HSC Mathematics Standard 2 is all about applying maths to real situations: paying for paint, reading a tax table, planning a project or converting fuel efficiency. The 2025 exam rewarded students who read each scenario carefully, chose the right formula and showed every step. NESA's marking feedback shows where students did this well, and where marks slipped away.
This guide breaks down the 2025 HSC Mathematics Standard 2 exam question by question. Every question is classified by syllabus topic using NESA's own mapping grid, so you can see exactly which areas carried the most marks. It also covers the answers, what better responses did and the areas NESA's markers said students need to improve. For the previous year's analysis, see our 2024 HSC Maths Standard examiner report breakdown.
Key Takeaways
- Measurement was the biggest strand, worth 30 of the 100 marks. Financial Mathematics and Statistical Analysis were next, with 23 marks each.
- Rates and Ratios (11 marks) was the biggest single topic, followed by Types of Relationships, Applications of Measurement and Critical Path Analysis (10 marks each).
- Many lost marks came from unit conversions: cents to dollars, miles per gallon to L/100 km, and annual interest rates to daily or monthly rates.
- In financial questions, markers flagged students who used a formula when the question said to use the table, or stopped one step short of the final answer.
- Several questions also appeared in the Maths Advanced exam (Q20, Q25, Q34, Q40 and three multiple-choice questions), so Standard 2 students faced some challenging shared content.
HSC Mathematics Standard 2 Examination Structure
| Feature | Section I | Section II |
|---|---|---|
| Question type | 15 multiple-choice questions | Short-answer and extended-response questions (Q16–40) |
| Marks | 15 marks | 85 marks |
| Suggested time | About 25 minutes | About 2 hours 5 minutes |
| Skills tested | Recognising graphs and networks, quick calculations, interpreting information | Working, reasoning, interpreting results and multi-step problem-solving |
The exam has 10 minutes of reading time and 2 hours and 30 minutes of working time, and is worth 100 marks. NESA-approved calculators are allowed and a reference sheet is provided. The HSC exam mark makes up 50% of the final HSC mark. The other 50% comes from school-based assessment.
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Marks by Topic in the 2025 Exam
Every question below is classified using the mapping grid in NESA's 2025 marking guidelines, which links each question to a syllabus topic.
| Strand | Questions | Marks | Share of Exam |
|---|---|---|---|
| Measurement | MC 5, 9, 12, 14; Q16, 21, 24, 26, 32, 35, 37, 38 | 30 | 30% |
| Financial Mathematics | MC 4; Q18, 23, 27, 31, 33, 34, 36 | 23 | 23% |
| Statistical Analysis | MC 7, 8, 13, 15; Q17, 25, 28, 29, 40 | 23 | 23% |
| Algebra | MC 2, 6, 10, 11; Q20, 30, 39 | 12 | 12% |
| Networks | MC 1, 3; Q19, 22 | 12 | 12% |
Marks by Syllabus Topic
| Topic | Strand | Marks |
|---|---|---|
| Rates and Ratios (MS-M7) | Measurement | 11 |
| Types of Relationships (MS-A4) | Algebra | 10 |
| Applications of Measurement (MS-M1) | Measurement | 10 |
| Critical Path Analysis (MS-N3) | Networks | 10 |
| Money Matters (MS-F1) | Financial Mathematics | 9 |
| Investment and Loans (MS-F4) | Financial Mathematics | 9 |
| Bivariate Data Analysis (MS-S4) | Statistical Analysis | 9 |
| Non-right-angled Trigonometry (MS-M6) | Measurement | 8 |
| The Normal Distribution (MS-S5) | Statistical Analysis | 6 |
| Annuities (MS-F5) | Financial Mathematics | 5 |
| Data Analysis (MS-S1) | Statistical Analysis | 4 |
| Relative Frequency and Probability (MS-S2) | Statistical Analysis | 4 |
| Formulae and Equations (MS-A1) | Algebra | 2 |
| Network Concepts (MS-N2) | Networks | 2 |
| Working with Time (MS-M2) | Measurement | 1 |
Source: NESA 2025 HSC Mathematics Standard 2 marking guidelines (mapping grid).
