A-Level Mathematics
Pure Mathematics, Statistics and Mechanics — 3 sessions per week, 2 hours each. 6 structured contact hours every week, taught by a PhD-qualified tutor.
A-Level Mathematics
A-Level Mathematics is one of the most highly regarded subjects at sixth-form level and is required or strongly recommended for degrees in Engineering, Computer Science, Economics, Physics and many more. At The Astute College, our full-time programme is built around genuine subject mastery, not just exam technique.
Our PhD-qualified tutor delivers 3 sessions of 2 hours each week — 6 contact hours per week. Over two years this equates to over 200 hours of direct tuition. Sessions balance new content, worked examples, problem solving and review, with written feedback on all marked work.
3
Sessions per week
2 hrs
Per session
6 hrs
Contact time per week
200+
Total tuition hours over 2 years
Weekly Lesson Schedule
New Content & Taught Examples
New syllabus content introduced through clear explanation and worked examples. Students practice under supervision with tutor guidance.
Problem Solving & Past Papers
Challenging multi-step and exam-style questions. Tutor addresses misconceptions and develops high-mark problem-solving strategies.
Mixed Practice & Consolidation
Cross-topic practice connecting ideas across the syllabus — essential as A-Level exams regularly combine multiple topics in single questions.
Year 12 — AS Level Content
Sept–June, 3×2hrs/weekAlgebra & Functions
- Laws of indices and surds
- Quadratic functions: factorising, completing the square
- Simultaneous and linear/quadratic inequalities
- Polynomials and factor theorem
- Graph transformations and modulus function
Coordinate Geometry
- Straight lines: gradient, midpoint, distance
- Equation of a line in various forms
- Circles: equation, properties, tangents
- Intersection of lines and curves
Sequences & Series
- Arithmetic and geometric sequences
- Sigma notation and sum formulae
- Binomial expansion (positive integer n)
- Real-world applications of sequences
Trigonometry
- Sin, cos, tan graphs and exact values
- Sine rule, cosine rule, area of triangle
- Trigonometric identities
- Solving trig equations in given intervals
Differentiation
- Gradient from first principles
- Differentiating polynomials and standard functions
- Chain, product and quotient rules
- Stationary points, tangents, normals
- Rates of change and optimisation
Integration
- Integration as reverse differentiation
- Definite integrals and area under a curve
- Area between two curves
- Introduction to integration by substitution
Statistics
- Sampling methods and data presentation
- Measures of location and spread
- Probability rules: addition and multiplication
- Binomial and Normal distributions
- Hypothesis testing (introduction)
Mechanics 1
- Kinematics: SUVAT equations
- Velocity-time and displacement-time graphs
- Newton's three laws of motion
- Connected particles and pulleys
- Variable acceleration using calculus
Year 13 — A2 Level Content
Further Pure & Proof
- Proof by contradiction and induction
- Functions: domain, range, composite, inverse
- Radians, arc length and sector area
- Further trig: addition formulae, double angle
- Reciprocal trig: sec, cosec, cot
Advanced Algebra
- Binomial expansion (any rational n)
- Partial fractions including repeated factors
- Parametric equations and differentiation
- Implicit differentiation
Advanced Calculus
- Integration by parts and substitution
- Integration using partial fractions
- Differential equations: formation and solution
- Numerical methods: Newton-Raphson, trapezium rule
- Volumes of revolution
Vectors
- Vectors in 2D and 3D, position vectors
- Scalar (dot) product and angle between vectors
- Vector equations of lines
- Applications in geometry and mechanics
Statistics 2
- Conditional probability and Venn diagrams
- Normal distribution and z-scores
- Normal approximation to Binomial
- Hypothesis testing in context
- PMCC and regression lines
Mechanics 2
- Projectile motion (horizontal and angled)
- Friction and limiting equilibrium
- Moments, turning forces and centres of mass
- Work, energy and power in mechanics
Exam Preparation
Weekly Past Paper Questions
Exam-style questions from AQA, Edexcel and OCR past papers tackled every week throughout the two-year programme.
Termly Full Mock Exams
Full timed mock papers under exam conditions at the end of each term, with detailed written feedback and grade targets.
Structured Revision Programme
Pre-exam revision sessions cover every area of the specification systematically, connecting topics as they appear in A-Level papers.
Individual Targets
Grade targets set and reviewed at each stage. Every student receives personalised feedback to keep them on track for their university application grades.
Careers
Engineering
Civil, Mechanical, Electrical and Aerospace Engineering all require A-Level Mathematics — often as an essential entry requirement.
Computer Science
Software development, AI, data science and cybersecurity all draw on the mathematical foundations built at A-Level.
Economics & Finance
Economics, banking, accountancy and actuarial science all value A-Level Mathematics highly at university and employer level.
Physics & Astrophysics
A-Level Mathematics is essential for university Physics — many courses require it alongside A-Level Physics.
Medicine & Research
Medical schools and research institutions value mathematical ability for statistics, data analysis and scientific reasoning.
Architecture
Structural calculations, spatial reasoning and technical drawing all rely on mathematical skills developed at A-Level.
Enrol on A-Level Mathematics
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