Sri Lanka G.C.E. Advance Level (A/L) Mathematics
In the rigorous landscape of analytical thought, mathematics serves as the absolute foundation of engineering and physical sciences. This course invites you to explore the depths of quantitative reasoning by moving from the logical structures of algebra to the dynamic modeling of mechanics. You will gain a solid command of calculus and trigonometric analysis, where you will learn to process complex equations and maintain precision in mathematical proofs. Crucially, you will develop the technical ability to solve problems in statics and dynamics while ensuring compliance with logical deduction and axiomatic systems. By mastering the interpretation of abstract concepts and the application of vector mechanics, you will be equipped to evaluate structural and kinematic challenges using mathematical rigor and make calculated decisions based on theoretical certainty.
Core Content Areas
The Sri Lankan GCE A/L Combined Mathematics syllabus is widely regarded as one of the most rigorous in the world, split distinctively into Pure Mathematics and Applied Mathematics.
1. Algebra and Real Numbers
Focuses on mathematical induction, polynomials, complex numbers (Argand diagrams), matrices, and inequalities.
2. Plane Trigonometry
Explores trigonometric identities, general solutions, inverse functions, and the properties of triangles (Sine/Cosine rules).
3. Calculus (Differentiation & Integration)
Covers limits, first principles, methods of integration, differential equations, and applications (rate of change, area, volume).
4. Coordinate Geometry
Deals with the Cartesian plane, properties of the straight line, the circle, and systems of circles.
5. Statics (Applied Maths)
Investigates coplanar forces, equilibrium of rigid bodies, friction, center of gravity, and vector algebra.
6. Dynamics (Applied Maths)
Focuses on Newton’s laws, linear motion, projectiles, relative velocity, circular motion, and simple harmonic motion.
Assessment Structure
The GCE A/L Combined Mathematics qualification is assessed by the Department of Examinations via two 3-hour written papers.
- Paper I (Pure Mathematics): A 3-hour exam. Part A consists of 10 short questions (25 marks). Part B consists of 7 structured essay questions, of which students must answer 5 (75 marks).
- Paper II (Applied Mathematics): A 3-hour exam covering Statics and Dynamics. Part A consists of 10 short questions. Part B requires answering 5 out of 7 essay questions.
- Grading: The marks from both papers are combined to calculate the final Z-score and grade (A, B, C, S, or F).