Cie International A-Level Maths: Pure Mathematics 1

Master the content from Paper 1 (Pure Mathematics 1) of Cambridge International A-Level Maths

What you'll learn

Quadratic Equations

Functions

Coordinate Geometry

Circular Motion

Trigonometry

Series

Differentiation

Integration

Requirements

A sound understanding of GCSE/IGCSE level maths or equivalent.

No prior knowledge of A-level maths required.

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 Paper 1 (Pure Mathematics 1) of the Cambridge International A-Level Maths Course, covered in the first year of study. It is also a great introduction to pure maths for anyone interested in getting started. The main sections of the course are:- Equations and Inequalities – we will look at a wide range of different functions, including quadratic, linear and cubic functions.- Quadratics - we look at quadratic functions, how to sketch and work with them, solve equations and inequalities and work with the discriminant.- Functions - we learn about domain, range, inverse and composite functions, as well as graph transformations.- Straight Line Graphs – we take this topic, familiar from GCSE, and push it to the next level, introducing new ways of using straight line graphs.- Circles – we learn how to represent circles in the coordinate plane, find tangents to circles and solve intersections with lines.- Trigonometry – in the two trigonometry chapters we look at how to use trigonometry to solve triangle problems, but also solve trigonometric equations, sketch tri graphs, and prove trigonometric identities.- Circular Measure - we learn how to work with radians to calculate sector areas, arc lengths and solve trigonometric equations.- Graphs – we will learn how to sketch and work with graphs, including higher order polynomials, as well as graph transformations.- Series - we learn about binomial expansion and the choose function, as well as how to work with arithmetic and geometric series.- Differentiation – in this huge chapter we introduce one of the most powerful and exciting ideas in mathematics. We look at gradients of curves, tangents, stationary points and optimisation problems.- Integration – here we look at the other side of calculus, and learn how to use integration to find areas under curves.- Exponentials and Logarithms – we learn about the exponential function, logarithms, the natural log, as well as how to use these ideas to model a range of real-world scenarios.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

Section 2: Quadratics

Lecture 2 Factorising to Solve a Quadratic

Lecture 3 The Quadratic Formula

Lecture 4 Calculator Use to Solve Quadratics

Lecture 5 Completing the Square to Solve Quadratics

Lecture 6 Completing the Square to Find the Turning Point of a Quadratic - Part 1

Lecture 7 Completing the Square to Find the Turning Point of a Quadratic - Part 2

