Master Cambridge A Level Maths — from first principles to full marks
Every topic on the 9709 syllabus — Pure, Statistics, and Mechanics — taught with complete worked solutions and the precise mathematical reasoning Cambridge examiners reward. Whether you're sitting AS next term or building toward A2, this is the structured, rigorous resource your revision has been missing.

"Understanding the method deeply is what allows you to adapt — and that's exactly what Cambridge examiners test."— Renstay

What you'll learn
What you'll be able to do
- Confidently solve Pure Mathematics problems across algebra, calculus, trigonometry, and series covered in the 9709 syllabus
- Apply differentiation and integration techniques to curve sketching, optimisation, and area/volume problems at A2 standard
- Tackle probability and statistics questions using correct distributions, hypothesis testing, and data interpretation
- Model and solve Mechanics problems involving kinematics, forces, Newton's laws, and energy in both AS and A2 contexts
- Decode any Cambridge A Level exam question by identifying the technique required and laying out fully-marked working
- Achieve exam-ready confidence with timed past-paper practice, mark-scheme literacy, and targeted gap analysis
How it works
A school that adapts to you
This isn't a set of static videos. Every lesson is generated live and tuned to where you actually are.
We learn your level
A quick placement check tailors your starting point so you're never bored or lost.
Lessons adapt as you go
Each lesson is written for your pace and your goal, adjusting as your skills grow.
Your AI coach keeps you moving
Checkpoints, feedback, and gentle nudges turn progress into a real result.
The curriculum
What's inside your school
6 modules · 29 lessons

