Year 12 QCE Maths - Essential Mathematics sample questions
Year 12 QCE Maths - Essential Mathematics practice preview
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Year 12 QCE Essential Mathematics practice questions
This public preview page identifies the planned Year 12 QCE Essential Mathematics demo route and links it to curriculum coverage while the reviewed sample question set is being completed.
Sample-question focus
The planned public sample is for Year 12 QCE Essential Mathematics practice and will open after the demo questions are reviewed.
Skills covered
Practice practical number, finance, measurement, rates, data, probability, and applied modelling.
Exercise and test mode
The route is public now; the exercise and test preview will become available after the curated question set is ready.
Curriculum link
Compare this demo with the QCE Year 11-12 Mathematics curriculum page to scan related topics, subtopics, and pathway coverage.
Sample QCE Year 12 Essential Mathematics questions
These sample questions are visible on the page before login. They show QCE Year 12 Essential Mathematics finance, measurement, rates, data, probability, and practical modelling explanations before opening the demo.
QCE 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.
QCE 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.
QCE 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.
QCE 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.
QCE 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.
QCE 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 QCE Year 12 Essential Mathematics support
QCE 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.
This demo is in progress
In progress
Year 12 QCE Maths - Essential Mathematics is available to purchase, and the public demo preview is still being prepared.
Students can use the purchased subject once subscribed; this anonymous preview will be opened after the curated public question set is ready.
Does this page include Year 12 QCE Essential Mathematics practice questions?
Not yet. The Year 12 QCE Essential Mathematics demo route is public, but the interactive sample questions will open after the reviewed public set is ready.
Can students try the demo without signing up?
No sign-up is required to view the preview status. The no-login interactive demo will be available after the sample set is completed.
How does this demo relate to curriculum coverage?
This demo is linked with the QCE Year 11-12 Mathematics curriculum coverage page, where parents can compare the broader topic and pathway structure used for Skill Align practice.
