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

Become a Further Maths Pro!

What you'll learn
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