MODULE 1: Foundations of Advanced Mathematics

• Algebraic fundamentals

• Functions, domains & ranges

• Transformations of functions

• Absolute value, polynomial & rational functions

• Exponential and logarithmic functions

• Trigonometric identities & equations

MODULE 2: Limits & Continuity (AP Calculus AB + A-Level Integration)

• Understanding limits

• One-sided & infinite limits

• Graphical & algebraic evaluation of limits

• Continuity and discontinuities

• Squeeze theorem

• Limits in piecewise functions

MODULE 3: Derivatives

• Concept of derivative as a rate of change

• Differentiation rules

  • Power rule

  • Product rule

  • Quotient rule

  • Chain rule

• Implicit differentiation

• Logarithmic & exponential differentiation

• Trigonometric & inverse trigonometric derivatives

• Higher-order derivatives

MODULE 4: Applications of Derivatives

• Increasing & decreasing functions

• Maxima & minima

• First & second derivative tests

• Concavity & points of inflection

• Optimization problems

• Related rates

• Motion along a line (velocity, speed, acceleration)

MODULE 5: Integration (Indefinite & Definite)

• Antiderivatives

• Basic integration rules

• Substitution method

• Integration using trigonometric identities

• Definite integrals & properties

• Area under curves

• Accumulation functions

MODULE 6: Applications of Integrals

• Area between curves

• Volumes of revolution (disc & washer methods)

• Motion problems using integration

• Average value of a function

• Differential equations & slope fields

• Logistic growth model

MODULE 7: A & AS Level Pure Mathematics

A Level Pure Math Topics

• Algebra & inequalities

• Coordinate geometry

• Series & sequences

• Binomial expansions

• Logarithms & exponentials

• Trigonometric functions & identities

• Vectors

• Matrices

• Complex numbers

MODULE 8: A-Level Mechanics (If required by student)

• Kinematics: displacement, velocity, acceleration

• Dynamics & Newton’s laws

• Forces, friction, & tension

• Moments

• Work, energy & power

• Momentum & collisions

MODULE 9: A-Level Statistics (Optional Based on Student Needs)

• Data representation

• Probability

• Discrete random variables

• Normal distribution

• Hypothesis testing

MODULE 10: Problem-Solving & Exam Practice

• Topic-wise high-level problem sets

• AP Free-Response Questions (FRQs)

• A & AS Level past papers

• Speed-building drills

• Section-wise time management

• Mock tests & performance evaluation