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AQA 8365 includes differentiation: finding a gradient or rate of change. This constructed example shows the difference between substituting into a formula and understanding what the result means.

The task: for the curve y = x³ − 4x, find the gradient at x = 2. A learner substitutes 2 and gets y = 8 − 8 = 0. That locates the point (2, 0) on the curve. It does not tell us the slope there.

The correction: differentiate first. The derivative, written dy/dx, gives the gradient: dy/dx = 3x² − 4. At x = 2, this is 3 × 4 − 4 = 8. The curve therefore passes through height 0 while its tangent has gradient 8. A tangent is the straight line matching the curve’s direction at that point.

A better response: “The point is (2, 0) and the gradient is 8, so the tangent is y = 8(x − 2).” Each number now has a purpose.

For a follow-up, use the same curve at x = 1. The point is (1, −3) and the gradient is −1. Ask the learner to explain why −3 and −1 answer different questions before moving to a longer exam problem.

A tutor enquiry becomes more useful when it names the part of Further Maths that is difficult. For example, AQA A-level students take two options from mechanics, statistics and discrete mathematics. Pearson Edexcel uses two Core Pure papers and two optional papers from permitted combinations of further pure, further statistics, further mechanics and decision mathematics. Check the combination your school is teaching before selecting practice papers.

Describe the problem in your own words. These are examples of details to include when the topic is on your course:

Use a recent question the learner has attempted, together with the course materials, to agree an initial priority. A useful plan connects tuition to school learning and checks what the learner can do independently. The sequence below is a suggested approach to discuss with a tutor.

For a learner who finds dense notation overwhelming, request one change per line and a brief explanation of each new symbol. For someone who can calculate accurately but struggles to justify a result, make the explanation the practice task. State any access or learning needs in the enquiry so you can discuss appropriate adjustments.

Latimer tutors offer a free introductory meeting before paid lessons. Use that conversation to discuss your course, goals and lesson arrangements; it is not normally a full teaching lesson.

Check the tutor’s profile for relevant subject and stage experience, then ask about the exact papers or options you need. A useful enquiry might say: “I’m taking AQA A-level Further Maths with mechanics and statistics. My algebra is secure, but I struggle to set up mechanics questions. Could we focus on explaining the setup before doing timed practice?” Replace those details with your own.

Bring one attempted question to describe the difficulty. Discuss how the tutor would help when an explanation does not make sense, how you will share written work and what practice would fit between lessons. If you need a particular teaching background or experience of a learning need, ask about that directly.

After teaching begins, assess fit through the learner’s work: can they explain a step they previously copied, or attempt a similar question with less help? Use those observations to review the priorities and pace together.