Year 12 TAS Maths - Mathematics Methods sample questions
Year 12 TAS Maths - Mathematics Methods sample questions
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Year 12 Mathematics Methods practice questions
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Skills covered
Practice functions, calculus, probability, statistics, and mathematical modelling.
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Sample TASC Year 12 Mathematics Methods questions
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TASC Year 12Mathematics MethodsIntegral calculushardtangent and area graph
1. What is the exact value of the integral from 0 to 2 of (3x² - 2x) dx?
Choices
4
8
2
12
Explanation:
An antiderivative is x³ - x^2. Evaluating from 0 to 2 gives 8 - 4 = 4.
TASC Year 12Mathematics MethodsDifferential calculushardtangent graph
2. For f(x) = ln(x² + 1), the tangent T is drawn at P where x = 2. What is the gradient of 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 12Mathematics MethodsExponential and logarithmic modellinghardmodel graph
3. A population is modelled by P(t) = 1200 / (1 + 5e^(-0.4t)). What is the exact time when P(t) = 800?
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 12Mathematics MethodsContinuous probabilityharddensity graph
4. For the continuous random variable X with density f(x) = c(2x + 1), 0 <= x <= 3, what is P(X > 2)?
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 12Mathematics MethodsNormal distributionhardnormal 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?
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 12Mathematics MethodsFunctions and logarithmshardmodel graph
6. For f(x) = 3e^(0.5x) - 2, what exact value of x satisfies f(x) = 10?
Choices
4 ln 2
2 ln 2
ln 4
4
Explanation:
Set 3e^(0.5x) - 2 = 10, so e^(0.5x) = 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
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Practice Summary
Year 12 · TAS Maths - Mathematics Methods · Test mode · 5 questions · 10 min
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Correct answersPending
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