Mathematics

1. 1 Hyperbolic Functions Notes
   • Definitions
   • Logarithmic form
   • Series of hyperbolic sine and cosine
2. 2 Probability Theory Notes
   • Counting principles
   • Independent and dependent events
   • Probability distributions
3. 3 Random Variables Notes
   • Expectation
   • Variance
   • Standard deviation
4. 4 Differential Equations Notes
   • Linearity, degree and order
   • First and second order equations
   • Homogeneity and solutions
5. 5 Applications of Differential Equations Notes
   • Growth and decay
   • Cooling of bodies
   • Falling bodies
   • Electrical circuits
6. 6 Numerical Methods Notes
   • Errors
   • Secant method
   • Newton-Raphson method
   • Trapezoidal rule and Simpson's rule
7. 7 Advanced Coordinate Geometry Notes
   • Parabola
   • Ellipse
   • Hyperbola
   • Polar coordinates
8. 8 Vectors Notes
   • Ratio theorems
   • Dot product
   • Cross product
   • Vector differentiation and integration
9. 9 Applications of Vectors Notes
   • Displacement, velocity and acceleration of a particle
   • Work done by forces
   • Projections
10. 10 Complex Numbers Notes
    • Modulus and argument
    • Argand diagram
    • Polar form
    • De Moivre's theorem and Euler's formula

Source: Mathematics Syllabus for Advanced Secondary Education, Form V-VI (TIE 2023). Sub-topic wording follows the syllabus and is checked as each topic's notes are written.