A-Level Further Maths: Core Pure 1




What you'll learn
Complex numbers
Matrices and matrix algebra
Vectors
Proof by induction
Sums of series
Volumes of revolution
Roots of polynomials
Requirements
A good understanding of AS Level Maths (or equivalent)
Description
A-Level Further Maths: Core Pure 1 is a course for anyone studying A-Level Further Maths.This course covers all the content in the first Core Pure paper. The course has been modelled around the Edexcel exam board, but it matches all the content in OCR as well. It's also a great option for anyone looking to learn more advanced pure mathematics.The main sections of the course are:- Complex Numbers - we will explore what a complex number is, how to work with them, and how to represent them graphically.- Series - we will learn how to find sums and partial sums of natural numbers, squares and cubes.- Roots of polynomials - we'll look at the relationship between a polynomial and its roots.- Volumes of revolution - we'll learn how to find the volume of a solid formed by rotating a function around the x or y axes.- Proof by induction - we'll learn how to prove statements about series, divisibility and matrices using induction.- Matrices - we'll explore the fascinating world of matrices and matrix algebra, and learn how to find inverses and explore transformations in 2 and 3 dimensions.- Vectors - we'll learn how to represent lines and planes in 3 dimensions using vectors, and explore how these interact.What you get in this course:Videos: Watch as I explain each topic, introducing all the key ideas, and then go through a range of different examples, covering all the important ideas in each. In these videos I also point out the most common misconceptions and errors so that you can avoid them.Quizzes: Each sub-section is followed by a short quiz for you to test your understanding of the content just covered. Most of the questions in the quizzes are taken from real A-Level past papers. Feel free to ask for help if you get stuck on these!Worksheets: At the end of each chapter I have made a collection of different questions taken from real A-Level past papers for you to put it all together and try for yourself. At the bottom of each worksheet is a full mark-scheme so you can see how you have done.This course comes with:· A 30 day money-back guarantee.· A printable Udemy certificate of completion.· Support in the Q&A section - ask me if you get stuck!I really hope you enjoy this course!Woody
Overview
Section 1: Introduction
Lecture 1 Introduction
Section 2: Complex Numbers
Lecture 2 What is a Complex Number?
Lecture 3 Addition and Subtraction of Complex Numbers
Lecture 4 Multiplication of Complex Numbers
Lecture 5 Division and Complex Conjugates
Lecture 6 Calculator Use - Multiplication and Division
Lecture 7 Square Roots of Complex Numbers
Lecture 8 Complex Roots of Quadratics
Lecture 9 Complex Roots of Cubics and Quartics
Lecture 10 The Argand Diagram
Lecture 11 Modulus and Argument
Lecture 12 Modulus-Argument Form
Lecture 13 Multiplication and Division in Modulus-Argument Form - Part 1
Lecture 14 Multiplication and Division in Modulus-Argument Form - Part 2
Lecture 15 The Geometric Effect of Multiplication, Division and Conjugates
Lecture 16 Complex Loci - Circles - Part 1
Lecture 17 Complex Loci - Circles - Part 2
Lecture 18 Complex Loci - Bisectors
Lecture 19 Complex Loci - Arguments
Lecture 20 Complex Numbers - Past Paper Questions
Section 3: Series
Lecture 21 Sums of Natural Numbers
Lecture 22 Sums of Squares and Cubes - Part 1
Lecture 23 Sums of Squares and Cubes - Part 2
Lecture 24 Optional: Proof of Sum of Squares
Lecture 25 Series - Past Paper Questions
Section 4: Roots of Polynomials
Lecture 26 Roots of Quadratic Equations
Lecture 27 Roots of Cubic Equations
Lecture 28 Roots of Quartic Equations
Lecture 29 Linear Transformation of Roots
Lecture 30 Non-Linear Transformation of Roots
Lecture 31 Roots of Polynomials - Exam Questions
Section 5: Volumes of Revolution
Lecture 32 Volumes of Revolution - Intro
Lecture 33 Volumes of Revolution Around the X-Axis
Lecture 34 Volumes of Revolution Around the Y-Axis
Lecture 35 Addition and Subtraction of Regions
Lecture 36 Modelling with Volumes of Revolution
Lecture 37 Volumes of Revolution - Exam Questions
Section 6: Matrices
Lecture 38 Introduction to Matrices
Lecture 39 Addition and Subtraction of Matrices
Lecture 40 Multiplication of Matrices
Lecture 41 Matrix Multiplication on the Calculator
Lecture 42 Determinant of a 2x2 Matrix
Lecture 43 Singular Matrices
Lecture 44 Determinant of a 3x3 Matrix - Part 1
Lecture 45 Determinant of a 3x3 Matrix - Part 2
Lecture 46 Calculating a Determinant on the Calculator
Lecture 47 The Inverse of a 2x2 Matrix - Part 1
Lecture 48 The Inverse of a 2x2 Matrix - Part 2
Lecture 49 The Inverse of a 3x3 Matrix - Part 1
Lecture 50 The Inverse of a 3x3 Matrix - Part 2
Lecture 51 Systems of Linear Equations
Lecture 52 Geometric Interpretations of Systems of Linear Equations - Part 1
Lecture 53 Geometric Interpretations of Systems of Linear Equations - Part 2
Lecture 54 Geometric Interpretations of Systems of Linear Equations - Part 3
Lecture 55 Reflections
Lecture 56 Rotations
Lecture 57 Enlargements and Stretches
Lecture 58 Successive Transformations
Lecture 59 3d Transformations - Reflections
Lecture 60 3d Transformations - Rotations
Lecture 61 The Inverse of a Transformation
Lecture 62 Invariant Points
Lecture 63 Invariant Lines - Part 1
Lecture 64 Invariant Lines - Part 2
Lecture 65 Lines of Invariant Points
Lecture 66 Matrices - Exam Questions
Section 7: Proof by Induction
Lecture 67 Proof by Induction - Series - Part 1
Lecture 68 Proof by Induction - Series - Part 2
Lecture 69 Proof by Induction - Divisibility - Part 1
Lecture 70 Proof by Induction - Divisibility - Part 2
Lecture 71 Proof by Induction - Matrices
Lecture 72 Proof by Induction - Exam Questions
Section 8: Vectors
Lecture 73 The Vector Equation of a Line - Part 1
Lecture 74 The Vector Equation of a Line - Part 2
Lecture 75 The Intersection of Two Lines
Lecture 76 The Cartesian Equation of a Line in 3D
Lecture 77 The Scalar Product - Derivation
Lecture 78 The Scalar Product - Part 1
Lecture 79 The Scalar Product - Part 2
Lecture 80 Shortest Distances - Part 1
Lecture 81 Shortest Distances - Part 2
Lecture 82 The Vector Equation of a Plane
Lecture 83 The Scalar Product and Cartesian Equations of a Plane
Lecture 84 The Angle Between a Line and Plane - Part 1
Lecture 85 The Angle Between a Line and Plane - Part 2
Lecture 86 The Angle Between Two Planes
Lecture 87 Reflecting in a Plane
Lecture 88 Vectors - Exam Questions
People studying A Level Further Maths,People who want to learn some more advanced pure mathematics



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