Cie International A-Level Maths: Pure Mathematics 2/3

Master the content from Papers 2 & 3 (Pure Mathematics 2 & 3) of Cambridge International A-Level Maths

What you'll learn

Calculus

Trigonometry

Differential Equations

Complex Numbers

Vectors

Algebra

Requirements

A good understanding of the content covered in my CIE International: A-Level Maths: Pure Mathematics 1 course, or equivalent AS maths knowledge.

Description

CIE International A-Level Maths is a course for anyone studying the Cambridge International A-Level Maths:This course covers all the pure content in Papers 2 and 3 (Pure Mathematics 2 and 3) of the Cambridge International A-Level Maths Course. It is also a great course for anyone interested in learning some more advanced pure maths.The main sections of the course are:- Algebra - we'll learn about the modulus function and how to solve equations and inequalities using it, as well as polynomial division, remainders and the factor theorem.- Logarithms and Exponentials Functions - we'll learn what these are, and how to use them to solve many different styles of problems. We'll also learn about e^x and the natural logarithm.- Trigonometry - we'll learn three new trig functions (sec, cosec and cot) as well as explore many new trigonometric identities, including double angles.- Differentiation - we'll learn how to different almost any function you can think of! We'll use the chain, product and quotient rules and also look at implicit and parametric differentiation.- Integration - we'll learn a range of techniques to integrate most functions we've seen so far.- Numerical Solutions to Equations - We'll explore ways of finding approximate solutions to equations with no analytical solutions, including iteration.- Further Algebra - we'll learn how to split algebraic fractions into partial fractions, and how to extend binomial expansion to include negative and fractional powers.- Further Integration - We'll extend what we've already covered, and look at reverse chain rule, substitution and integration by parts.- Vectors - we'll learn how to work with vectors in 3d and how to use the vector equation of straight lines and the scalar (dot) product.- Differential Equations - we'll explore how to set up and solve differential equations, and how to apply these in real world contexts.- Complex Numbers - we'll explore the fascinating world of complex numbers, including the argand diagram, polar and exponential forms, and complex loci.Those of you studying for Paper 3 will cover all of these section. If you're studying for Paper 2, you will study up to Numerical Solutions to Equations.Please note: This course is intended for people studying the Cambridge International A-Level Maths Syllabus, and not the UK syllabus (covered by Edexcel, OCR, AQA and MEI exam boards). If you are looking for these, check out my other courses on these!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 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

Lecture 2 What's the Difference Between Paper 2 and Paper 3?

Section 2: Algebra

Lecture 3 The Modulus Function - Graphs - Part 1

Lecture 4 The Modulus Function - Graphs - Part 2

Lecture 5 The Modulus Function - Equations and Inequalities - Part 1

Lecture 6 The Modulus Function - Equations and Inequalities - Part 2

Lecture 7 Polynomial Division

Lecture 8 Polynomial Division - Examples - 1

Lecture 9 Polynomial Division - Examples - 2

Lecture 10 Remainders - Part 1

Lecture 11 Remainders - Part 2

Lecture 12 The Factor Theorem

Lecture 13 The Long Division Method

Section 3: Logarithms and Exponential Functions

Lecture 14 Exponential Functions - Intro

Lecture 15 THE Exponential Function

Lecture 16 Differentiating e^x

Lecture 17 Exponential Modelling

Lecture 18 Logarithms - Intro

Lecture 19 Simplifying Logarithms

Lecture 20 Logarithms Laws

Lecture 21 Using Log Laws

Lecture 22 Logarithmic Equations - Part 1

Lecture 23 Logarithmic Equations - Part 2

Lecture 24 The Natural Logarithm

Lecture 25 Logarithmic Graph

Lecture 26 Non-Linear Data - Exponential Models

Lecture 27 Non-Linear Data - Polynomial Models

Lecture 28 Non-Linear Data - Exam Questions

Section 4: Trigonometry

Lecture 29 Sec, Cosec and Cot

Lecture 30 Graphs of Sec, Cosec and Cot

Lecture 31 Sec, Cosec and Cot - Simple Identities

Lecture 32 Sec, Cosec and Cot - Simple Equations

Lecture 33 The Pythagorean Identities

Lecture 34 The Pythagorean Identities - Proving Identities

Lecture 35 The Pythagorean Identities - Solving Equations

Lecture 36 The Pythagorean Identities - Exam-Style Problems

Lecture 37 Inverse Trig Functions - Graphs

Lecture 38 Inverse Trig Functions - Calculations

Lecture 39 The Addition Formulae

Lecture 40 Using The Addition Formulae

Lecture 41 The Double Angle Formulae

Lecture 42 The Double Angle Formulae - Solving Equations - Part 1

Lecture 43 The Double Angle Formulae - Solving Equations - Part 2

Lecture 44 The Double Angle Formulae - Proving Identities

Lecture 45 The Double Angle Formulae - Exam-Style Problems

Lecture 46 Harmonic Form: acos(x) + bsin(x)

Lecture 47 Harmonic Form - Solving Equations

Lecture 48 Harmonic Form - Minimum and Maximum Points - Part 1

Lecture 49 Harmonic Form - Minimum and Maximum Points - Part 2

Lecture 50 Modelling With Trigonometric Equations

Section 5: Differentiation

Lecture 51 Differentiating Sin(x) and Cos(x)

Lecture 52 Using the Derivatives of Sin(x) and Cos(x)

Lecture 53 Differentiating Exponential Functions

Lecture 54 Differentiating Ln(x)

