AS & A Level Mathematics
Pure Mathematics · Statistics · Mechanics — the complete Cambridge A Level Mathematics programme
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About AS & A Level Mathematics (9709)
Cambridge International AS & A Level Mathematics (9709) is the most widely studied A Level worldwide and a gateway to virtually every STEM, business, and economics degree at top universities. The course spans three components — Pure Mathematics, Probability & Statistics, and Mechanics — each demanding rigorous algebraic manipulation, logical reasoning, and problem-solving under exam conditions.
Our programme covers the complete 9709 syllabus from AS to A Level — Pure 1, Pure 2, Pure 3, Statistics 1 & 2, and Mechanics 1 & 2. Every session is tightly aligned to the Cambridge mark scheme, with extensive past paper practice and regular timed assessments.
Pure, Statistics & Mechanics all covered
Cambridge-specialist Maths tutors
Step-by-step mark scheme training
P1, P2, P3, S1, S2, M1 & M2 mastery
The foundation of A Level Mathematics — functions, algebra, trigonometry, series, and an introduction to differential and integral calculus. Assessed in both AS and A Level exams.
- Quadratics — completing the square, discriminant, solving quadratic equations and inequalities
- Coordinate Geometry — straight lines, circles, tangents, normals, intersection of curves
- Trigonometry — sine and cosine rules, identities, solving trigonometric equations
- Differentiation — first principles, chain, product and quotient rules, stationary points
- Functions — domain, range, composite and inverse functions, transformations of graphs
- Circular Measure — arc length, sector area, radians, trigonometric equations in radians
- Series — binomial expansion, arithmetic and geometric progressions, sigma notation
- Integration — indefinite and definite integration, area under and between curves
Extending Pure 1 with advanced algebra, logarithms, complex trigonometric identities, implicit and parametric differentiation, integration techniques, and vectors. P2 is AS only; P3 is full A Level.
- Algebra — partial fractions, polynomials, modulus function, factor and remainder theorem
- Trigonometry (Advanced) — sec, cosec, cot, compound and double angle formulae, R sin/cos form
- Integration (Advanced) — by parts, by substitution, volumes of revolution, differential equations
- Vectors — 3D vectors, scalar product, equations of lines, angles between lines
- Logarithms & Exponentials — laws of logs, exponential growth and decay, ln(x) and eˣ
- Differentiation (Advanced) — implicit, parametric differentiation, related rates of change
- Numerical Methods — Newton-Raphson method, iterative methods, sign change locating roots
- Complex Numbers — Argand diagram, modulus-argument form (selected schools)
From data representation and probability distributions (binomial, Poisson, normal) to hypothesis testing, confidence intervals, and chi-squared tests.
- Data Representation — stem-and-leaf, box plots, histograms, cumulative frequency
- Probability — addition and multiplication rules, conditional probability, tree diagrams
- Normal Distribution — standardisation, z-scores, inverse normal, continuity correction
- Poisson Distribution — conditions, mean, approximation to binomial (S2)
- Measures of Central Tendency & Spread — mean, median, mode, variance, standard deviation
- Binomial Distribution — conditions, mean, variance, cumulative probabilities
- Hypothesis Testing — null and alternative hypotheses, critical regions, p-values
- Sampling & Estimation — confidence intervals, unbiased estimators, chi-squared tests (S2)
Applied mathematics using Newton’s laws, kinematics, energy and momentum principles, circular motion, and moments — developing mathematical modelling skills for engineering and physics degrees.
- Kinematics — displacement, velocity, acceleration graphs; equations of constant acceleration
- Energy, Work & Power — conservation of energy, work-energy theorem, power of a force
- Circular Motion — centripetal acceleration and force, conical pendulums, banked tracks (M2)
- Forces & Newton's Laws — equilibrium, connected particles, friction, inclined planes
- Momentum — conservation of linear momentum, impulse-momentum theorem
- Moments — turning forces, equilibrium of rigid bodies, couples, centre of mass (M2)
AS Level Exam Papers
Comprehensive preparation for every paper component
Paper 1 — Pure 1
Core Pure Mathematics for AS Level — algebra, functions, coordinate geometry, trigonometry, series, differentiation, and integration
⏱ Duration:
1 hr 45 min
📑 Total Marks:
75 marks
Paper 2 — Pure 2
Extension of Pure 1 — algebra, logarithms, trigonometric identities, further differentiation, integration, and numerical methods
⏱ Duration:
1 hour 15minutes
📑 Total Marks:
50 marks
Paper 4 — Mechanics
AS Level Mechanics — forces, kinematics, Newton's laws, energy, work, power, and momentum in one and two dimensions
⏱ Duration:
1 hr 15 min
📑 Total Marks:
50 marks
Paper 5 — Statistics 1
AS Level Probability & Statistics — data analysis, probability distributions (binomial, normal), and hypothesis testing
⏱ Duration:
1 hr 15 min
📑 Total Marks:
50 marks
A Level Exam Papers
Comprehensive preparation for every paper component
Paper 3 —
Pure 3
Full A Level Pure Mathematics — advanced algebra, exponentials, complex trigonometry, implicit differentiation, integration techniques, vectors, and differential equations
⏱ Duration:
1 hr 45 min
📑 Total Marks:
75 marks
Paper 6 — Statistics 2
Advanced Probability & Statistics — Poisson distribution, sampling theory, estimation, confidence intervals, and chi-squared tests
⏱ Duration:
1 hour 15 minutes
📑 Total Marks:
50 marks
Paper 7 — Mechanics 2
Advanced Mechanics — circular motion, moments, equilibrium of rigid bodies, coefficient of restitution, and complex Newton's law applications
⏱ Duration:
1 hour 15 minutes
📑 Total Marks:
50 marks
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