Section I: Multiple-Choice Breakdown
| Question | Topic | What It Tested | Answer |
|---|---|---|---|
| 1 | Networks | Degree of a vertex | B |
| 2 | Algebra | Recognising the graph of y = 4ˣ | A |
| 3 | Networks | Largest edge in a minimum spanning tree | C (9) |
| 4 | Financial Maths | Annual leave loading | D ($1645.00) |
| 5 | Measurement | Ordering numbers in scientific notation | D |
| 6 | Algebra | Changing the subject of a formula | B (p = m − nq) |
| 7 | Statistical Analysis | Stratified sampling | C (50) |
| 8 | Statistical Analysis | Matching a spinner to a frequency histogram | A |
| 9 | Measurement | Scale ratio with unit conversion | B (7.7 cm) |
| 10 | Algebra | Writing an electricity cost formula | A (C = 71 + 37U − 5P) |
| 11 | Algebra | Inverse variation | C (divided by 4) |
| 12 | Measurement | Time zones | D (6:40 am Wednesday) |
| 13 | Statistical Analysis | Relative frequency | A (1/17) |
| 14 | Measurement | Bearings | C (between 090° and 180°) |
| 15 | Statistical Analysis | Normal distribution when the mean equals the standard deviation | D (84%) |
Source: NESA 2025 HSC Mathematics Standard 2 marking guidelines (answer key and mapping grid). Descriptions of what each question tested are our own.
Multiple-Choice Questions to Watch
- Question 4: Leave loading is 17.5% of four weeks' pay: 0.175 × $1400 = $245. The total pay is $1400 + $245 = $1645. Option A ($245) is only the loading.
- Question 9: Convert first: 4.9 m = 490 cm, and 490 ÷ 64 ≈ 7.7 cm.
- Question 11: Surface area depends on r², so doubling the radius multiplies the surface area by 4. Thickness varies inversely, so it's divided by 4.
- Question 12: Sydney (UTC +10) is 15 hours ahead of Quito (UTC −5), so 3:40 pm Tuesday becomes 6:40 am Wednesday.
- Question 13: 72 of the 153 rolls were a 1, leaving 81 rolls shared equally between the other 9 numbers. That's 9/153 = 1/17 each.
- Question 15: If the mean equals the standard deviation, 0° is one standard deviation below the mean. 50% + 34% = 84% are above zero.
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Section II: Question-by-Question Breakdown
| Question | Topic | What It Tested | Marks | Answer |
|---|---|---|---|---|
| 16 | Measurement (rates) | Best buy for 80 litres of paint | 2 | Saves $160 |
| 17 | Statistical Analysis | Line of best fit from two points | 3 | y = −2x + 14 |
| 18 | Financial Maths (annuities) | Future value using an interest factor table | 2 | $61 440 |
| 19(a) | Networks (critical path) | Immediate prerequisites | 2 | Table |
| 19(b) | Networks (critical path) | Critical path and minimum duration | 2 | BDEFH, 26 days |
| 19(c) | Networks (critical path) | Effect of a longer activity | 1 | No, A has 3 days of float |
| 20(a) | Algebra | Turning point of a quadratic | 2 | t = 4, h = −4 |
| 20(b) | Algebra | Symmetry of a parabola | 1 | t = 8 |
| 21(a) | Measurement (rates) | Cost of electricity | 1 | $4.35 |
| 21(b) | Measurement (rates) | Average hours of heating per day | 2 | 7.5 hours |
| 22(a) | Networks (flow) | Capacity of a cut | 1 | 62 L/min |
| 22(b)(i) | Networks (flow) | Inflow equals outflow | 2 | x = 30 |
| 22(b)(ii) | Networks (flow) | Pipes at full capacity | 1 | DE, CF, DG, FG |
| 22(b)(iii) | Networks (flow) | Path to reach maximum flow | 1 | ACEG |
| 23 | Financial Maths | Comparing dividend yields | 2 | Company B (about 21% vs 19%) |
| 24 | Measurement (ratios) | Capture–recapture | 2 | 4 snails |
| 25(a) | Statistical Analysis | Form and direction of bivariate data | 2 | Linear, negative |
| 25(b) | Statistical Analysis | Interpreting slope and y-intercept in context | 2 | Interpretation |
