Year 12 HSC Maths - Mathematics Standard 2 sample questions
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Year 12 HSC Mathematics Standard 2 practice questions
Use this no-login public demo to preview Skill Align's Year 12 HSC Mathematics Standard 2 sample questions, explanations, exercise mode, and test mode before regular practice.
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Try a short public sample of Year 12 HSC Mathematics Standard 2 questions selected from the reviewed Skill Align demo set.
Skills covered
Practice practical algebra, measurement, financial mathematics, networks, statistics, probability, and everyday modelling.
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Curriculum link
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20 tasks · Guided practice · Syllabus 2024 · HSC 2027
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Responses stay on this page. Written reasoning is self-assessed separately from automatically marked answers.1. Interpret the model
A school stall models cost as C = 120 + 8n and revenue as R = 20n, in dollars, for n items sold. What does 120 represent?
2. Find break-even
For C = 120 + 8n and R = 20n (dollars), calculate the number of items needed to break even and the revenue at that point.
items
AUD
3. Check the idea
A loan opens at $5,000 with interest of 0.5% per month and a $300 monthly repayment. Which expression calculates the first month's interest?
Interest is added to the opening balance before the end-of-month repayment. There are no fees. Round each month's interest to the nearest cent before finding the closing balance.
4. Apply the method
A $5,000 loan has monthly interest of 0.5% and a $300 repayment. Find the closing balance after the first month.
Interest is added to the opening balance before the end-of-month repayment. There are no fees. Round each month's interest to the nearest cent before finding the closing balance.
AUD
5. Check payment timing
An account opens with $0. Interest is 1% per month, added before a $200 deposit at the end of each month. With no fees, what is the balance just after the second deposit?
6. Complete the annuity table
Interest is 1% per month, added before each $200 end-of-month deposit. Complete month 3. There are no fees; round each month's interest to the nearest cent.
| Month | Opening | Interest | Deposit | Closing |
|---|---|---|---|---|
| 1 | 0.00 | 0.00 | 200.00 | 200.00 |
| 2 | 200.00 | 2.00 | 200.00 | 402.00 |
| 3 | 402.00 | ? | 200.00 | ? |
AUD
AUD
7. Choose a rule
The diagram shows survey points A, B and C. Which expression gives the distance BC in metres?
8. Calculate distance and area
Use the survey diagram to calculate BC and the area of triangle ABC. Give both answers to 2 decimal places.
m
m²
9. Connect a scale and a rate
On a map with scale 1 : 25,000, a walking route measures 7.2 cm. Find the actual distance in kilometres and the walking time in minutes at a constant 5 km/h, with no stops.
km
min
10. Estimate collected rainfall
Use the site data to calculate the volume of rain falling on the horizontal rectangular roof and the volume reaching the tank, in litres. Assume uniform rainfall, an initially empty tank with enough capacity, and 1000 L = 1 m³.
| Measurement | Value |
|---|---|
| Roof length | 20 m |
| Roof width | 15 m |
| Rainfall depth | 12 mm |
| Collection efficiency | 75% |
L
L
11. Read a directed network
Arrows show allowed directions; edge labels are capacities in L/s. Flow is conserved at A and B. Which vertex is the source?
12. Establish maximum flow
Arrows show allowed directions; edge labels are capacities in L/s. Flow is conserved at A and B. Find the maximum possible flow from S to T. Explain how a cut and a feasible flow establish your answer.
L/s
13. Interpret precedence
Activities are shown in boxes with their durations in days. Arrows show dependencies. Start at day 0; an activity must wait for all its predecessors to finish. Independent activities can run in parallel with sufficient resources. When may activity D start?
14. Find the earliest completion
Activities are shown in boxes with their durations in days. Arrows show dependencies. Start at day 0; an activity must wait for all its predecessors to finish. Independent activities can run in parallel with sufficient resources. Find the earliest start time of D and the minimum project completion time.
days
days
15. Describe an association
Six students reported their study time before a practice quiz. Their results appear in the scatter plot. Which statement best describes these data?
16. Use and interpret a fitted model
A fitted model for quiz mark y (out of 100) and study time x (hours) is y = 40 + 5x, based on study times from 1 to 6 hours. Predict the marks for 4.5 hours and 3 hours. Explain the meaning of the gradient 5 in this context.
marks
marks
17. Check replacement
A bag contains 3 red and 2 blue counters. Draw a counter at random, replace it, mix the bag and draw again. What is the probability of red on both draws?
18. Change the assumption
A bag contains 3 red and 2 blue counters. Draw two counters at random WITHOUT replacement. Find the probability that both are red. Explain why it differs from the probability 0.36 with replacement.
probability
19. Interpret a z-score
A result has a z-score of −1.5. What does this mean?
20. Standardise and reverse
Bottle fill volumes are modelled by a normal distribution with mean 500 mL and standard deviation 8 mL. Calculate the z-score of a 512 mL bottle, then the volume corresponding to z = −2.
z-score
mL
Automatically marked: 0 / 20 correct
Written responses self-assessed: 0 / 3
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Browse HSC Mathematics Standard 1 and Standard 2 Exams and Practice PapersHSC Mathematics Standard 2 practice questions FAQ
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