A-Level Further Maths: Core Pure 1

Master the Core Pure 1 content from A-level Further Maths, and practice on real past paper exam questions.

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