| 25(c) | Statistical Analysis | Prediction from a regression line | 1 | 34.9 minutes |
| 25(d) | Statistical Analysis | Why extrapolation isn't appropriate | 1 | Explanation |
| 26(a) | Measurement | Trapezoidal rule (two applications) | 2 | 34.68 cm² |
| 26(b) | Measurement | Surface area of a prism | 2 | 582.64 cm² |
| 26(c) | Measurement | Percentage error | 2 | 0.490% |
| 27 | Financial Maths (loans) | Credit card interest compounding daily | 3 | $3.41 |
| 28 | Statistical Analysis | Box-plot from a cumulative frequency graph | 3 | 130, 135, 140, 160, 180 |
| 29 | Statistical Analysis (probability) | Probability without replacement | 2 | 19/40 |
| 30 | Algebra | Writing simultaneous linear equations | 2 | P = 11B and 465P + 350B = 494 000 000 |
| 31 | Financial Maths | Working backwards from tax payable | 3 | $178 600 |
| 32 | Measurement | Volumes of spheres and a pyramid | 3 | h = 16 cm |
| 33 | Financial Maths | Stamp duty and a simple interest loan | 5 | $835.31 per month |
| 34 | Financial Maths (annuities) | Matching a lump sum with an annuity | 3 | $306.78 per month |
| 35 | Measurement (trigonometry) | Sine rule, ambiguous case and angle of depression | 3 | TA ≈ 35.29 m |
| 36 | Financial Maths (depreciation) | Declining-balance depreciation in the 10th year | 4 | $1476.40 |
| 37 | Measurement (trigonometry) | Cosine rule, triangle area and rates | 4 | About 7 minutes |
| 38 | Measurement (rates) | Converting mpg to L/100 km | 3 | 7.9 L/100 km |
| 39 | Algebra | Exponential model y = kaˣ | 3 | About 5.4 mg |
| 40(a) | Statistical Analysis | Normal distribution and z-scores | 4 | x = 89.8 kg |
| 40(b) | Statistical Analysis | Comparing two normal distributions | 1 | Explanation |
Answers are from the sample answers in NESA's 2025 marking guidelines. Topics follow NESA's mapping grid. Questions 20, 25, 34 and 40 also appeared in the Mathematics Advanced exam.
What the Markers Said: Measurement (30 marks)
Question 16 – Best buy
- Better responses found the full cost of 80 litres for each can size ($1640 and $1800) and then the difference.
- Some students only found the saving for 1 litre instead of the whole 80 litres.
Question 21 – Electricity costs
- Better responses converted cents to dollars before calculating, and wrote a clear, labelled expression for the cost.
- In 21(b), students needed the heating figure (3.2 kW) only, not a combination of heating and cooling. Dividing the total cost by the number of days wasn't enough: every step to get to hours per day needed to be shown.
Question 24 – Capture–recapture
- Better responses wrote the capture–recapture ratios as fractions and set them equal: 18/90 = tagged/20, so 4 snails.
- Markers noted students needed to work backwards here, because the question asked for the number of tagged snails rather than the population.
Question 26 – Trapezoidal rule, surface area and error
- Better responses identified the strip width h = 5.1 (half of 10.2) and used two applications of the trapezoidal rule.
- In 26(b), the curved surface was the total minus the two cross-sections and the two flat rectangular faces.
- In 26(c), the absolute error is half the precision: measurements to the nearest millimetre have an absolute error of 0.05 cm. Markers flagged inconsistent mm ↔ cm conversions and rounding to 3 significant figures.
Question 32 – Volume
- Better responses found the volume of one sphere, multiplied by 30, added the empty space (634 cm³) and then solved V = (1/3)Ah for h.
- Markers reminded students to use the given information (30 spheres) rather than counting spheres in the diagram, and to know the volume formulas for a pyramid and a sphere.
