Further Pure Mathematics 1
For exam success in CAIE A Level Further Mathematics (9231)
With this course, you will build up a strong grasp of A Level Further Pure Mathematics concepts. You child will learn all the key concepts through prerecorded tutorial videos. Through this course you will also receive ample practice through worksheets to master all the concepts. The difficulty level for this course is moderate since I use simple explanations to explain tough concepts. This course is only suitable for serious learners who want to see serious results!
Key concepts of each topic explained
How to handle common exam questions
High-quality questions to ensure sufficient practice
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
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
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
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
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
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
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