Walter Maths Academy

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Introduction to Roots of Polynomial Equations

Quadratic: Roots of Quadratic Polynomial Equations

Quadratic: Forming new equations 1

Quadratic - Forming new equations 2

Quadratic: Symmetric functions of the roots

Roots of Cubic polynomial equations

Algebraic Manipulation with Cubic polynomial equations

Cubic Algebraic Manipulation (Worked Examples)

Forming new Cubic polynomial equations by substitution

Obtaining sum of cubes formula from equation

Roots of Quartic polynomial equations

Forming new Quartic polynomial equations by substitution

Recurrence relations of the roots

Introduction

Vertical Asymptotes

Horizontal Asymptotes

Stationary Points

Stationary Points - Worked Examples

Oblique Asymptotes

Oblique Asymptotes - Worked Example 1

Oblique Asymptotes - Worked Example 2

The Graph y = |f(x)|

The Graph y = |f(x)| - Worked Example

The Graph y = f (|x|)

The Graph y^2 = f(x)

Introduction

General Term of a Series - Worked Example 1

General Term of a Series - Worked Example 2

Standard Results

Standard Results - Worked Examples

Limits at Infinity

Limits at Infinity - Worked Example

Method of Differences

Method of Differences - Worked example 1

Method of Differences - Worked example 2

Method of Differences - Worked example 3

Method of Differences - Worked example 4

Convergence and Sum to Infinity

Convergence and Sum to Infinity - Worked Example

Divergent and Oscillating Series

Introduction

Addition, Subtraction and Scalar Multiplication

Multiplication of Matrices

Multiplication of Matrices (worked examples)

Determinant and Inverse of a 2 x 2 Matrix

Determinant of a 3 x 3 Matrix

Inverse of a 3 x 3 Matrix

Singular Matrices

The product of a matrix and it’s inverse

Inverse of the product of two matrices

Transformations (Introduction)

Reflection

Rotation

Enlargement

Shear

Stretch

Successive transformations

Area Scale Factor

Invariant Points

Invariant Points - Worked Example

Invariant lines

Worked Example 1

Worked Example 2

Worked Example 3

Introduction

Plotting points on a Polar graph

Converting between Polar and Cartesian coordinates

Converting equations from Cartesian to Polar form

Converting equations Polar to Cartesian form

Sketching Polar Graphs

Sketching Circles

Cardioid Graphs

Area enclosed by a Polar graph

Cardioid Graphs - Worked Example

Finding the area enclosed by two Polar Graphs

Sketching Polar graphs for any given equation

Greatest distance of a point from the pole

Greatest distance of a point from the pole (worked example)

The point furthest from the initial line

The point furthest from the vertical line

Equation of plane 1

Vector Product

Equation of plane 2

Equation of plane (worked examples)

A line parallel to a plane

Distance of a plane from the origin

Distance from a point to a plane 1

Distance from a point to a plane 2

Perpendicular distance from a point to a line

Worked Example 1

Shortest distance between two skew lines

Angle between a line and a plane

Worked Example 2

Angle between two planes

Worked Example 3

Worked Example 4

Worked Example 5