Complete High School Pure Math Course : A/As Level Pure Math

Learn ALL CAIE A Level Pure Math Topics, AS Level Math Papers 1, 2, 3 (Pure Math) - Beyond GCSE / iGCSE

What you'll learn

Pure Math topics tested in A Level

Algebra

Numerical Methods

Differentiation and Integration

Differential Equations

Vectors

Functions

Calculus

Requirements

Middle School Math (iGCSE or GCSE Math) or a willingness to learn

Description

Welcome to this course on A Level Pure Math Master Class, designed for Cambridge International A Level Maths students. This comprehensive program focuses on all the Pure Math topics assessed in A Level Math - Papers 1, 2 and 3, providing you with the knowledge and skills needed to excel in the exams.The topics tested in Paper 1 are:1. Quadratics2. Coordinate Geometry3. Circular Measure4. Series5. Functions6. Trigonometry7.  Differentiation and its application8. Integration and its applicationThe topics tested in Paper 2 are:1. Algebra 2. Logarithmic and exponential functions 3. Trigonometry 4. Differentiation 5. Integration 6.Numerical solution of equationsThe topics tested in Paper 3 are:1. Algebra 2. Logarithmic and exponential functions 3. Trigonometry 4 Differentiation 5 Integration 6 Numerical solution of equations 7 Vectors 8 Differential equations 9 Complex numbersAnd we will be covering ALL THESE TOPICS!In this course, we'll go through the all the concepts tested the Pure Math section of Paper 1, 2 and 3 of the Cambridge International A Level Maths Paper. By the end of the course, you'll be familiar with the concepts tested in CAIE (previously CIE) A Level Maths Pure Math. Whether you are taking A Level (Paper 1 and 3), or AS Level (Papers 1 and 2),  this course is suitable for you.The goal of this course is to allow students to grasp the theoretical aspects, and also gain confidence in solving real exam-style questions. Get ready to elevate your A Level Maths skills and achieve outstanding results for A Level Math Paper 1, and also Papers 2 or 3.About the InstructorRL Wong is a prolific tutor who had taught many students one-to- one or in group setting in Maths and Sciences. Being a Chemical Engineer for more than a decade, she's familiar with the practical side of Math and Science to the real world, as well, as the concepts behind. 

Overview

Section 1: Introduction

Lecture 1 Introduction

Section 2: Quadratics (Paper 1)

Lecture 2 Introduction

Lecture 3 Shapes of Quadratic Curves

Lecture 4 Complete the square

Lecture 5 Maximum and Minimum

Lecture 6 Solving Quadratic Equations

Lecture 7 Discriminant 1

Lecture 8 Curve of Quadratic Graphs

Lecture 9 Inequality sign and the number line

Lecture 10 Solving Linear Inequalities

Lecture 11 Solving Quadratic Inequalities

Lecture 12 Simultaneous Equations 1

Lecture 13 Simultaneous Equations 2

Lecture 14 Simultaneous Equations 3

Lecture 15 Point of intersection

Lecture 16 Discriminant 2

Lecture 17 Discriminant 3

Section 3: Functions (Paper 1)

Lecture 18 Introduction

Lecture 19 Functions

Lecture 20 Examples

Lecture 21 Domain and Range

Lecture 22 One- One Function

Lecture 23 Inverse Function - An Illustration

Lecture 24 Inverse Functions

Lecture 25 Restriction of domain

Lecture 26 Relationship between f and f⁻¹

Lecture 27 Finding inverse function

Lecture 28 Composite Functions

Lecture 29 Transformation of Graphs 1

Lecture 30 Transformation of Graphs 2

Section 4: Coordinate Geometry (Paper 1)

Lecture 31 2 Points

Lecture 32 Equations of Straight Lines 1

Lecture 33 Equations of Straight Lines 2

Lecture 34 Information from Gradient

Lecture 35 Points of Intersection

Lecture 36 Perpendicular Bisector

Lecture 37 Circles in Coordinate Geometry 1

Lecture 38 Circles in Coordinate Geometry 2

Lecture 39 Circles in Coordinate Geometry 3

Lecture 40 Circles in Coordinate Geometry 4

Lecture 41 Circle Properties

Section 5: Modulus Functions (Papers 2 and 3)

Lecture 42 Modulus Function

Lecture 43 How to sketch y = |ax+b|

Lecture 44 Assignment: Sketch y = |ax+b|

Lecture 45 Properties of Modulus Functions 1

Lecture 46 Solving Equations with | | : Part 1

Lecture 47 Solving Equations with | | : Part 2

Lecture 48 Assignment: Solving equations involving | |

Lecture 49 Solving Inequalities with | |

Lecture 50 Assignment: Solving inequalities with | |

Section 6: Polynomials (Papers 2 and 3)

