A-Level Pure Mathematics

A-level Pure Mathematics

What you'll learn

1 – Algebraic Methods - partial fractions and algebraic division

2 – Functions & Graph transformations, modulus function and more

3 – Arithmetic and Geometric Sequences & Series, sum of series and sum to infinity

4 – Advanced Binomial Expansion

5 – Radians, Small angle approximation

6 – Trigonometric Functions: Secant, cosecant, and cotangent and their inverses and Trig. Identities involving those

7 – Trigonometry & Modelling with Double Angle Formula (addition and subtraction) formula for Sin, Cos and Tan

8 – Parametric Equations

9 – Differentiation, from first principles, differentiating exponentials and logs, trig functions, chain rule, product rule and quotient rule

10 – Numerical Methods

11 – Integration

12 – Vectors

Requirements

AS - level or basic understanding of Trigonometry

IGCSE or GCSE Mathematics

Description

These videos are for A2 level pure maths, so if you are taking AS level maths this course is for you next year. Please find AS-level video suitable for your needs. This course does not guarantee success at A2-level mathematics, but it does increase your chances. I have taught A-level mathematics as well as the IB programme mathematics in Italy and Spain. I have taught maths in English based school and my students have had very good results in the past because they worked hard and they complemented what I showed them with practice and exercises from their text book. If you want to take this course please ensure that you also complement it with the work required on your behalf. In this course I will explain all the concepts from the Pure book only, in the order that the book covers the material. One video corresponds to one exercise from the book. The examples used in these lectures are identical to those from the course but I do explain the theory in more detail than the book and add some complementary material for you to work with too. I suggest you download them as they include the example questions that I will be solving and you can solve them along as you pause the video.

Overview

Section 1: Algebraic Methods

Lecture 1 Introduction to year 2 pure mathematics

Lecture 2 Introduction

Lecture 3 1A - Proof by contradiction

Lecture 4 1B Multiplying & Dividing Algebraic Fractions

Lecture 5 1C Adding & Subtracting Algebraic Fractions

Lecture 6 1D Partial Fractions

Lecture 7 1E Partial Fractions with Repeated Roots

Lecture 8 1F & 1G Improper Fractions & Algebraic Division

Section 2: Chapter 2 - Functions & Graphs

Lecture 9 Introduction to Graphs and Functions

Lecture 10 2A – The Modulus Function

Lecture 11 2B – Functions & Mappings

Lecture 12 2C – Composite Functions

Lecture 13 2D – Finding Inverse of a Function

Lecture 14 2E – Graphs of Modulus Functions

Lecture 15 2F – Combining Graph Transformations

Lecture 16 2G – Solving Problems involving Modulus Functions & Graphs

Section 3: 3 - Sequences & Series

Lecture 17 Introduction to Sequences & Series

Lecture 18 3A – Arithmetic Sequences

Lecture 19 3B – Arithmetic Series

Lecture 20 3C – Geometric Sequences

Lecture 21 3D – Geometric Series

Lecture 22 3E – Sum to infinity

Lecture 23 3F – Sigma Notation

Lecture 24 3G – Recurrence Relations

Lecture 25 3H – Increasing, Decreasing & Periodic Sequences & Series

Lecture 26 3I – Modelling real life scenarios with Sequences & Series

Section 4: 4 - Advanced Binomial Expansion

Lecture 27 Introduction to Advanced Binomial Expansion

Lecture 28 4A – Expanding (?+?)^? with n as a fraction and or negative value

Lecture 29 4B Expanding (?+??)^?

Lecture 30 4C – Using Partial Fractions in Binomial Expansion

Section 5: 5 - Radians as a unit to measure angles

Lecture 31 Introduction to Radians

Lecture 32 5C – Arc length

Lecture 33 5D – Area of sectors

Lecture 34 5E - Area of Segments

Lecture 35 5E - Solving trigonometric Equations in radians

Lecture 36 5F – Small angle approximation

Lecture 37 Solving Trigonometric Equations with Multiple answers

Lecture 38 Solving Trigonometric Equations on Casio FX-GC50

Section 6: 6 - Trigonometric Functions

Lecture 39 6A – Secant, Cosecant and Cotangent

Lecture 40 6B – Graphs of Secant, Cosecant and Cotangent

Lecture 41 6C – Using Secant, Cosecant and Cotangent

Lecture 42 6D – New Trigonometric Identities

Lecture 43 6E – Inverse trigonometric functions

Section 7: Trigonometry and Modelling with Double Angles

Lecture 44 Introduction to Trigonometry & double angles

Lecture 45 7A – Derivation of Addition and Subtraction formulas

Lecture 46 7B – Using the Addition and Subtraction formulas

Lecture 47 7C – Double Angle formulas

Lecture 48 7D – Solving Trigonometric Equations

Lecture 49 7E – Expressing two trig. curves as one, Simplifying A cos(x) ± ? sin⁡(?)

Lecture 50 7F – Proving Trigonometric Identities

Lecture 51 7G – Modelling with Trigonometric Functions

Section 8: 8 - Parametric Equations

Lecture 52 8- Introduction to Parametric Equations

Lecture 53 8A – Calculating the Cartesian equation from Parametric Equations

Lecture 54 8B – Parametric Equations with Trigonometric Identities

Lecture 55 8C – Curve Sketching with Casio FXGC-50

Lecture 56 8D – Points of Intersection

Lecture 57 8E – Modelling Real life scenarios with Parametric Equations

Section 9: 9 - Differentiation

Lecture 58 9A – Differentiating Sin(x) and Cos(x)

Lecture 59 9B – Differentiating Exponentials and logs

Lecture 60 9C – The Chain Rule

Lecture 61 9D – The Product Rule

Lecture 62 9E – The Quotient Rule

Lecture 63 9F – Differentiating Trigonometric Functions

Lecture 64 9G – Differentiating Parametric Functions

Lecture 65 9H – Implicit differentiation

Lecture 66 9I – Using the second derivative

Lecture 67 9J – Rates of Change and applications of differentiation

Section 10: 10 - Numerical Methods

Lecture 68 10 - Numerical Methods & locating roots

Lecture 69 10B – Iterations

Lecture 70 10C – The Newton Raphson Method

Lecture 71 10D – Applications to Modelling

Section 11: 11 - Integration

Lecture 72 11A – Integrating standard functions

Lecture 73 11B – Integrating f(ax+b) linear functions

Lecture 74 11C – Integrating with Trigonometric Identities

Lecture 75 11D – Reverse Chain Rule

Lecture 76 11E – Integration with substitution

Lecture 77 11F – Integration by parts

Lecture 78 11G – Integration involving partial fractions

Lecture 79 11H – Finding the area under the curves & Integrating Parametric Equations

Lecture 80 11I – Approximating with the Trapezium Rule

Lecture 81 11J – Solving Differential Equations

Lecture 82 11K - Modelling with Differential Equations

Lecture 83 11L – Integration as the limit of a sum

Section 12: 12 - Vectors

Lecture 84 12A – Coordinate System in 3 Dimensions

Lecture 85 12B – Vectors in 3 Dimensions

Lecture 86 12C – Solving Geometric Problems in 3D

Lecture 87 12D – Application of Vectors in Mechanics

Ideal for A-level mathematics students in year 12-13 in British Curriculum (16-18) years of age.,Students taking IB program Higher Level and other English based Curriculum requiring advanced knowledge of Trignometry