key syllabus topics, including algebra, financial mathematics, measurement, statistical analysis, probability, and networks. Many questions reflected real-life applications, reinforcing the course’s focus on practical numeracy and decision-making skills.
Easiest Question
The easiest question in the 2024 Mathematics Standard exam was a basic scale conversion question in the Mathematics Standard 1 paper (Question 11). Students were given a scale drawing and asked to calculate the real-life height of a tree. Stronger responses demonstrated correct multiplication and unit conversion from centimetres to metres.
Hardest Question
The most challenging question was an extended-response question requiring students to analyse and compare statistical distributions using box plots (Question 28 in the Mathematics Standard 2 paper). High-scoring responses correctly identified skewness, median, interquartile range, and spread, while many students struggled with interpreting and clearly comparing the distributions.
This exam highlighted the importance of showing clear working, using mathematical reasoning effectively, and applying concepts in a structured manner. The questions reinforced the syllabus' aim of equipping students with practical mathematical skills relevant to everyday life and various career pathways.
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Key Skills and Common Mistakes in the 2024 HSC Mathematics Standard Exam
Success in the 2024 HSC Mathematics Standard exam required clear mathematical reasoning, structured working out, and careful interpretation of questions. The examination report provided valuable insights into what distinguished high-scoring responses from weaker ones, as well as the most common pitfalls students encountered.
What Do Strong Responses Look Like?
Students who performed well in the exam consistently demonstrated:
- Clear mathematical reasoning – showing all necessary calculations rather than skipping steps.
- Understanding of key terms – recognising words like "hence," "evaluate," "solve," and "show" to guide their response correctly.
- Effective use of the Reference Sheet – applying formulas correctly in relevant contexts.
- Precision in rounding – rounding answers only in the final step to avoid errors.
- Structured working out – setting out responses logically so that the flow of calculations was easy to follow.
- Graphing accuracy – neat, well-labelled graphs with correctly plotted points, drawn using a ruler.
- Correct calculator usage – knowing when to apply calculator functions correctly, particularly for statistics and finance-related questions.
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Common Mistakes in the 2024 Exam
A number of common errors were observed across both Mathematics Standard 1 and 2:
- Misinterpreting questions – students often overlooked key details, leading to incorrect solutions.
- Rounding too early – leading to inaccurate final answers, especially in finance and probability questions.
- Misuse of formulas – applying the wrong formula or failing to correctly substitute values.
- Weak algebraic manipulation – struggling to rearrange and solve equations, particularly in finance, trigonometry, and statistics.
- Graphing errors – omitting labels, scales, or misinterpreting information in data analysis questions.
- Incorrect probability understanding – failing to apply complementary probability or confusing independent and dependent events.
- Unit conversions – students often miscalculated unit changes, particularly in measurement and financial maths questions.
Key Takeaways from Specific Questions
The examination report highlighted specific areas where students either excelled or struggled:
- Algebra and Graphing (Least-Squares Regression Line – Question 19, Standard 2)
- Strong responses: Used the graph correctly to determine the equation rather than relying solely on a calculator.
- Common mistakes: Misidentifying the gradient (B) and intercept (A) when using a calculator in statistics mode.
- Financial Mathematics (Annuities and Investments – Question 20, Standard 2)
- Strong responses: Correctly identified table values and adjusted for compounding periods.
- Common mistakes: Using the wrong table values or attempting to use a formula when the table was explicitly required.
- Measurement (Scale Drawings – Question 11, Standard 1)
- Strong responses: Understood the scale ratio and unit conversion process.
- Common mistakes: Misinterpreted what the scale represented or converted to incorrect units.
- Probability and Statistics (Box Plots and Skewness – Question 28, Standard 2)
- Strong responses: Correctly compared median, interquartile range (IQR), and skewness.
- Common mistakes: Described distributions vaguely without referencing specific data points.
- Networks (Shortest Path and Minimum Spanning Tree – Questions 16 & 20, Standard 1 & 2)
- Strong responses: Labelled vertices correctly and calculated path distances methodically.
- Common mistakes: Omitting start and end points, miscalculating total path lengths, or assuming diagrams were to scale.
- Trigonometry and Geometry (Right-Angled Triangles – Question 14, Standard 1)
- Strong responses: Applied Pythagoras’ Theorem and trigonometric ratios correctly.
- Common mistakes: Mixed up sine, cosine, and tangent, or did not correctly interpret bearings.
- Financial Mathematics (Simple vs. Compound Interest – Question 25, Standard 2)
- Strong responses: Understood that simple interest calculates interest only, while compound interest accumulates over time.
- Common mistakes: Confused future value and total interest earned, or mishandled compounding periods.
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Advice to Students
The 2024 Mathematics Standard exam highlighted the importance of reading questions carefully, structuring responses clearly, and applying mathematical reasoning effectively. To improve performance, students should:
- Practise past papers regularly, focusing on time management.
- Review syllabus terminology, ensuring they understand command words and key concepts.
- Use the Reference Sheet effectively – knowing where and how to apply formulas.
- Check all calculations carefully, avoiding common errors in rounding and unit conversions.
- Ensure all graphs are neatly drawn and correctly labelled.
- Work on algebraic manipulation skills, particularly when rearranging equations.
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Final Thoughts
The 2024 HSC Mathematics Standard exam reinforced the importance of clear mathematical reasoning, structured problem-solving, and careful interpretation of questions. While Section I required quick thinking and strong foundational knowledge, Section II tested students' ability to apply concepts systematically and communicate their working effectively.
The examination report highlighted key areas for improvement, including algebraic manipulation, financial mathematics, probability, and graph interpretation. The most successful students demonstrated precise calculations, logical organisation, and accurate use of formulas and graphs.
By applying these strategies, students can approach the HSC Mathematics Standard exam with confidence and clarity, ensuring they maximise their marks and demonstrate strong numeracy skills essential for life beyond school.