Lecture 8 Quadratic Graphs - Part 1

Lecture 9 Quadratic Graphs - Part 2

Lecture 10 Proof of the Quadratic Formula

Lecture 11 The Discriminant - Introduction

Lecture 12 Applications of the Discriminant

Lecture 13 Quadratic Simultaneous Equations - Part 1

Lecture 14 Quadratic Simultaneous Equations - Part 2

Lecture 15 Linear Inequalities and Set Notation

Lecture 16 Quadratic Inequalities - Part 1

Lecture 17 Quadratic Inequalities - Part 2

Lecture 18 Quadratic Inequalities - Part 3

Lecture 19 Disguised Quadratics - Part 1

Lecture 20 Disguised Quadratics - Part 2

Lecture 21 Modelling with Quadratics - Part 1

Lecture 22 Modelling with Quadratics - Part 2

Lecture 23 Quadratics - Past Paper Questions Pack

Section 3: Functions

Lecture 24 Mappings

Lecture 25 Domain and Range

Lecture 26 Composite Functions

Lecture 27 Inverse Functions

Lecture 28 Translations - Part 1

Lecture 29 Translations - Part 2

Lecture 30 Stretches - Part 1

Lecture 31 Stretches - Part 2

Lecture 32 Reflections

Lecture 33 The Prison Method

Lecture 34 Applications of Transformations

Lecture 35 Functions - Past Paper Question Pack

Section 4: Coordinate Geometry - Straight Lines

Lecture 36 y = mx + c

Lecture 37 Gradients

Lecture 38 The Equation of a Straight Line

Lecture 39 Straight Line Problem Solving

Lecture 40 Parallel Lines

Lecture 41 Perpendicular Lines

Lecture 42 Perpendicular Bisectors

Lecture 43 Length Problems

Lecture 44 Area Problems

Lecture 45 Modelling with Straight Lines

Lecture 46 Straight Lines - Past Paper Question Pack

Section 5: Coordinate Geometry - Circles

Lecture 47 Circles - Introduction

Lecture 48 The Equation of a Circle

Lecture 49 Calculating the Centre and Radius of a Circle

Lecture 50 Problem Solving with Circles

Lecture 51 Intersecting Lines and Circles - Part 1

Lecture 52 Intersecting Lines and Circles - Part 2

Lecture 53 Tangents to Circles

Lecture 54 Tangents to Circles Examples - Part 1

Lecture 55 Tangents to Circles Examples - Part 2

Lecture 56 Circles and Triangles - Part 1

Lecture 57 Circles and Triangles - Part 2

Lecture 58 Circles and Triangles - Part 3

Lecture 59 Circles - Past Paper Question Pack

Section 6: Trigonometry - Triangles and Graphs

Lecture 60 Sine Rule for Lengths

Lecture 61 Sine Rule for Angles

Lecture 62 Cosine Rule for Lengths

Lecture 63 Cosine Rule for Angles

Lecture 64 Cosine Rule with Algebra

Lecture 65 The Area of a Triangle

Lecture 66 The Sine Graph

Lecture 67 The Cosine Graph

Lecture 68 The Tan Graph

Lecture 69 Transformations of Trig Functions

Lecture 70 Applications of Transformations

Section 7: Trigonometry - Equations and Identities

Lecture 71 Multiple Solutions to Sine Equations

Lecture 72 Multiple Solutions to Cosine Equations

Lecture 73 Multiple Solutions to Tan Equations

Lecture 74 Trigonometric Identities

Lecture 75 Solving Trigonometric Equations with the Tan Identity

Lecture 76 Solving Quadratic Trig Equations - Part 1

Lecture 77 Solving Quadratic Trig Equations - Part 2

Lecture 78 Further Trig Equations - Part 1

Lecture 79 Further Trig Equations - Part 2

Lecture 80 Proving Trig Identities - Part 1

Lecture 81 Proving Trig Identities - Part 2

Lecture 82 Trigonometry - Past Paper Question Pack

Section 8: Circular Measure

Lecture 83 Radians - Introduction

Lecture 84 Arc Length

Lecture 85 Sector Area

Lecture 86 Solving Trig Equations in Radians

Lecture 87 Circular Measure - Past Paper Question Pack

Section 9: Series

Lecture 88 The Choose Function

Lecture 89 Choose Function Problem Solving

Lecture 90 Binomial Expansion - Part 1

Lecture 91 Binomial Expansion - Part 2

Lecture 92 Binomial Expansion - Ascending Powers of x

Lecture 93 Binomial Problem Solving

Lecture 94 Binomial Estimation

Lecture 95 Arithmetic Sequences

Lecture 96 Arithmetic Series

Lecture 97 Geometric Sequences - Part 1

Lecture 98 Geometric Sequences - Part 2

Lecture 99 Geometric Series

Lecture 100 Sums to Infinity

Lecture 101 Recurrence Relations

Lecture 102 Series - Past Paper Question Pack

Section 10: Differentiation

Lecture 103 Gradients of Curves

Lecture 104 Differentiation from First Principles at a Point

Lecture 105 Differentiation from First Principles in General

Lecture 106 The x^n Rule

Lecture 107 Differentiating Basic Polynomials

Lecture 108 Differentiating Negative Powers

Lecture 109 Differentiating Fractional Powers

Lecture 110 Differentiating Mixed Functions

Lecture 111 Using Gradient Functions

Lecture 112 Tangents and Normals - Part 1

Lecture 113 Tangents and Normals - Part 2

Lecture 114 Increasing and Decreasing Functions

Lecture 115 Stationary Points

Lecture 116 The Chain Rule

Lecture 117 Second Derivatives

Lecture 118 Sketching Gradient Functions

Lecture 119 Optimisation - Part 1

Lecture 120 Optimisation - Part 2

Lecture 121 Connected Rates of Change - Part 1

Lecture 122 Connected Rates of Change - Part 2

Lecture 123 Calculator Use in Differentiation

Lecture 124 Differentiation - Past Paper Question Pack

Section 11: Integration

Lecture 125 Integration Introduction

Lecture 126 Finding Functions

Lecture 127 Integration to Find Areas

Lecture 128 Area Under the x-Axis

Lecture 129 Area Between Functions

Lecture 130 Integrating (ax+b)^n

Lecture 131 Integrating (ax+b)^n - Areas

Lecture 132 Integration Problem Solving - Part 1

Lecture 133 Integration Problem Solving - Part 2

Lecture 134 Integration Problem Solving - Part 3

Lecture 135 Calculator Use in Integration

Lecture 136 Why Integration Gives Area

Lecture 137 Integration - Past Paper Question Pack

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