A Level Maths Notes: FP1



Summation of Series and Telescoping Series

Manipulation of Factorials

Standard Expressions for Sums of Powers of Integers

Factorising Polynomials With Complex Roots

Finding the Equations of Tangents and Normals to Parametric Curves

Multiplying and Dividing Complex Numbers

Parametric Coordinates – Converting Between Rectangular or Cartesian and Parametric Form

Argand Diagrams – Polar and Coordinate Forms of Complex Numbers

Properties of Summation

Series – Standard Expressions for Sums of Powers of Integers

Solving Differential Equations – The Integrating Factor Method

Summation of Polynomial Series

The Fundamental Theorem of Algebra

The Newton Raphson Method of Finding Roots Equations

Transforming Differential Equations

Integration on Polar Coordinates

Solving More Advanced Inequalities

Linear Interpolation

Solving Second Order Linear Homogeneous Differential Equations

Algebraic Method For Finding the Square Roots of Complex Numbers

Solving Second Order Linear Non – Homogeneous Differential Equations

Advanced Inequalities

Finding the Area Between Two Curves in Polar Coordinates

Finding Turning Points of Polar Curves

Integration in Polar Coordinates

Proof by Induction

The Definition of Constant Coefficient Linear Homogeneous, Linear Non Homogeneous, Non Linear Homogeneous and Non Linear Non Homogeneous Second Order Differential Equations

Sketching Curves in Polar Coordinates

Roots of Polynomial Equations With Real Coefficients


Transforming a Non Separable into a Separable Differential Equation

2x2 Matrices – Sums, Products, Determinants and Inverses

Recurrence Relations and Closed Forms

Transforming and Solving Non Linear, Non Homogeneous Differential Equations





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