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VICMath Methods2024

VCE Math Methods 2024

Walkthrough of the 2024 VCE math methods exam: what it assessed, strategy tips, and the common errors flagged in the official marker report.

Marks: 80
Time: 120 min
Authority: VCAA
Updated: 2026-05-29

Open the official PDF ->Official marking notes

What this paper assessed

This VCAA Mathematical Methods Units 3 & 4 examination is an 80-mark technology-active (CAS) paper sat over 120 minutes (plus 15 minutes reading time) - the structure of Exam 2, with Section A multiple choice and Section B extended response. It assesses the four areas of study:

Functions, relations and graphs - polynomial, power, exponential, logarithmic and circular functions; transformations; domain, range and inverse functions.
Algebra - solving equations, simultaneous equations, and using the CAS for exact and numerical solutions.
Calculus - differentiation (chain, product, quotient rules), applications (rates, tangents, optimisation), and integration (definite integrals, area, average value).
Probability and statistics - discrete and continuous random variables, the binomial and normal distributions, and sample proportions / confidence intervals.

Calculator-active items reward careful CAS syntax and interpretation. The 2024 paper leaned harder on application where the context was unfamiliar but the underlying skill was core.

Structure and timing

80 marks in 120 minutes is 1.5 minutes per mark:

Section A (~20 MC marks): ~25-30 minutes - bank quick marks early, ~1.3 min each.
Section B (~60 marks): ~90 minutes at ~1.5 min/mark. A 5-mark optimisation or probability item deserves ~7-8 minutes including setup.
Reserve the final ~8-10 minutes to check answers, exact forms where required, and that each result addresses the context.

Always write the rule being applied before using the CAS, and state exact answers where the question demands them.

Worked practice questions (exam-style)

Worked example

Question 1 (4 marks): For $f(x) = x e^{-2x}$ , find $f'(x)$ and determine the exact coordinates of the stationary point.

The function is a product of two factors, so we apply the product rule. The stationary point is found by setting the derivative to zero and using a key property of the exponential function.

Step 1: Apply the product rule

Let $u = x$ and $v = e^{-2x}$ , giving $u' = 1$ and $v' = -2e^{-2x}$ (chain rule). Then:

f'(x) = u'v + uv' = e^{-2x} + x(-2e^{-2x}) = e^{-2x}(1 - 2x).

Step 2: Solve $f'(x) = 0$

Since $e^{-2x} > 0$ for all real $x$ , the factor $e^{-2x}$ is never zero. So we need only solve $1 - 2x = 0$ , giving $x = \tfrac{1}{2}$ .

Step 3: Find the $y$ -coordinate and state the answer

f\!\left(\tfrac{1}{2}\right) = \tfrac{1}{2}e^{-2 \cdot \frac{1}{2}} = \tfrac{1}{2}e^{-1} = \frac{1}{2e}.

Final answer: $f'(x) = e^{-2x}(1 - 2x)$ and the stationary point is at $\left(\tfrac{1}{2},\ \dfrac{1}{2e}\right)$ .

Worked example

Question 2 (5 marks): The continuous random variable $X$ has probability density function $f(x) = kx$ for $0 \le x \le 4$ , and $0$ otherwise. Find $k$ , then find $P(X > 3)$ .

For a valid pdf the total probability over the support must equal 1. We use this condition to pin down $k$ , then integrate over the required tail to find the probability.

Step 1: Find $k$ from the normalisation condition

Integrate over the entire support $[0, 4]$ and set equal to 1:

\int_0^4 kx\,dx = k\left[\frac{x^2}{2}\right]_0^4 = k \cdot \frac{16}{2} = 8k = 1.

So $k = \dfrac{1}{8}$ .

Step 2: Integrate the pdf over the tail $[3, 4]$

With $k = \dfrac{1}{8}$ , integrate from 3 to the upper bound of the support:

P(X > 3) = \int_3^4 \frac{1}{8}x\,dx = \frac{1}{8}\left[\frac{x^2}{2}\right]_3^4 = \frac{1}{8}\cdot\frac{16 - 9}{2} = \frac{1}{8}\cdot\frac{7}{2} = \frac{7}{16}.

Final answer: $k = \dfrac{1}{8}$ and $P(X > 3) = \dfrac{7}{16}$ ( $\approx 0.4375$ ).

Worked example

Question 3 (5 marks): In a large population, 30% of items are defective. A random sample of 10 items is taken. Using the binomial distribution, find the probability that exactly 2 are defective, and state the mean number of defectives expected.

Each sampled item is independently either defective or not, with a constant probability of 0.3, so the count of defectives follows a binomial distribution. We apply the formula, then recall the mean formula.

Step 1: Define the distribution and write the formula

Let $X$ be the number of defectives. Then $X \sim \text{Bin}(n=10,\ p=0.3)$ . The binomial probability formula gives:

P(X = 2) = \binom{10}{2}(0.3)^2(0.7)^8.

Step 2: Evaluate each factor

Compute the binomial coefficient and the two powers separately: $\binom{10}{2} = 45$ , $(0.3)^2 = 0.09$ , $(0.7)^8 \approx 0.05765$ .

P(X = 2) = 45 \times 0.09 \times 0.05765 \approx 0.2335.

So $P(X = 2) \approx 0.233$ .

Step 3: State the expected number of defectives

For a binomial distribution the mean is $E(X) = np$ :

E(X) = 10 \times 0.3 = 3.

Final answer: $P(X = 2) \approx 0.233$ and the expected number of defectives is $3$ .

Common errors students made

The 2024 VCAA examination report flagged that students lost marks by:

chain-rule slips on composite functions;
sign errors when integrating (and forgetting the constant);
skipping domain or restriction statements;
using the wrong conditional setup in probability questions.

Further traps to avoid:

Giving decimal approximations where an exact answer is required (and vice versa).
CAS syntax errors - mis-entering domains, brackets or distribution parameters, then trusting the wrong output.
Forgetting to verify a maximum/minimum or to check a pdf integrates to 1.
Not addressing the original context in an applied item, or rounding too early.

How to use this paper

Sit Section A in ~25-30 minutes, then Section B in ~90 minutes, with your CAS and reference materials ready.
Self-mark against the official VCAA assessment report and answers at the links in the frontmatter, awarding method marks line by line.
Re-attempt any item scored below half, writing the relationship first, then using the CAS deliberately and checking the output makes sense.
Keep an error log of recurring algebra/CAS slips and review it before each timed re-sit.

Use this paper well

Sit the paper under exam conditions (120 minutes, 80 marks).
Mark yourself against the official VCAA marking notes.
Compare against the Math Methods hub to find the syllabus dot points this paper tested.

What this paper assessed

Structure and timing

Worked practice questions (exam-style)

Common errors students made

How to use this paper

Use this paper well

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