Advanced Programme Mathematics Paper 1

proof by induction steps and examples summation and division.

Partial fractions: linear factors, repeated linear factors, irreducible quadratic factors, degree of denominator less than numerator , examples.

optimization steps and examples

Matrices rules and properties, determinant, inverse, transpose and trace, gauss elimination, system of equations, linear equations, nature of solutions linear matrix, solutions in 3d space, transformations, gauss Jordan reduction.

cases for differentiable f(x), solving various types of limits, removable and jump discontinuity, steps to solving limits, continuity and discontinuity.

the definite integral, Riemann sums, open integral, closed integral, areas integration, integration by substitution, use of double and compound angles, integration by parts, chain rule.

Steps and examples on piece-wise functions. fog,gof, rational functions interpretation and sketching.

First principles, fundamental rules (general, product, quotient, chain), slope at a point, use of trig and examples.

Complex numbers, argand diagrams, argument of z, complex numbers equations, quadratic equations, roots, inspection, finding the equation of an unknown.

Notes and examples on Absolute values ( basics, inequalities, graphs, and equations.)