A Level Further Maths Pure Maths 1 (AS) - Exam-Ready Series

Form new equations by substitution and by algebraic relationships. Solve problems involving roots of quadratic, cubic, and quartic equations.
Summation of series. use the method of differences to obtain the sum of a finite series.
Sketch rational graphs. Understand how to sketch modulus graphs.
Carry out basic operations with Matrices. Find the determinant and inverse of a square matrix. Understand geometric transformations using matrices.
Understand the relations between Cartesian and polar coordinates. Sketch simple Polar curves and find area enclosed by a curve
Solve Vector problems involving planes. Solve problems involving the interaction between two planes or a plane and a line
Prove different formulae by the Principle of Mathematical Induction.
Requirements
Have good foundational knowledge of Mathematics (GCSE level).
Ideally the student must have studied the majority of AS & A Level Mathematics
Description
This Exam-Ready Series Course for A Level Further Pure Maths 1 has been designed with passion to take you all the way to mastery. The course is relevant to most International Exam Boards like Cambridge CIAE, Edexel, OCR, AQA and MEI etc. In the course I simplify all the difficult concepts to help you become a Pro in no time! With over 100 past exam questions used in the videos as worked examples, you will get to see how the questions you normally find in the papers are answered. This course will take you from the basic foundational concepts you have already learnt in your GCSEs and A Level Pure Mathematics and builds up to the more advanced concepts - without you feeling not even a bit of pain of difficulty. I would advised you to make sure you go through each section in the sequence of the videos as the concepts build up incrementally till the end of the section or topic.You will access concisely explained videos, with a concept upon concept approach to help you master each topic. By enrolling into this course, you get to access all the interactive videos covering all the examinable concepts in your syllabus. I have gained considerable experience teaching A Level Maths and I pour our my wealth of knowledge in this course. So I hope you will learn a lot from this course.
Overview
Section 1: Roots of Polynomial Equations
Lecture 1 Introduction to Roots of Polynomial Equations
Lecture 2 Quadratic: Roots of Quadratic Polynomial Equations
Lecture 3 Quadratic: Forming new equations by substitution
Lecture 4 Quadratic: Symmetric functions
Lecture 5 Roots of Cubic polynomial equations
Lecture 6 Algebraic Manipulation with Cubic polynomial equations
Lecture 7 Cubic Algebraic Manipulation (Worked Examples)
Section 2: Summation of Series
Lecture 8 Introduction
Lecture 9 Sum and General Term of a series (Worked Example 1)
Lecture 10 Sum and General Term of a series (Worked Example 2)
Lecture 11 Standard Results
Lecture 12 Standard Results (Worked Example)
Lecture 13 Limits at Infinity
Lecture 14 Limits at Infinity (Worked Example)
Lecture 15 Method of differences
Lecture 16 Method of differences (Worked Example 1)
Lecture 17 Method of differences (Worked Example 2)
Lecture 18 Method of differences (Worked Example 3)
Lecture 19 Method of differences (Worked Example 4)
Section 3: Matrices
Lecture 20 Introduction
Lecture 21 Addition, Subtraction and Scalar Multiplication
Lecture 22 Multiplication of Matrices
Lecture 23 Multiplication of Matrices (worked examples)
Lecture 24 Determinant and Inverse of a 2 x 2 Matrix
Lecture 25 Determinant of a 3 x 3 Matrix
Lecture 26 Inverse of a 3 x 3 Matrix
Lecture 27 Singular Matrices
Lecture 28 The product of a matrix and it's inverse
Lecture 29 Inverse of the product of two matrices
Section 4: Matrices (Transformations)
Lecture 30 Transformations (Introduction)
Lecture 31 Reflection
Lecture 32 Rotation
Lecture 33 Enlargement
Lecture 34 Shear
Lecture 35 Stretch
Lecture 36 Successive transformations
Lecture 37 Area scale factor
Lecture 38 Invariant Points
Lecture 39 Invariant Lines
Lecture 40 Worked Example 1
Lecture 41 Worked Example 2
Lecture 42 Worked Example 3
Section 5: Polar Coordinates
Lecture 43 Introduction
Lecture 44 Plotting points on a Polar graph
Lecture 45 Converting between Polar and Cartesian coordinates
Lecture 46 Converting equations from Cartesian to Polar form
Lecture 47 Converting equations Polar to Cartesian form
Lecture 48 Sketching Polar Graphs
Lecture 49 Sketching Circles
Lecture 50 Cardioid Graphs
Lecture 51 Area enclosed by a Polar graph
Lecture 52 Cardioid Graphs (worked example)
Lecture 53 Finding the area enclosed by two Polar Graphs
Lecture 54 Sketching Polar graphs for any given equation
Lecture 55 Greatest distance of a point from the pole
Lecture 56 Greatest distance of a point from the pole (worked example)
Lecture 57 The point furthest from the initial line
Lecture 58 The point furthest from the vertical line
Section 6: Vectors
Lecture 59 Equation of a plane 1
Lecture 60 Vector Product
Lecture 61 Equation of a plane 2
Lecture 62 Equation of plane (worked examples)
Lecture 63 A line parallel to a plane
Lecture 64 Distance of a plane from the origin
Lecture 65 Distance from a point to a plane 1
Lecture 66 Distance from a point to a plane 2
Lecture 67 Perpendicular distance from a point to a line
Lecture 68 Worked Example 1
Lecture 69 Shortest distance between two skew lines
Lecture 70 Angle between a line and a plane
Lecture 71 Worked Example 2
Lecture 72 Angle between two planes
Lecture 73 Worked Example 3
Lecture 74 Worked Example 4
Lecture 75 Worked Example 5
Section 7: Proof By Induction
Lecture 76 Matrices (worked example)
Lecture 77 Divisibility (worked example 1)
Lecture 78 Divisibility (worked example 2)
Lecture 79 Divisibility (worked example 3)
Lecture 80 Divisibility (worked example 4)
Lecture 81 Divisibility (worked example 5)
Lecture 82 Sequences (worked example 1)
Lecture 83 Sequences (worked example 2)
Lecture 84 Sequences (worked example 3)
Lecture 85 Sequences (worked example 4)
Lecture 86 Differentiation (worked example 1)
Lecture 87 Differentiation (worked example 2)
Lecture 88 Differentiation (worked example 3)
Lecture 89 Series (worked example 1)
Lecture 90 Series (worked example 2)
Lecture 91 Series (worked example 3)
AS/A Level students,Anyone who's willing to learn

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