Year 12 ACT Maths - Essential Mathematics sample questions
Year 12 ACT Maths - Essential Mathematics sample questions
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Year 12 Essential Mathematics practice questions
Use this no-login public demo to preview Skill Align's Year 12 Essential Mathematics sample questions, explanations, exercise mode, and test mode before regular practice.
Sample-question focus
Try a short public sample of Year 12 Essential Mathematics questions selected from the reviewed Skill Align demo set.
Skills covered
Practice practical number, finance, measurement, rates, data, probability, and applied modelling.
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Sample ACT BSSS Year 12 Essential Mathematics questions
These sample questions are visible on the page before login. They show ACT BSSS Year 12 Essential Mathematics finance, measurement, rates, data, probability, and practical modelling explanations before opening the demo.
ACT BSSS Year 12Essential MathematicsDepreciationhardfinance graph
1. A laptop worth $4200 depreciates by 18% p.a. on a reducing-balance basis. What is its value after 3 years, to the nearest cent?
Choices
$2,315.75
$3,444.00
$2,268.00
$2,904.77
Explanation:
Reducing-balance depreciation gives V = 4200(0.82)3 = 2315.7456, so the value is $2315.75 to the nearest cent.
ACT BSSS Year 12Essential MathematicsLoans and recurrencehardfinance graph
2. A loan balance follows Bₙ₊₁ = 1.006Bₙ - 420 with B₀ = 12000. What is B₂, to the nearest cent?
Choices
$11,301.91
$11,652.00
$12,072.00
$10,812.00
Explanation:
B₁ = 1.006 x 12000 - 420 = 11652. Then B₂ = 1.006 x 11652 - 420 = 11301.912, so B₂ is $11,301.91.
ACT BSSS Year 12Essential MathematicsScale and costhardscale plan
3. A car park is 6.8 cm by 4.5 cm on a 1:500 plan. Resurfacing costs $18 per square metre. What is the resurfacing cost?
Choices
$13,770
$1,377
$7650
$18,360
Explanation:
The actual dimensions are 34 m by 22.5 m, so the area is 765 m2. At $18 per square metre, the cost is 765 x 18 = $13,770.
ACT BSSS Year 12Essential MathematicsConditional probabilityhardprobability tree
4. Machine A makes 55% of items with defect probability 0.04. Machine B makes 45% of items with defect probability 0.07. What is the probability a randomly selected item is defective?
Choices
0.0535
0.1100
0.0315
0.0550
Explanation:
Add the defective branches: 0.55 x 0.04 + 0.45 x 0.07 = 0.022 + 0.0315 = 0.0535.
ACT BSSS Year 12Essential MathematicsNetworkshardnetwork diagram
5. A minimum cable network uses selected edges with lengths 6 m, 8 m, 5 m, 9 m, and 7 m. What total cable length is needed?
Choices
35 m
30 m
40 m
45 m
Explanation:
A minimum spanning network connects all required points without a loop. Add the selected edge lengths: 6 + 8 + 5 + 9 + 7 = 35 m.
ACT BSSS Year 12Essential MathematicsUtility modellinghardbreak-even graph
6. A water bill charges a fixed $83 plus $2.18 per kilolitre. A household uses 1.4 kL per day for 92 days. What is the total bill, to the nearest cent?
Choices
$363.78
$280.78
$211.84
$446.78
Explanation:
The usage is 1.4 x 92 = 128.8 kL. The usage charge is 128.8 x $2.18 = $280.78 to the nearest cent. The total bill is $83 + $280.78 = $363.78.
For parents comparing ACT BSSS Year 12 Essential Mathematics support
ACT BSSS Year 12 Essential Mathematics practice should make finance, measurement, rates, data, probability, and practical modelling feel structured rather than guessable. These examples preview that style before the no-login Essential Mathematics demo.
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Answer questions in a short test-style session.
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Practice Summary
Year 12 · ACT Maths - Essential Mathematics · Test mode · 2 questions · 10 min
Questions attempted0 / 2
Correct answersPending
Score-
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This demo is linked with the ACT Year 11-12 Mathematics curriculum coverage page, where parents can compare the broader topic and pathway structure used for Skill Align practice.
