Course curriculum

1
Roots of Polynomial Equations
 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
 Worksheet 1
 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
 Solving Problems Involving Matrices
 Roots of Quartic polynomial equations
 Forming new Quartic polynomial equations by substitution
 Recurrence relations of the roots
 Worksheet 2
 Worksheet 3

2
Rational Functions and Graphs
 Introduction
 How to find the asymptotes of a rational graph
 Determining the behaviour of a rational graph about the asymptotes
 Sketching modulus graphs
 Sketching modulus graphs (Worked example)
 Oblique asymptotes 1
 Oblique asymptotes 1 (worked example)
 Oblique asymptotes 2
 Oblique asymptotes 2 (worked example)
 Oblique asymptotes and Modulus graphs (worked example)
 The graph y = f (x)
 Worksheet 1
 Worksheet 2

3
Summation of series
 Introduction
 Sum and General Term of a series (Worked Example 1)
 Sum and General Term of a series (Worked Example 2)
 Standard Results
 Standard Results Worked Example
 Limits at Infinity
 Limits at Infinity Worked Example
 Method of differences
 Differences Worked example 2
 Differences Worked example 1
 Differences Worked example 3
 Differences Worked example 4
 Worksheet 1
 Worksheet 2

4
Matrices
 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
 Worksheet 1
 Worksheet 2

5
Polar Coordinates
 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
 Worksheet 1
 Worksheet 2

6
Vectors
 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
 Worksheet 1
 Worksheet 2

7
Proof by Induction
 Introduction
 Matrices (worked example)
 Divisibility (worked example 1)
 Divisibility (worked example 2)
 Divisibility (worked example 3)
 Divisibility (worked example 4)
 Divisibility (worked example 5)
 Sequences (worked example 1)
 Sequences (worked example 2)
 Sequences (worked example 3)
 Sequences (worked example 4)
 Differentiation (worked example 1)
 Differentiation (worked example 2)
 Differentiation (worked example 3)
 Series (worked example 1)
 Series (worked example 2)
 Series (worked example 3)
 Worksheet 1
 Worksheet 2
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