SkillAlign Skill Align
Years 7–12 PracticeDevelopment
Home

/

School Learning

/

Tasmania Year 11-12 Mathematics Practice

/

Year 12 TAS Maths - Mathematics Methods sample questions

Year 12 TAS Maths - Mathematics Methods practice preview

This public preview is being prepared so visitors can try the subject before subscribing.

No sign-up required Preview in progress

Year 12 Mathematics Methods practice questions

This public preview page identifies the planned Year 12 Mathematics Methods 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 Mathematics Methods practice and will open after the demo questions are reviewed.

Skills covered

Practice functions, calculus, probability, statistics, and mathematical 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 Tasmania Year 11-12 Mathematics curriculum page to scan related topics, subtopics, and pathway coverage.

View Tasmania Year 11-12 Mathematics curriculum coverageBrowse all sample question demos
Sample TASC Year 12 Mathematics Methods questions

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

TASC Year 12 Mathematics 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.

TASC Year 12 Mathematics 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.

TASC Year 12 Mathematics 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.

TASC Year 12 Mathematics 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.

TASC Year 12 Mathematics 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.

TASC Year 12 Mathematics 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 TASC Year 12 Mathematics Methods support

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

This demo is in progress
In progress

Year 12 TAS Maths - Mathematics Methods 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.

View Pricing Browse Demos

Mathematics Methods practice questions FAQ

Does this page include Year 12 Mathematics Methods practice questions?

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