Mathematics (A2)

Description

Topics

Unit 1: Pure Mathematics (Advanced)

Sub-Unit 1.1: Algebra & Functions

• Rational functions & inequalities
• Modulus functions & equations
• Further transformations of graphs

Sub-Unit 1.2: Complex Numbers

• Definition of i=−1i = \sqrt{-1}
• Argand diagrams (points, vectors, loci)
• Modulus–argument form
• De Moivre’s theorem & applications (powers, roots of unity)

Sub-Unit 1.3: Further Sequences & Series

• Binomial theorem for any rational index
• Recurrence relations
• Maclaurin series expansions (sin, cos, exe^x, ln(1+x))

Sub-Unit 1.4: Advanced Calculus

• Differentiation: parametric, implicit, logarithmic differentiation
• Integration: substitution, integration by parts, partial fractions
• Differential equations (first-order, separable, modeling growth/decay)

Sub-Unit 1.5: Vectors (3D Geometry)

• Scalar & vector products
• Equation of a straight line in 3D
• Equation of a plane
• Intersections (line–plane, line–line)

Unit 2: Trigonometry & Further Geometry

Sub-Unit 2.1: Trigonometric Functions

• Radian measure (arc length, area of sector, area of segment)
• Graphs of sin⁡,cos⁡,tan⁡\sin, \cos, \tan in radians
• Small angle approximations

Sub-Unit 2.2: Advanced Trigonometric Identities

• Addition & subtraction formulae
• Double angle, triple angle, half angle formulae
• R-form (expressions like asin⁡x+bcos⁡xa \sin x + b \cos x)

Unit 3: Mechanics (M2)

Sub-Unit 3.1: Motion in Two Dimensions

• Vectors in mechanics
• Relative velocity

Sub-Unit 3.2: Forces & Equilibrium

• Forces in equilibrium (coplanar/non-coplanar)
• Friction (limiting equilibrium, inclined planes)

Sub-Unit 3.3: Work, Energy & Power (advanced)

• Work–energy principle
• Power in variable force systems

Sub-Unit 3.4: Circular Motion

• Motion in horizontal & vertical circles
• Banking of roads, tension in strings

Sub-Unit 3.5: Centre of Mass & Moments

• Centre of mass for uniform rods, composite bodies
• Conditions for equilibrium

Unit 4: Probability & Statistics (S2)

Sub-Unit 4.1: Probability

• Conditional probability (tree diagrams, Bayes’ theorem)
• Probability distributions (discrete & continuous)

Sub-Unit 4.2: Random Variables

• Expectation, variance of discrete distributions
• Continuous random variables (density functions, mean, variance)

Sub-Unit 4.3: Normal Distribution (advanced)

• Linear combinations of normal variables
• Approximations using normal distribution

Sub-Unit 4.4: Poisson Distribution

• Definition, mean & variance
• Poisson approximation to Binomial

Sub-Unit 4.5: Hypothesis Testing

• One-tail & two-tail tests
• Using binomial, Poisson & normal distributions in hypothesis tests