A cup of coffee cools so that its temperature T °C after t minutes is T = 20 + 65e^(−0.08t). a. Find the rate at which the coffee is cooling after 10 minutes, correct to two decimal places. b. Explain what happens to the temperature of the coffee as t becomes very large, and why.

a. dT/dt = 65 × (−0.08)e^(−0.08t) = −5.2e^(−0.08t). At t = 10: −5.2e^(−0.8) ≈ −2.34 °C per minute. b. As t → ∞, e^(−0.08t) → 0, so T → 20. The coffee approaches 20 °C, the temperature of the room, and never falls below it.

Find the area enclosed between the curve y = x² − 4 and the x-axis.

The curve cuts the x-axis at x = −2 and x = 2, and lies below the axis between them. Area = −∫₋₂² (x² − 4) dx = −[x³/3 − 4x]₋₂² = −((8/3 − 8) − (−8/3 + 8)) = 32/3 square units.

Is Maths Methods harder than General Maths?

It asks for different things rather than simply more. Methods is built on calculus and algebraic fluency and assumes you can move between a graph, an equation and a worded context without losing the thread. Students who enjoy that find it manageable; students who want procedures to follow find it relentless.

Do I need a calculator for Methods?

For one of the two exams, yes, and you should know it well. For the other there is no calculator at all, which is why exact-value work and clean algebra by hand are worth practising deliberately rather than assumed.

How do I get better at the harder questions?

Work backwards from the marks. A five-mark question is telling you it wants roughly five creditable steps, so the question is what those steps are — not whether you can see the whole answer at once. Most students who freeze on long questions can do every individual step in them.

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VCE · Units 1–4

VCE Maths Methods practice exams and worked solutions

Methods rewards students who can move between a graph, an equation and a context without losing the thread. These papers ask for the working, not just the answer, because that is where the marks live.

What the course asks of you

Functions and graphs: Transformations, domain and range, and reading a graph back into an equation.
Calculus: Differentiation and integration in context — rates, areas, and finding where a rate matters.
Probability: Discrete and continuous distributions, and the normal distribution in applied problems.
Algebra: Solving exactly, and knowing when an exact answer is required rather than a decimal.

Sample questions

Written for this site, in the style of the exam. Answer first, then see the model response and what the marks were for.

Question 1
1 mark
The function f is defined by f(x) = 2(x − 3)² − 8. The range of f is:
Question 2
4 marks
A cup of coffee cools so that its temperature T °C after t minutes is T = 20 + 65e^(−0.08t). a. Find the rate at which the coffee is cooling after 10 minutes, correct to two decimal places. b. Explain what happens to the temperature of the coffee as t becomes very large, and why.
Question 3
2 marks
The random variable X is normally distributed with mean 70 and standard deviation 8. Find Pr(X > 82), correct to three decimal places.
Question 4
3 marks
Find the area enclosed between the curve y = x² − 4 and the x-axis.

How the Methods exams differ from each other

Methods is examined twice, and the two papers reward different things. Preparing for one shape and meeting the other is the commonest way a well-taught student underperforms.

One paper is technology-free: No calculator. Exact values, clean differentiation, and algebra you can carry in your head. Students who have done every practice question with technology to hand find this paper slow in a way that has nothing to do with whether they understand the mathematics.
The other allows technology, and expects you to use it well: Knowing that a calculator can solve something is not the same as knowing when reaching for it is faster than doing it by hand. Time is lost both ways.
A formula sheet is provided: Memorising it is wasted effort; finding a formula on it quickly is not. Practise with the sheet beside you so that on the day you are reading it rather than searching it.
Marks are for working, not just answers: A correct answer with no working can score less than a wrong answer with sound method. Show the step that shows you knew what you were doing.

Where Methods marks are actually lost

Not usually in the hard question at the end. They go in ones and twos across the paper: an exact value given as a decimal, a domain left off a restricted function, a rate answered without its units, a graph sketched without its intercepts labelled.

The second big loss is stopping at the first answer. Methods questions routinely ask for something the first calculation only sets up — the maximum rate rather than the rate, the value of x rather than the point. Reading the last line of the question again before writing the answer costs seconds and saves marks.

The third is the technology-free paper, where fluency with exact values decides how much of the paper you reach at all.

Common questions

Is Maths Methods harder than General Maths?: It asks for different things rather than simply more. Methods is built on calculus and algebraic fluency and assumes you can move between a graph, an equation and a worded context without losing the thread. Students who enjoy that find it manageable; students who want procedures to follow find it relentless.
Do I need a calculator for Methods?: For one of the two exams, yes, and you should know it well. For the other there is no calculator at all, which is why exact-value work and clean algebra by hand are worth practising deliberately rather than assumed.
How do I get better at the harder questions?: Work backwards from the marks. A five-mark question is telling you it wants roughly five creditable steps, so the question is what those steps are — not whether you can see the whole answer at once. Most students who freeze on long questions can do every individual step in them.

32 full papers for Maths Methods

Complete practice exams with a model answer for every part, and your own marks saved question by question so you can see where they went.

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