Lecture 51 Division

Lecture 52 Division of polynomials

Lecture 53 Assignment: Division of polynomials

Lecture 54 Factor and Remainder Theorem

Lecture 55 Assignment: Factor and Remainder Theorem

Section 7: Circular Measure (Paper 1)

Lecture 56 Angles in Rad vs Degree

Lecture 57 Arc length vs Sector Area

Lecture 58 Example

Section 8: Series and Progression Introduction (Paper 1)

Lecture 59 Series and Progression 1

Lecture 60 Examples of Series and Progressions

Section 9: Binomial Expansion Part 1 (Paper 1)

Lecture 61 Factorial

Lecture 62 nCr

Lecture 63 Binomial Expansion

Lecture 64 Binomial Questions

Section 10: AP & GP (Paper 1)

Lecture 65 Arithmetic Progression

Lecture 66 Geometric Progression

Section 11: Partial Fractions (Paper 3 ONLY)

Lecture 67 Partial Fractions - Introduction

Lecture 68 Proper and Improper Fractions

Lecture 69 Partial Fractions - Decompose polynomial fractions into partial fractions

Lecture 70 Assignment: Partial Fractions

Section 12: Binomial Expansion Part 2 (Paper 3 only)

Lecture 71 Binomial Expansion - Introduction

Lecture 72 Using formula 2 in binomial expansion

Section 13: Logarithm and Exponential (Papers 2 and 3)

Lecture 73 What's tested in Logarithm and Exponential

Lecture 74 Logarithm - An Introduction

Lecture 75 Assignment: Binomial Expansion

Lecture 76 Assignment: Make x the subject

Lecture 77 Common Log

Lecture 78 ln and e

Lecture 79 Graphs

Lecture 80 Rules of inequalities

Lecture 81 Solving equations

Lecture 82 Assignment: Solving equations

Lecture 83 Solving inequalities

Lecture 84 Assignment: Solving inequalities

Lecture 85 Transforming into a linear relationship

Lecture 86 Assignment: Transforming into a linear relationship

Section 14: Trigonometry (Paper 1)

Lecture 87 Sine Graphs

Lecture 88 More Sine Graphs

Lecture 89 More Sine Graphs 2

Lecture 90 Cosine Graphs

Lecture 91 Tangent Graphs

Lecture 92 Four Quadrants 1

Lecture 93 Four Quadrants 2

Lecture 94 Special Values 1

Lecture 95 Special Values 2

Lecture 96 Trigonometric Identities

Lecture 97 Proving Identities

Lecture 98 Solving Trigonometric Equations 1

Lecture 99 Solving Trigonometric Equations 2

Section 15: Trigonometry (Papers 2 and 3)

Lecture 100 What's tested in Trigonometry section of Papers 2 and 3

Lecture 101 Prerequisite Knowledge for Trigonometry

Lecture 102 sec, cosec, cot

Lecture 103 Quiz: sec cosec cot

Lecture 104 Graph of y = cosec x

Lecture 105 Graph of y = sec x

Lecture 106 Graph of y= cot x

Lecture 107 Identities 1

Lecture 108 Assignment 1: Identities 1

Lecture 109 Worked solutions for Assignment 1: Identities 1

Lecture 110 Assignment 2: Identities 1

Lecture 111 Worked solutions for Assignment 2: Identities 1

Lecture 112 Identities 2

Lecture 113 Assignment 1: Identities 2

Lecture 114 Worked solutions for Assignment 1: Identities 2

Lecture 115 Assignment 2: Identities 2

Lecture 116 Worked solutions for Assignment 2: Identities 2

Lecture 117 Identities 3

Lecture 118 Assignment 1: Identities 3

Lecture 119 Worked solutions for Assignment 1: Identities 3

Lecture 120 Assignment 2: Identities 3

Lecture 121 Worked solutions for Assignment 2: Identities 3

Lecture 122 Assignment 3: Identities 3

Lecture 123 Worked solutions for Assignment 3: Identities 3

Lecture 124 R- formula

Lecture 125 Assignment: Applying the R formula

Lecture 126 Worked solutions for Assignment on R formula

Section 16: Differentiation (Paper 1)

Lecture 127 Differentiation - Introduction

Lecture 128 Representing Differentiation

Lecture 129 d/dx (constant)

Lecture 130 d/dx (xⁿ)

Lecture 131 Addition and Subtraction in differentiation

Lecture 132 d/dx [f(x)]ⁿ

Section 17: Differentiation (Papers 2 and 3)

