A good A Level pure maths tutor fixes algebra foundations first, then builds confidence in functions, trigonometry and calculus with clear methods and regular exam-style practice. Pure maths carries most of the marks in A Level Maths, and gaps from earlier years show up quickly. This guide explains what helps.

Written by Tutopiya, an online tutoring company that teaches A Level maths one-to-one.

Key takeaways

• Algebra is the foundation for everything.
• Trigonometry and calculus are common weak points.
• Clear working earns method marks.
• Exam-style practice builds speed.

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What does A Level pure maths cover?

Pure maths covers algebra, functions, coordinate geometry, sequences and series, trigonometry, exponentials and logarithms, differentiation, integration, vectors and proof. Cambridge students follow the Cambridge A Level Mathematics 9709 syllabus.

Area	Examples
Algebra	Quadratics, inequalities, partial fractions
Functions	Composite, inverse, transformations
Trigonometry	Identities, equations, radians
Calculus	Chain rule, integration by parts
Exponentials	Logarithms, modelling
Vectors	Lines and planes (later units)

Where do students lose marks?

Problem	Example
Algebra slips	Expanding brackets wrongly
Trig identities	Choosing the wrong one
Calculus rules	Chain vs product rule
Missing working	Losing method marks
Proof	Weak logical steps

Signs your child needs a pure maths tutor

• algebra slows them down;
• trig and calculus feel overwhelming;
• marks fall on longer questions;
• the jump from IGCSE or GCSE feels large.

How to choose a pure maths tutor: step by step

1. Confirm the board and papers.
2. Check experience with that syllabus.
3. Ask how they diagnose gaps.
4. Ask about exam practice.
5. Book a trial lesson.
6. Set goals.

Browse our A Level maths tutors and A Level maths tuition.

What should a good tutor offer?

What to check	Why it matters
Diagnosis	Finds root gaps
Clear methods	Reliable working
Board knowledge	Paper styles
Exam practice	Speed and accuracy

What does a good lesson look like?

1. Warm-up algebra.
2. Teach one topic.
3. Worked examples.
4. Exam-style questions.
5. Feedback and homework.

Fixing algebra first

Many A Level difficulties are really algebra difficulties. A tutor can check factorising, fractions, indices and rearranging, and practise until they are automatic.

When should students start?

Starting early in the first year prevents gaps from building. In the final year, focus on mixed past papers.

How to tell tutoring is working

• algebra is faster and more accurate;
• working is clearer;
• trig and calculus feel manageable;
• better test scores.

How parents can help

• encourage short daily practice;
• ask your child to explain a method;
• keep past papers organised.

Questions to ask a tutor

1. Which board have you taught?
2. How do you diagnose gaps?
3. How will we track progress?

A sample term plan

Weeks	Focus
1–2	Algebra diagnostic and fixes
3–5	Functions and coordinate geometry
6–8	Trigonometry
9–12	Calculus and past papers

How much tutoring is enough?

One weekly lesson works for most students. Students with big algebra gaps may benefit from two lessons a week for a few weeks.

Calculus step by step

1. Learn standard derivatives and integrals.
2. Practise chain, product and quotient rules.
3. Apply to tangents, normals and stationary points.
4. Integrate using substitution and parts.
5. Apply to areas.

Trigonometry identities

Students should know which identities appear in the formula booklet and which must be remembered. A tutor can practise choosing the right identity quickly.

Proof

Proof questions reward clear logic. A tutor can teach proof by deduction, exhaustion and contradiction with simple examples first.

Online lessons for pure maths

Online whiteboards make it easy to work through algebra and graphs together. Students can photograph working for feedback between lessons.

The jump from IGCSE or GCSE

The biggest change at A Level is the amount of algebra in every question and the need to string several steps together. Students who earned top grades at 16 can still find the first term hard, especially if they relied on calculators or memorised methods. A tutor can identify exactly which earlier skills need strengthening, such as surds, indices, completing the square or rearranging formulae, and practise them inside A Level questions rather than as separate drills. That way students rebuild foundations while still keeping up with school. See also IGCSE to A Level bridging tutoring.

Tip: keep a list of every mistake from homework and tests; reviewing it weekly stops the same errors repeating.

How Tutopiya tutoring works

Tutopiya offers one-to-one online tutoring.

• A tutor matched to your child’s subject, level and exam board.
• A free first trial lesson, with no card needed.
• From 4 hours a month per subject. Each tutor sets their own rate, shown before booking.
• AI lesson analysis gives a written summary, flashcards and quiz questions after each lesson.

See A Level maths tuition.

Common mistakes

• Skipping algebra practice → fix foundations.
• No working → show every step.
• Memorising without understanding → learn why.
• Avoiding hard topics → practise them.

Talk to us

For related guides, see an A Level mechanics tutor and how to choose an A Level further maths tutor. Or contact our team.

Summary: an A Level pure maths tutor fixes algebra first, then builds clear methods in trig and calculus with regular exam practice.

Frequently asked questions

What is pure maths at A Level? +

Pure maths is the core of A Level Maths: algebra, functions, coordinate geometry, sequences, trigonometry, exponentials, calculus, vectors and proof.

Which papers are pure maths? +

Cambridge 9709 has Pure Mathematics 1 and 3, Edexcel A Level Maths 9MA0 has Papers 1 and 2, and Edexcel International A Level has P1 to P4.

Why do students struggle with pure maths? +

Weak algebra from GCSE or IGCSE, gaps in trigonometry and the step up in calculus are the most common causes.

How quickly can a tutor help? +

Many students see clearer working within a few weeks. Fixing algebra foundations can take a term, depending on the gaps.

Does Tutopiya offer A Level pure maths tutoring? +

Yes. Tutopiya offers one-to-one online A Level maths tutoring for Cambridge, Edexcel and IAL. The first trial lesson is free with no card required.

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