Maths Methods Paper 2: what to expect in 2026

Maths Methods Paper 2 is on Friday 13 November, the same day as Paper 1. If you have already read what to expect on Paper 1, this post is the other half. Paper 2 asks quite different questions, so it is worth going in with a different plan.

I went back through every past QCAA Mathematical Methods Paper 2 from 2020 to 2025: 60 multiple choice questions and 56 short response questions, each sorted by topic. Six question shapes have appeared on almost every Paper 2, and the normal distribution and exponential models are the two I would prepare first. The multiple choice pages on this site also show how Queensland students answered from 2021 to 2025, so we can see which questions caught us out.

First, a quick reminder of how the paper is set out. Paper 2 is technology-active. Questions 1 to 10 are multiple choice, and the short response section has been worth 45 marks since 2021 (it was 50 marks in 2020). Since 2022 there have been nine short response questions, and 2020 and 2021 had ten. The complex unfamiliar questions come at the end: Questions 18 and 19 from 2023 to 2025, and Questions 17 to 19 in 2022.

Keep in mind that a pattern is a guide, not a guarantee. 2026 is also the first external exam on the new 2025 syllabus, so I will point out where that changes things.

Paper 2 at a glance

These are the Paper 2 question shapes that keep coming back. Every question number below opens the worked solution.

Paper 1 is calculus and probability by hand. Paper 2 is the modelling and statistics paper: if a question needs a normal probability, a numerical solve or an integral you could not do by hand, it belongs here.

The normal distribution: the topic to prepare first

The normal distribution has been on every Paper 2 since 2020, and in every one of those years it was in a complex familiar or complex unfamiliar question. If you only have one evening, I would spend a good part of it here.

• Forwards: a probability or a value. 2022 Q12 gives the mean and standard deviation of the distance vehicles travel in a year, and asks for a probability and then a 60th-percentile distance. 2023 Q17 gives award categories for the top 15%, the next 15% and the next 15% of bridge loads, and wants the gap between two of the cut-off loads to the nearest gram.
• Backwards: find the mean or standard deviation. This is the version I would practise the most. In 2020 Q16 the mean is 591 mL and 35% of bottles hold 593 mL or more, so you find \(\sigma\) from the inverse normal, then the 20th percentile. 2024 Q15 works backwards to a mean: someone 210 cm tall is taller than exactly 90% of another country, so find that country’s \(\mu\), then its “extremely tall” cut-off of three standard deviations above it. 2024 Q19 hides \(\sigma\) inside the normal formula: \(p(10)=0.0135\) for e-scooter speeds with a mean of 18 km/h.
• Normal, then something else. 2022 Q18 turns a normal probability (an IQ of at least 120) into the \(p\) of a binomial with nine people. 2025 Q19 mixes two species of beetle and asks for a conditional probability: given a short horn, how likely is it to be species A?

A detail worth knowing from 2024 Q19. Solving \(p(10)=0.0135\) on the calculator gives two values, \(\sigma\approx4.00\) and \(\sigma\approx28.4\). The marking guide rejects 28.4 because three standard deviations below a mean of 18 km/h would be a negative speed. When a solve gives two answers, say which one you are keeping and why.

New notation. The 2025 syllabus writes a normal random variable as \(X\sim N\left(\mu,\sigma^2\right)\). QCAA has not printed it on a past paper, but if you see it, remember that the second number is the variance, not the standard deviation. Be careful if you check the 2024 marking guide, as its Q19 solution puts the standard deviation, 4.00, in that spot, which is not the syllabus convention.

Exponential and log models: the other big topic

Exponential and log models in context were on five of the six Paper 2s, often two or three times. 2022 is the exception: logs only appeared there inside motion questions. In 2024, three of the four simple familiar questions were models of this kind.

The simple familiar versions are chains of short parts: find the constant, solve for a time, find a rate. Work through 2025 Q12 (cockroaches: 100 at the start and 120 after three weeks, so find \(k\), then \(P'(t)\)), 2024 Q13 (termites) and 2024 Q14 (the height of a football kick over a training clinic).

The harder versions hide one step:

• 2025 Q16 gives \(M=100b^t\) and one data point, then asks for the rate of growth when there are five times as many fish. To differentiate \(b^t\), write it as \(e^{t\ln(b)}\) first.
• 2021 Q18 asks for the population when it is growing fastest. Growing fastest means the maximum of \(P'\), so graph \(P'\) and find its maximum (or solve \(P''=0\)).
• 2023 Q19 gives the hill as an integral, so differentiate first to get \(h(x)=ae^{bx}\). Then find \(a\) and \(b\) from two points, locate the tree stumps from their gradients, and judge a prediction.

Logs to bases other than \(e\), like the earthquake magnitudes in 2024 Q12, are now Unit 2 assumed knowledge. They can still appear as a step, so keep the log laws handy.

Trig models have replaced the triangles

A trig model in context was on Paper 2 in four of the six years, and the simple familiar ones follow a pattern: build or use a sine or cosine model, then use its derivative.

• 2023 Q12: the water level under a bridge, from a graph through three points. Build the cosine model first.
• 2025 Q14: tourist numbers over a year. Find when they first reach 36 000, then use the second derivative at the minimum and explain what its sign tells you.
• 2022 Q13: the width of a beach as the tide comes and goes.

Meanwhile, the sine and cosine rules have become less common on Paper 2. The last standalone triangle question was 2023 Q14 (a paddock split by a fence), then there was only a multiple choice question in 2024 and nothing in 2025. They have not gone away, though. The cosine rule was a hidden step in 2023 Q18 (the window) and the core of a complex question on Paper 1 in 2024 (2024 Paper 1 Q18). They are still in the syllabus, including the ambiguous case, so revise them.