Lecture 133 Differentiation of trigonometric functions

Lecture 134 Differentiation of tan⁻¹x

Lecture 135 Differentiation of exponential functions

Lecture 136 Differentiation of logarithmic functions

Lecture 137 Product Rule

Lecture 138 Quotient Rule

Lecture 139 Parametric equations

Lecture 140 Implicit Differentiation

Section 18: Application of Differentiation (Paper 1)

Lecture 141 Tangent and Normal

Lecture 142 Increasing and Decreasing Functions

Lecture 143 Rate of change 1

Lecture 144 Rate of change 2

Lecture 145 Maximum and Minimum

Section 19: Integration (Paper 1)

Lecture 146 Introduction to integration

Lecture 147 Integrate constants

Lecture 148 Integrate xⁿ, n≠-1

Lecture 149 Integrate (ax+b)ⁿ, n≠-1

Lecture 150 Addition and Subtraction

Lecture 151 More on integration

Lecture 152 Finding y given dy/dx

Lecture 153 Definite vs Indefinite Integrals

Lecture 154 Properties of Definite Integrals

Section 20: Integration (Papers 2 and 3)

Lecture 155 Integration of exponential functions

Lecture 156 Integration of 1/ (ax+b)

Lecture 157 Integration of Trigonometric Functions

Section 21: Integration (Paper 3)

Lecture 158 Integration of algebraic fractions 1

Lecture 159 Integration of algebraic fractions 2

Lecture 160 Integration of algebraic fractions 3

Lecture 161 More Integration of Trigonometric Functions

Lecture 162 Integration by Parts

Lecture 163 More examples of integration by parts

Lecture 164 Integration by Substitution

Section 22: Application of Integration (Paper 1)

Lecture 165 Area 1

Lecture 166 Area 2

Lecture 167 Area 3

Lecture 168 Area 4

Lecture 169 Volume 1

Lecture 170 Volume 2

Section 23: Application of Integration (Paper 2 and 3)

Lecture 171 Trapezium Rule

Section 24: Numerical Solution of equations (Papers 2 and 3)

Lecture 172 Numerical Solution - Change of Sign Method

Lecture 173 Numerical Solution: Iterative Method

Lecture 174 Numerical Solution - More about Iterative Method

Section 25: Vectors (Paper 3)

Lecture 175 Introduction

Lecture 176 Other ways to represent vectors (2D)

Lecture 177 Position Vectors

Lecture 178 Equal Vectors

Lecture 179 Magnitude of Vectors

Lecture 180 Unit Vectors

Lecture 181 Addition of Vectors

Lecture 182 Subtraction of vectors

Lecture 183 Parallel Vectors

Lecture 184 Collinear Vectors

Lecture 185 Applying Vectors to 3D Scenarios

Lecture 186 More on Vectors in 3D

Lecture 187 Vector Equations of Lines

Lecture 188 2 Lines

Lecture 189 Scalar Product

Section 26: Differential Equations (Paper 3)

Lecture 190 Introduction

Lecture 191 Forming Simple Statements involving rate of change

Lecture 192 How to solve differential equations

Lecture 193 Variable Separable

Lecture 194 General Solution vs Particular Solution

Section 27: Complex Numbers (Paper 3)

Lecture 195 What are complex numbers

Lecture 196 What is i

Lecture 197 Different powers of i

Lecture 198 3 ways to represent complex numbers

Lecture 199 Cartesian form

Lecture 200 Representing Cartesian From on the argand diagram

Lecture 201 Polar Form

Lecture 202 Exponential Form

Lecture 203 Representing polar and exponential form on the argand diagram

Lecture 204 arg(z)

Lecture 205 Conversion between the different forms 1

Lecture 206 Conversions between the different form 2

Lecture 207 Operations involving complex numbers

Lecture 208 Addition and subtraction

Lecture 209 Multiplication with a constant

Lecture 210 Multiplication between complex numbers

Lecture 211 Conjugates

Lecture 212 Rationalize the denominator

Lecture 213 Division 1

Lecture 214 Division 2

Lecture 215 Division 3

Lecture 216 Powers

Lecture 217 Solving polynomial equations

Lecture 218 Finding the square root of a complex number

Lecture 219 More on argand diagram 1

Lecture 220 More on argand diagram 2

Lecture 221 More on argand diagram 3

Lecture 222 Introduction to loci

Lecture 223 Loci 1

Lecture 224 Loci 2

Lecture 225 Loci 3

Anyone who want to study for A Level Math,Anyone who is interested in Pure Math