Question 35 – Sine rule and the ambiguous case
- Better responses placed the angle of depression correctly, recognised it as equal to the angle of elevation (alternate angles), and used the sine rule.
- The sine rule gives an acute angle of about 60°, but the question said angle PTA is obtuse, so it must be 120°. Recognising this ambiguous case was the key step.
Question 37 – Area and rates
- Better responses used the cosine rule to find a side of the inner equilateral triangle, then the area formula A = ½ab sin C.
- Markers noted students needed to use geometric properties to find angles (each angle of an equilateral triangle is 60°) and apply the mowing rate as a ratio.
Question 38 – Converting fuel efficiency
- Better responses converted 30 miles per gallon into 3.8 L per 48 km, then scaled it to 100 km.
- Markers advised doing one conversion at a time and writing words beside each step to keep track of distance and volume.
What the Markers Said: Financial Mathematics (23 marks)
Question 18 – Annuity table
- Better responses found the right factor in the table (12.288 for 10 years at 4.5%) and multiplied it by $5000.
- Some students multiplied by 10 years as well, or used a formula instead of the table provided.
Question 23 – Dividend yield
- Better responses calculated the yield for both companies, compared them and wrote a clear conclusion: Company B has the higher yield.
- Watch the units: Company B's dividend was in cents (45c), so convert to $0.45 first.
Question 27 – Credit card interest
- Better responses counted the interest days correctly (68 − 45 = 23 days) and used the compound interest formula with a daily rate (13.74% ÷ 365).
- The most common errors were converting the interest rate and the time period to the wrong unit.
Question 31 – Working backwards from tax payable
- Better responses chose the correct tax bracket ($135 001–$190 000), stayed in it for the whole calculation, and divided by 0.37 at the right point.
- Markers flagged confusion between tax payable and taxable income.
Question 33 – Stamp duty and a car loan
- Stamp duty is $3 for every $100 or part thereof, calculated on the sale price: $24 200 ÷ 100 × $3 = $726.
- Better responses charged interest on the total amount borrowed (car, registration and stamp duty), not just the car, then divided the total repayable by 36 months.
Question 34 – Annuities
- Better responses converted to monthly values (n = 84, r = 0.005), found Lin's future value with A = P(1 + r)ⁿ, and divided by the table factor of 104.07393.
- Markers flagged confusion about when to use the formula and when to use the table, and when to divide or multiply by the factor.
Question 36 – Declining-balance depreciation
- Better responses found the rate from the graph (20%), then calculated the values after 9 and 10 years and found the difference.
- "During the 10th year" means the drop in value across that year, not the value at the end of it. Markers also noted that declining-balance depreciation is a percentage, not a fixed amount each year.
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What the Markers Said: Statistical Analysis (23 marks)
Question 17 – Line of best fit
- Better responses plotted (0, 14) and (5, 4), drew the line with a ruler, and found the gradient (−2) and y-intercept (14).
- Common errors included getting the sign of the gradient wrong (a line sloping down from left to right has a negative gradient) and not knowing what m and c represent.
Question 25 – Bivariate data
- Use the syllabus terms: the form is linear and the direction is negative.
- Better responses interpreted the slope and y-intercept in context. Each extra minute of television is associated with 0.7 fewer minutes of exercise, and someone who watches no television is predicted to exercise for about 64.3 minutes. Markers noted that the slope is not the correlation coefficient.
- In 25(d), better responses converted 2 hours to 120 minutes, noted it's outside the dataset and showed that the line predicts a negative amount of exercise.
Question 28 – Box-plot from a cumulative frequency graph
- Better responses read Q₁, the median and Q₃ from the graph and listed the five-number summary before drawing the box-plot.
- Markers recommended practising reading values from a cumulative frequency histogram and ogive.
Question 29 – Probability without replacement
- Better responses drew a tree diagram with the second-stage fractions out of 15, multiplied along the branches and added the blue–blue and yellow–yellow outcomes.
- Common errors were not adjusting for "without replacement" and confusing when to add and when to multiply.
Question 40 – Normal distribution
- Better responses found 600 male sheep (12 600 ÷ 21). 15 of them is 2.5%, which matches a z-score of 2, so x = 76.2 + 2 × 6.8 = 89.8 kg.