Binomial and confidence intervals, with technology

Both have been on every Paper 2. The binomial questions usually hide one step before the calculator does the work:

• 2024 Q17: 3% of fruit is bruised and boxes hold four pieces. First find the probability that a box contains bruised fruit, then the expected number of boxes out of 140.
• 2025 Q15: a 65% chance of seeing a whale each day, over 40 days.
• 2022 Q11: a 20% chance of a sale to each of 25 customers, for the mean and standard deviation.

The confidence interval questions run forwards and backwards:

• Forwards: 2023 Q11 finds \(\hat{p}\) for 17 out of 50, then a 95% interval. 2025 Q13 makes you read the sample proportion off a column graph first.
• Backwards: 2025 Q18 gives only the lower end of a 95% interval (0.648) and the sample size (500). Recover \(\hat{p}\), then judge a claim that more than 75% of employees are satisfied.
• A claim against a threshold: in 2024 Q16, a council only discusses proposals with more than 80% support.
• A sample size: 2020 Q17 wants 95% confidence to within \(\pm0.02\).

Areas, totals and motion

An area, a trapezoidal estimate or an accumulated total has been on every Paper 2.

The total area question that caught us out

2024 MC8 asked for the total area between \(y=x^2-x-6\) and the \(x\)-axis from \(x=1\) to \(x=5\). Only 27.3% got it right, and 62.3% chose 5.33, which is the value of the integral. The graph crosses the axis at \(x=3\), so split the integral there and add the sizes of the pieces to get 20. The same mistake caught 58.9% of students on Paper 1 in 2025 (2025 Paper 1 MC8).

The other forms to know are these:

• The trapezoidal rule. 2024 Q11 asks you to state the rule, then use it with six strips, showing every substitution. Write the rule out in full, even though your calculator could do the integral.
• Areas between curves. 2023 Q13 finds the intersections, writes the integral, then evaluates it.
• Accumulated totals. 2023 Q18 fits a parabola to a window’s dimensions, then turns its area into a mass at 5.6 kg per square metre. 2022 Q19 gives rates of flying foxes entering and leaving a region.

Straight-line motion has also been on every Paper 2. 2021 Q12 integrates a velocity to a displacement, 2022 Q17 has an ant chasing a snail, and 2024 Q18 asks for an average velocity while an object is within range of a motion sensor. If the velocity changes sign, distance and displacement differ, for the same reason as the area question above.

Probability density functions

Other probability density functions were on Paper 2 in five of the six years: 2025 Q17 asks for a mean viewing time, 2022 Q16 shifts a random variable by 11 minutes, and 2021 Q13 builds up to the variance over three parts. One multiple choice question is worth a look: in 2022 MC5, only 37.7% found the standard deviation, and slightly more chose 0.467, which is the variance. Remember to take the square root at the end.

One more multiple choice question worth a look

2025 MC9: the gradient of the line perpendicular to the tangent to \(y=\ln(4x)\). Only 30.6% got it right, and 37% chose 1.25, which is the gradient of the tangent itself. Remember that perpendicular means the negative reciprocal.

What is new for 2026

• General discrete random variables now sit in Unit 3. Past papers have only touched them lightly (a probability read off a frequency graph in 2025 Paper 1 MC10), and none has asked for \(E(X)\) from a general probability table. On Paper 2, the likeliest form is an expected value from a table of outcomes, used to make a decision: which option earns more on average, or whether a game is fair. Know \(E(X)=\sum x\,p(x)\) and how to find the variance.
• Integrals outside the 2025 list. The 2025 syllabus integrates \(x^n\), \(e^x\), \(\frac{1}{x}\), sine, cosine and \(f(ax+b)\). Some older questions need more than that. For example, the velocity in 2023 Q16 integrates by an \(\frac{f'}{f}\) pattern, so on a question like that, integrate numerically on your calculator instead.

Calculator skills to have automatic

• Normal probabilities, and the inverse normal for both tails and the centre.
• Binomial probabilities, exactly and cumulatively.
• Definite integrals, including the area between curves.
• Solving an equation and finding where two graphs meet.
• Finding a maximum or minimum on a graph.
• Storing unrounded values, so the final answer rounds correctly.

A revision plan for Paper 2

Both papers are on the same day, so split your last few evenings. Do each question with your calculator, the way you will on the day, and give yourself about a minute and a half per mark. Then check your work against the marking guide, one mark at a time.

Session 1: statistics

• A normal back-solve: 2020 Q16.
• One complex unfamiliar normal question: 2024 Q19 or 2025 Q19.
• Normal into binomial: 2022 Q18.
• A confidence interval, then one worked backwards: 2023 Q11, then 2025 Q18.
• A binomial with a hidden step: 2024 Q17.

Session 2: models and calculus

• An exponential model chain: 2025 Q12, then 2025 Q16.
• A trig model: 2025 Q14.
• The total area question and the trapezoidal rule: 2024 MC8, then 2024 Q11.
• Motion: 2024 Q18.
• After that, put the books away and get a good night’s sleep.

The Methods game plans and topic guides are free until the end of 13 November. The normal distribution game plan would be a great one to read through the night before!

Best of luck

Nobody can promise what will be on Friday’s papers. This is the first year of a new syllabus, and general discrete random variables have barely been examined, so the 2026 papers might surprise us. Still, six years of past papers tell us a lot about where your last few hours of study will help the most.

Have a good breakfast, bring your calculator, and trust the work you have put in over the last two years. Be kind to yourself between the two papers, and best of luck on Friday!

If you are a Year 11 student starting Units 3 and 4 and want help building these skills earlier, that is what tutoring is for.