Pure Mathematics I — Algebra & Functions
Builds the algebraic foundations required across the entire 9709 syllabus, from surds to polynomials and rational functions.
- 1.1Surds, Indices & Laws of LogarithmsIncluded
- 1.2Quadratics: Completing the Square & DiscriminantIncluded
- 1.3Functions: Domain, Range & Inverse FunctionsIncluded
- 1.4Polynomial Division & the Factor TheoremIncluded
- 1.5Inequalities & Modulus FunctionsIncluded
Pure Mathematics II — Coordinate Geometry, Trigonometry & Series
Covers the AS-level geometry, trigonometry, and series content that forms a major share of Paper 1 marks.
- 2.1Coordinate Geometry: Lines, Circles & Parametric IntroIncluded
- 2.2Trigonometric Ratios, Identities & EquationsIncluded
- 2.3Radians, Arcs & SectorsIncluded
- 2.4Binomial ExpansionIncluded
- 2.5Arithmetic & Geometric SeriesIncluded
Pure Mathematics III — Calculus & Advanced Pure (A2)
Develops AS differentiation and integration into the full A2 calculus toolkit, including differential equations and complex functions.
- 3.1Differentiation: Chain, Product & Quotient RulesIncluded
- 3.2Applications of Differentiation: Optimisation & Curve SketchingIncluded
- 3.3Integration Techniques: Substitution, Parts & Partial FractionsIncluded
- 3.4Area, Volume of Revolution & Differential EquationsIncluded
- 3.5Further Pure: Implicit Differentiation, Parametric Equations & Maclaurin SeriesIncluded
Pure Mathematics IV — Advanced Trigonometry, Vectors & Numerical Methods
Completes the A2 Pure content by mastering compound-angle identities, 3-D vectors, and iterative numerical techniques.
- 4.1Compound & Double Angle FormulaeIncluded
- 4.2R sin(θ + α) and Inverse Trigonometric FunctionsIncluded
- 4.3Vectors in 3-D: Lines & Scalar ProductIncluded
- 4.4Numerical Methods: Iteration & Newton–RaphsonIncluded
Probability & Statistics (Papers 5 & 6)
Covers the full 9709 Statistics component — data representation, probability, distributions, and hypothesis testing.
- 5.1Data Representation & Measures of Central Tendency and SpreadIncluded
- 5.2Probability: Laws, Conditional Probability & Permutations and CombinationsIncluded
- 5.3Discrete Random Variables & the Binomial DistributionIncluded
- 5.4The Normal Distribution & ApproximationsIncluded
- 5.5Hypothesis Testing & the Poisson DistributionIncluded
Mechanics (Papers 4 & 5)
Covers the full 9709 Mechanics component — kinematics, forces, Newton's laws, energy, and connected-body problems.
- 6.1Kinematics in a Straight Line: suvat & Calculus MotionIncluded
- 6.2Forces, Equilibrium & Resolving in Two DimensionsIncluded
- 6.3Newton's Laws of Motion & Connected ParticlesIncluded
- 6.4Work, Energy, Power & Conservation LawsIncluded
- 6.5Exam Strategy: Mark-Scheme Literacy, Timed Practice & Gap AnalysisIncluded
Who it's for
Is this you?
Year 13 A Level students
Facing full A2 papers and needing complete, syllabus-precise coverage of calculus, vectors, and statistics to close gaps before exam season.
AS Level students
Working through their first year of 9709 and wanting clear, step-by-step teaching of algebra, coordinate geometry, and introductory calculus from the ground up.
International school students
Studying the Cambridge syllabus in schools worldwide where class sizes or resources make a reliable, self-contained supplementary resource essential.
Independent self-studiers
Preparing for Cambridge A Level exams without a classroom teacher, and needing a resource that explains every concept fully enough to progress alone.
Adult returners to maths
Returning to formal mathematics after a break and using the structured progression from first principles to rebuild confidence and reach A Level standard.
Cambridge maths teachers
Looking for a mathematically rigorous, syllabus-aligned resource to support lesson planning, student revision, or as a shared reference across a sixth-form cohort.
Questions
Frequently asked
Your teacher
A note from your teacher
Renstay
If you're reading this, there's a reasonable chance that Cambridge A Level Mathematics feels like an enormous amount of content, spread across an equally enormous specification document, and you're not entirely sure where the gaps in your understanding actually are. That's an uncomfortable position to be in — particularly when the exam is real, the mark schemes are unforgiving, and the stakes are high. I've seen that uncertainty in students many times. This school exists to replace it with something more useful: clarity.
What I've built here is a complete, syllabus-aligned treatment of the 9709 course — every topic, every technique, every strand of Pure, Statistics, and Mechanics — taught in the way a careful sixth-form teacher would actually explain it to you across a two-year course. That means we never skip the reasoning. When I show you how to integrate by substitution, you understand why the substitution works, not just what to write. When we work through a hypothesis testing question, you understand what the null hypothesis actually represents and why the critical region is where it is. Understanding the method deeply is what allows you to adapt when a question phrases things in an unfamiliar way — which Cambridge examiners do, frequently and deliberately.
I want to address the most common objection directly: "I've watched videos and read the textbook and I still can't do it in the exam." This almost always comes down to two things. First, passive understanding — following a solution you've been shown is not the same as constructing one yourself. Second, mark-scheme literacy — not knowing how to translate a correct mathematical idea into the structured, stepwise layout that actually earns marks. Both problems are addressed head-on here. The worked examples are annotated at the decision level, not just the calculation level. The exam strategy component teaches you to read questions the way a marker reads answers.
The school is for you whether you are sitting AS papers next term, building toward full A Level, re-sitting to improve a grade, studying independently without a school to support you, or teaching this course yourself and looking for a resource you can trust to be both mathematically precise and pedagogically sound. The level of rigour does not change depending on which of those descriptions fits you — Cambridge's standard is fixed, and so is mine.
Come in, work through the material carefully, and ask questions in the community. The mathematics is absolutely learnable. Let's get on with it.
— Renstay
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- 6 modules, 29 lessons
- AI-adaptive lessons tuned to your level
- Quizzes & checkpoints to lock in progress
- Your own AI learning coach
- Learn on any device, at your pace
- Full access for as long as you're subscribed