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Year 12 WACE Maths - Mathematical Methods sample questions

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Year 12 WACE Mathematical Methods practice questions

This public preview page identifies the planned Year 12 WACE Mathematical Methods demo route and links it to curriculum coverage while the reviewed sample question set is being completed.

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The planned public sample is for Year 12 WACE Mathematical Methods practice and will open after the demo questions are reviewed.

Skills covered

Practice functions, relations, algebra, calculus, probability, transformations, graphs, and mathematical modelling.

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Curriculum link

Compare this demo with the WA Year 11-12 Mathematics curriculum page to scan related topics, subtopics, and pathway coverage.

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Sample WACE Year 12 Mathematical Methods questions

These sample questions are visible on the page before login. They show WACE Year 12 Mathematical Methods functions, calculus, probability, modelling, and statistics explanations before opening the demo.

WACE Year 12 Mathematical Methods Integral calculus hard tangent and area graph

1. What is the exact value of the integral from 0 to 2 of (3x2 - 2x) dx?

Definite integral from a curve P T R
Choices
  • 4
  • 8
  • 2
  • 12
Explanation:

An antiderivative is x3 - x2. Evaluating from 0 to 2 gives 8 - 4 = 4.

WACE Year 12 Mathematical Methods Differential calculus hard tangent graph

2. For f(x) = ln(x2 + 1), the tangent T is drawn at P where x = 2. What is the gradient of T?

Tangent to a logarithmic curve P x = 2 T
Choices
  • 4/5
  • 2/5
  • 5/4
  • 1/5
Explanation:

Using the chain rule, f'(x) = 2x/(x2 + 1). At x = 2, f'(2) = 4/5.

WACE Year 12 Mathematical Methods Exponential and logarithmic modelling hard model graph

3. A population is modelled by P(t) = 1200/(1 + 5e-0.4t). What is the exact time when P(t) = 800?

Logistic growth threshold P L/2 S
Choices
  • (5 ln 10)/2 hours
  • (ln 10)/5 hours
  • 5 ln 2 hours
  • 10 ln 5 hours
Explanation:

Set 800 = 1200/(1 + 5e-0.4t), so 1 + 5e-0.4t = 3/2. Hence e-0.4t = 0.1 and t = ln(10)/0.4 = (5 ln 10)/2.

WACE Year 12 Mathematical Methods Continuous probability hard density graph

4. For the continuous random variable X with density f(x) = c(2x + 1), 0 ≤ x ≤ 3, what is P(X > 2)?

Right-tail probability from a linear density A B R
Choices
  • 1/2
  • 1/3
  • 2/3
  • 3/4
Explanation:

The unscaled total area is the integral from 0 to 3 of 2x + 1, which is 12. The unscaled area from 2 to 3 is 6, so P(X > 2) = 6/12 = 1/2.

WACE Year 12 Mathematical Methods Normal distribution hard normal curve

5. For X ~ N(μ, σ2), P(X < 58) = 0.1587 and P(X < 74) = 0.8413. Using Φ(-1) = 0.1587 and Φ(1) = 0.8413, what are μ and σ?

Normal curve with symmetric z-scores A B μ
Choices
  • μ = 66, σ = 8
  • μ = 66, σ = 16
  • μ = 58, σ = 8
  • μ = 74, σ = 8
Explanation:

The two values are one standard deviation below and above the mean. The mean is (58 + 74)/2 = 66, and the standard deviation is 74 - 66 = 8.

WACE Year 12 Mathematical Methods Functions and logarithms hard model graph

6. For f(x) = 3e0.5x - 2, what exact value of x satisfies f(x) = 10?

Exponential equation on a model graph P T L
Choices
  • 4 ln 2
  • 2 ln 2
  • ln 4
  • 4
Explanation:

Set 3e0.5x - 2 = 10, so e0.5x = 4. Taking logarithms gives 0.5x = ln 4, hence x = 2 ln 4 = 4 ln 2.

For parents comparing WACE Year 12 Mathematical Methods support

WACE Year 12 Mathematical Methods practice should make functions, calculus, probability, modelling, and statistics feel structured rather than guessable. These examples preview that style before the no-login Mathematical Methods demo.

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WACE Mathematical Methods practice questions FAQ

Does this page include Year 12 WACE Mathematical Methods practice questions?

Not yet. The Year 12 WACE Mathematical Methods 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.