Year 12 HSC Maths - Mathematics Standard sample questions
Year 12 HSC Maths - Mathematics Standard sample questions
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Year 12 HSC Mathematics Standard practice questions
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Try a short public sample of Year 12 HSC Mathematics Standard 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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Sample HSC Year 12 Mathematics Standard questions
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HSC Year 12Mathematics StandardFinancial mathematicshardpayslip diagram
1. A taxable income is $78,000. Tax is $5092 plus 32.5c for each dollar over $45,000, and the Medicare levy is 2% of taxable income. What is the total tax plus Medicare levy?
Choices
$17,377
$15,817
$16,652
$18,937
Explanation:
Tax is $5092 + 0.325 x ($78,000 - $45,000) = $15,817. The Medicare levy is 0.02 x $78,000 = $1560. The total is $15,817 + $1560 = $17,377.
HSC Year 12Mathematics StandardDepreciationhardfinance graph
2. A car worth $24,000 depreciates by 18% p.a. using the declining-balance method. What is the depreciation during the third year, to the nearest cent?
Choices
$2,904.77
$4,320.00
$3,197.09
$16,137.60
Explanation:
At the start of the third year, the value is $24,000 x 0.822 = $16,137.60. The third-year depreciation is 18% of this: 0.18 x $16,137.60 = $2,904.77.
HSC Year 12Mathematics StandardNetworkshardnetwork diagram
3. In the network, the shortest route from A to F uses A-C-D-F. If the edge weights on that route are 8, 6 and 7, what is the shortest distance?
Choices
21
19
22
27
Explanation:
Add the weights on the stated shortest route: 8 + 6 + 7 = 21. The other displayed routes are longer, so the shortest distance is 21.
HSC Year 12Mathematics StandardMeasurementhardmeasurement diagram
4. A storage tank is modelled as a rectangular prism 2.4 m by 1.5 m by 0.8 m. How many litres does it hold when full?
Choices
2880 L
288 L
28.8 L
4800 L
Explanation:
The volume is 2.4 x 1.5 x 0.8 = 2.88 m3. Since 1 m3 = 1000 L, the full tank holds 2880 L.
HSC Year 12Mathematics StandardStatisticshardnormal curve
5. A test score is modelled with mean 72 and standard deviation 8. What is the z-score for a mark of 86?
Choices
1.75
1.25
0.57
14
Explanation:
Use z = (x - μ)/σ. Here z = (86 - 72)/8 = 14/8 = 1.75.
HSC Year 12Mathematics StandardProbabilityhardprobability tree
6. A component is faulty with probability 0.04. A test detects a faulty component with probability 0.90 and gives a false positive on a working component with probability 0.06. What is P(test positive)?
Choices
0.0936
0.0360
0.0576
0.9000
Explanation:
Use the two branches that end in a positive test: 0.04 x 0.90 + 0.96 x 0.06 = 0.036 + 0.0576 = 0.0936.
For parents comparing HSC Year 12 Mathematics Standard support
HSC Year 12 Mathematics Standard practice should connect syllabus skills to tax, depreciation, routes, measurement, statistics, and conditional probability. These examples preview that applied reasoning before the no-login Mathematics Standard demo.
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Practice Summary
Year 12 · HSC Maths - Mathematics Standard · Test mode · 8 questions · 10 min
Questions attempted0 / 8
Correct answersPending
Score-
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