Lecture 55 The Chain Rule - f(x)^n

Lecture 56 The Chain Rule - Trigonometric Functions

Lecture 57 The Chain Rule - Exponential Functions

Lecture 58 The Chain Rule - Logarithmic Functions

Lecture 59 The Product Rule

Lecture 60 The Quotient Rule

Lecture 61 Derivatives of Tan, Sec, Cosec and Cot

Lecture 62 Using the Derivatives of Tan, Sec, Cosec and Cot

Lecture 63 Implicit Differentiation

Lecture 64 Implicit Differentiation - Stationary and Critical Points

Lecture 65 Second Derivatives - Convex and Concave Functions

Lecture 66 Parametric Equations - Introduction

Lecture 67 Converting Parametric Equations to Cartesian Form - Substitution

Lecture 68 Converting Parametric Equations to Cartesian Form - Pythagorean Identities

Lecture 69 Converting Parametric Equations to Cartesian Form - Double Angles

Lecture 70 Intersections of Parametric Equations and Lines

Lecture 71 Differentiating Parametric Curves

Lecture 72 Differentiating Parametric Curves - Stationary Points

Section 6: Integration

Lecture 73 Integrating Standard Functions

Lecture 74 Integrating f(ax + b)

Lecture 75 Trigonometric Identities For Integration - Pythagorean Identities

Lecture 76 Trigonometric Identities For Integration - Double Angle Formulae

Section 7: Numerical Solutions of Equations

Lecture 77 Locating Roots

Lecture 78 Iteration - Part 1

Lecture 79 Iteration - Part 2

Section 8: Further Algebra

Lecture 80 Partial Fractions - Two Factors

Lecture 81 Partial Fractions - Three Factors

Lecture 82 Partial Fractions - Repeated Factors

Lecture 83 Partial Fractions - Top Heavy Fractions

Lecture 84 The Binomial Expansion Formula (When n is Not a Positive Integer)

Lecture 85 Using the Binomial Expansion Formula

Lecture 86 Binomial Expansion When the First Term is Not 1

Lecture 87 Approximations

Lecture 88 Binomial Expansion - Algebraic Fractions

Lecture 89 Binomial Expansion - Partial Fractions

Section 9: Further Integration

Lecture 90 Reverse Chain Rule: f'(x)[f(x)]^n - Part 1

Lecture 91 Reverse Chain Rule: f'(x)[f(x)]^n - Part 2

Lecture 92 Reverse Chain Rule - Exponentials

Lecture 93 Reverse Chain Rule - Logarithmic Functions - Part 1

Lecture 94 Reverse Chain Rule - Logarithmic Functions - Part 2

Lecture 95 Mixed Reverse Chain Rule Problems

Lecture 96 Using Partial Fractions For Integration - Part 1

Lecture 97 Using Partial Fractions For Integration - Part 2

Lecture 98 Integration By Parts - Polynomial x Exponential

Lecture 99 Integration By Parts - Polynomial x Trigonometric

Lecture 100 Integration By Parts - Polynomial x Logarithmic

Lecture 101 Integration By Parts - Exponential x Trigonometric

Lecture 102 Integration By Substitution 1: Alternative to Reverse Chain Rule

Lecture 103 Integration By Substitution 2: u = f(x)

Lecture 104 Integration By Substitution 3: x = f(u)

Lecture 105 Integration By Substitution - Definite Integrals

Lecture 106 Integrating Arctan-Like Functions

Lecture 107 Problem Solving With Integration

Lecture 108 The Trapezium Rule

Section 10: Vectors

Lecture 109 The Vector Equation of a Straight Line

Lecture 110 Parallel and Skew Vectors

Lecture 111 Converting Vector Form to Cartesian Form

Lecture 112 The Scalar (Dot) Product - Introduction

Lecture 113 Using the Scalar Product to Find Angles

Lecture 114 Using the Scalar Product to Find Shortest Distances and Closest Points

Section 11: Differential Equations

Lecture 115 Differential Equations - Separating Variables - Part 1

Lecture 116 Differential Equations - Separating Variables - Part 2

Lecture 117 Forming Differential Equations

Lecture 118 Modelling with Differential Equations - Part 1

Lecture 119 Modelling with Differential Equations - Part 2

Section 12: Complex Numbers

Lecture 120 Complex Numbers - Introduction

Lecture 121 Addition, Subtraction and Multiplication of Complex Numbers

Lecture 122 Division of Complex Numbers

Lecture 123 Square Roots of Complex Numbers

Lecture 124 Complex Roots of Quadratic Equations

Lecture 125 Complex Roots of Cubic and Quartic Equations

Lecture 126 The Argand Diagram

Lecture 127 Modulus and Argument

Lecture 128 Modulus-Argument / Polar Form of a Complex Number

Lecture 129 Exponential Form of a Complex Number

Lecture 130 (Optional!) Explanation of Why the Exponential Form Works

Lecture 131 Multiplying and Dividing Numbers in Modulus-Argument / Exponential Form - Part 1

Lecture 132 Multiplying and Dividing Numbers in Modulus-Argument / Exponential Form - Part 2

Lecture 133 Multiplying and Dividing Numbers in Modulus-Argument / Exponential Form - Part 3

Lecture 134 Euler's Identity

Lecture 135 Complex Loci - Circles

Lecture 136 Complex Loci - Perpendicular Bisectors

Lecture 137 Complex Loci - Arguments

People studying the Cambridge International A-Level Mathematics AS or A-Level,People who want to study an intermediate-advanced course in pure mathematics