- Common errors included confusing a z-score with a percentage. Markers recommended a labelled sketch of the normal curve.
- In 40(b), 300 of 12 000 females is also 2.5%. Because the females have a smaller mean and standard deviation, fewer than 2.5% would be above x kg, so 300 couldn't be expected.
What the Markers Said: Algebra (12 marks)
Question 20 – Quadratics
- Better responses found the turning point from the axis of symmetry (t = 4), then substituted to find h. Some students confused the intercepts with the vertex.
- In 20(b), symmetry about t = 4 gives the other value immediately: t = 8.
Question 30 – Writing linear equations
- Better responses wrote two equations using the given pronumerals: P = 11B and 465P + 350B = 494 000 000.
- Some students didn't realise two equations were needed or weren't sure of the format of a linear equation. Tip: "11 times as many cars as motorcycles" means P = 11B. Check it by substituting B = 1.
Question 39 – Exponential model
- Better responses recognised the y-intercept gives k (k = 15), substituted (2, 9) to find a, and then found y when x = 4.
- Markers flagged students who couldn't distinguish between different types of graphs or didn't link the y-intercept to k.
What the Markers Said: Networks (12 marks)
Question 19 – Critical path analysis
- Better responses read the immediate prerequisites from the network, then used forward and backward scanning to find the earliest and latest starting times.
- The critical path was BDEFH, giving a minimum duration of 26 days.
- In 19(c), increasing activity A by 2 days doesn't change the critical path because A has 3 days of float. Markers noted that a longer activity may or may not affect the critical path.
Question 22 – Flow networks
- The capacity of a cut only counts edges flowing from the source side to the sink side.
- Better responses used inflow = outflow at each vertex to find x, and identified a path that could carry extra flow to reach the maximum of 50 L/min.
- Markers noted some students confused a flow network with a critical path network.
💡 Unsure whether Standard or Advanced suits you? Read our guide to HSC Maths: which course is right for you.
Common Mistakes Across the 2025 Exam
- Unit conversions: Cents to dollars (Q21, Q23), mm to cm (Q26), miles and gallons (Q38) and annual to daily or monthly rates (Q27, Q34) all cost students marks.
- Stopping one step short: Finding a cost per litre instead of for 80 litres (Q16), or the value after 10 years instead of the depreciation during the 10th year (Q36).
- Using the wrong tool: Using a formula when the question gave a table (Q18), or not recognising when the sine rule's ambiguous case applies (Q35).
- Misreading key words: "Without replacement", "or part thereof", "during the 10th year", "immediate prerequisite" and "extrapolate".
- Interpreting without context: Describing slope and intercept in general terms instead of using the scenario and values given.
- Rounding too early: Markers again reminded students to round only at the final step.
How to Prepare for HSC Mathematics Standard 2
- Know the reference sheet well, including the trapezoidal rule, volume formulas, the sine and cosine rules, and the normal distribution percentages.
- Practise unit conversions step by step, writing the unit beside every number.
- Learn to read every type of table in the course: tax tables, annuity factor tables and stamp duty rates.
- Practise networks questions regularly, especially critical path analysis and flow networks, which carried 12 marks.
- Write conclusions in context for statistics and finance questions, such as which investment is better and why.
- Complete full past papers under timed conditions to practise managing 2 hours and 30 minutes of working time.
For more preparation:
- see everything you need to know for HSC Maths Standard
- studying Advanced too? See our 2025 HSC Maths Advanced examiner report breakdown
- brush up on key words with our guide to HSC command terms
- understand HSC performance bands
- see the HSC exam timetable 2026 for this year's exam date.
Need Help With HSC Maths Standard 2?
Our HSC Maths Standard tutors have scored highly in the subject themselves and work one-on-one with students to master financial maths, networks, measurement and statistics, and to avoid the mistakes highlighted in NESA's marking feedback.
Sources: NSW Education Standards Authority, 2025 HSC Mathematics Standard 2 examination, marking guidelines and HSC marking feedback 2025.
