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Year 12 WACE Maths - Essential Mathematics sample questions

Year 12 WACE Maths - Essential Mathematics practice preview

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Year 12 WACE Essential Mathematics practice questions

This public preview page identifies the planned Year 12 WACE 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 WACE 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 WA Year 11-12 Mathematics curriculum page to scan related topics, subtopics, and pathway coverage.

Sample WACE Year 12 Essential Mathematics questions

These sample questions are visible on the page before login. They show WACE Year 12 Essential Mathematics finance, measurement, rates, data, probability, and practical modelling explanations before opening the demo.

WACE Year 12 Essential Mathematics Depreciation hard finance 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?

Reducing-balance depreciation V₃ n $
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.

WACE Year 12 Essential Mathematics Loans and recurrence hard finance graph

2. A loan balance follows Bₙ₊₁ = 1.006Bₙ - 420 with B₀ = 12000. What is B₂, to the nearest cent?

Loan balance after two repayments B₂ n $
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.

WACE Year 12 Essential Mathematics Scale and cost hard scale 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?

Scale plan for resurfacing 6.8 4.5 1:500
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.

WACE Year 12 Essential Mathematics Conditional probability hard probability 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?

Defect probability tree A D +
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.

WACE Year 12 Essential Mathematics Networks hard network 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?

Minimum cable network A F 35
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.

WACE Year 12 Essential Mathematics Utility modelling hard break-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?

Linear utility cost model C B 128.8
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 WACE Year 12 Essential Mathematics support

WACE 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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Year 12 WACE 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.

WACE Essential Mathematics practice questions FAQ

Does this page include Year 12 WACE Essential Mathematics practice questions?

Not yet. The Year 12 WACE 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 WA Year 11-12 Mathematics curriculum coverage page, where parents can compare the broader topic and pathway structure used for Skill Align practice.