A-level exam readiness

By MathLab · Updated 10 October 2026

This guide helps you identify your next revision task. The short questions below are original MathLab examples, not a full diagnostic, official exam questions or a prediction of your grade.

A practical readiness checklist

Use recent attempts rather than confidence alone. Keep “not yet taught” separate from “studied but needs repair”. For complete coverage, use your specification alongside the revision guide.

Try a short mixed check

Attempt each question before opening the worked answer. Write a method as well as a result. There is no pass mark: use the pattern of difficulties to decide what to practise next.

Try a sample

01

MathLab practice

Algebra and domains

Sample

Solve $\log_2(x-1)+\log_2(x-3)=3$ over the real numbers.

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Worked answer: combine the logs, then check the domain

Both logarithms require $x>3$. Combine them to get $(x-1)(x-3)=2^3=8$, so $x^2-4x-5=0$. Factorising gives $(x-5)(x+1)=0$. The roots are $5$ and $-1$, but only $x=5$ satisfies the original domain.

If you kept both roots, practise checking answers and logarithmic equations.

02

MathLab practice

Calculus and classification

Sample

Find and classify the stationary points of $y=x^3-3x^2+2$.

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Worked answer: differentiate and classify each point

$y'=3x^2-6x=3x(x-2)$, so the stationary points occur at $x=0$ and $x=2$. Their coordinates are $(0,2)$ and $(2,-2)$. Since $y''=6x-6$, the second derivative is negative at $0$ and positive at $2$. Therefore $(0,2)$ is a local maximum and $(2,-2)$ is a local minimum.

If you found only the values of $x$, revisit communicating reasoning and curve analysis.

03

MathLab practice

Statistics and assumptions

Sample

A model gives each of four independent attempts a success probability of $0.3$. Find the probability of at least one success. Explain why the model might fail if the person learns between attempts.

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Worked answer: use the complement and state the limitation

The probability of no successes is $0.7^4=0.2401$. Therefore the probability of at least one is $1-0.7^4=0.7599$. Learning could change the probability of success between attempts, so the constant-probability assumption may fail; independence may also be questionable.

If you added four probabilities of $0.3$, revisit the binomial distribution. If you omitted the explanation, practise interpreting context.

04

MathLab practice

Mechanics and a reversal

Sample

A particle moves along a straight line with velocity $v=6-2t$ metres per second for $0\le t\le5$. Find its displacement and total distance travelled.

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Worked answer: split distance where velocity changes sign

The displacement is $[6t-t^2]_0^5=30-25=\mathbf{5\text{ m}}$. Velocity is zero at $t=3$. The positive triangular area from $0$ to $3$ is $\tfrac12(3)(6)=9$ m; the negative triangular area from $3$ to $5$ has magnitude $\tfrac12(2)(4)=4$ m. Total distance is $9+4=13$ m.

If your two answers were the same, practise kinematics graphs. A correct numerical answer should still state the quantity and units.

Swipe to explore the questions.

Turn the evidence into a next step

Choose one or two priorities and put them into your weekly revision plan. After repair, use fresh questions to check improvement rather than repeating a solution you now remember.

How do you know whether you are ready?

Look for a consistent pattern across more than one representative paper: independent starts, clear methods, accurate completion and sensible timing. Mark with the official mark scheme and seek feedback on explanations you cannot judge yourself. No short checklist or four-question score can establish a predicted grade.

Do I need to finish every worksheet?

Completion is not the same as readiness. Use varied questions to establish that you can retrieve and apply a skill, and return to it in mixed work. Spend more time where your attempts reveal a gap.

Should every practice session be timed?

Allow untimed work when repairing understanding. Introduce timing when you can use the method independently, then practise whole-paper decisions such as moving on and returning later.

Does this cover my exam board?

The guide supports the common A-level Mathematics content in England. Paper structure, large data sets and assessment details depend on your board. Check the DfE subject content and your board’s current specification. The examples are deliberately selective; use the complete specification for coverage.