High School A-Level Pure Mathematics 1 Made Easy

An easy-to-understand guide to the Cambridge A-level Pure Mathematics Course (Paper 1)

What you’ll learn
Number families, surds and indices
Rationalizing a denominator
Functions and relations
Compound (composite) functions
Coordinate geometry
Quadratics
Requirements
GCSE Mathematics or equivalent level of prior mathematical knowledge
Description
Are you finding pure mathematics confusing? Are you overwhelmed by complex concepts, intimidating formulae, and mathematical jargon? Are you looking for an easy-to-understand, video-based learning platform to help you ace your exams?Well if so, then this course is perfect for you! I designed this mathematics course combining my years of experience, teaching at one of the most prestigious high schools in South Africa. Through my teaching methods I helped countless students demystify mathematical concepts; grow in their mathematical confidence; and attain top results in their year-end exams. A-level Pure Mathematics 1 Made Easy is an easy-to-understand video-based learning platform, which is designed to fit hand-in-hand with the prescribed Cambridge Pure Mathematics A-level textbook. The visual-learning based format of the course accelerates learning, and provides an engaging delivery mechanism for the study of mathematics. Many of my previous students have found the use of visual aids or animations to be an invaluable tool in understanding more complex mathematical concepts. As a result I have combined some of the most helpful illustrations and examples into the course material. This course provides a conversational-style and concise learning resource, which acts as an invaluable tool for students studying in full-time learning institutions, and also for students studying via distance learning. This course is recommended for students studying for their A-level mathematics qualification through the Cambridge University syllabus. It is however also applicable to almost all of the coursework contained in the Oxford A-level mathematics syllabus as well.

Overview

Section 1: Chapter 1: Number Families, Surds and Indices

Lecture 1 Number Families

Lecture 2 Surds and Indices

Lecture 3 Rationalizing a Denominator

Section 2: Chapter 2: Functions

Lecture 4 Functions

Lecture 5 Domain and Range

Section 3: Chapter 3: Coordinate Geometry

Lecture 6 Coordinate Geometry

Lecture 7 Straight-line Graphs

Section 4: Chapter 4: Quadratics

Lecture 8 Polynomials

Lecture 9 Quadratic Functions

Lecture 10 Quadratic Functions Worked Examples

Lecture 11 The Quadratic Formula

Lecture 12 The Discriminant

Lecture 13 Disguised Quadratics

Lecture 14 Quadratic Inequalities

Lecture 15 Completing the Square

Lecture 16 Summary

Section 5: Chapter 5: Trigonometry

Lecture 17 Trigonometry

Lecture 18 Reference Angles

Lecture 19 Special Angles

Lecture 20 Graphs of Trigonometric Functions and the CAST Diagram

Lecture 21 Negative Angles

Lecture 22 Compound Angles

Lecture 23 Trigonometric Equations

Lecture 24 General Compound Angles

Lecture 25 Trigonometric Identities

Section 6: Circular Measure

Lecture 26 Circular Measure

Lecture 27 Arc Length and Sector Area

Lecture 28 Graphs of Trigonometric Functions in Radians

Lecture 29 Solving Trigonometric Equations in Radians

Lecture 30 Summary

Section 7: Vectors

Lecture 31 Vectors

Lecture 32 3D Vectors

Lecture 33 Different Types of Vectors

Lecture 34 Dot Product of Vectors

Lecture 35 The Angle Between Vectors

Lecture 36 Parallel and Perpendicular Vectors

Section 8: Sequences and Series

Lecture 37 Sequences and Series

Lecture 38 Arithmetic Series

Lecture 39 Geometric Series

Lecture 40 Converging Geometric Series

Lecture 41 Binomial Series

Lecture 42 Using Combination Functions for Binomial Expansions

Lecture 43 Pascal’s Triangle and the Combination Function

Lecture 44 Summary

Section 9: Differentiation

Lecture 45 Differentiation

Lecture 46 General rules for Differentiation

Lecture 47 The Chain Rule

Lecture 48 The Chain Rule Mental Substitution

Lecture 49 The Second Derivative

Section 10: Integration

Lecture 50 Integration

Lecture 51 Using Integration to Calculate Areas

Lecture 52 Integrating Compound Functions

Lecture 53 Definite Integrals

Lecture 54 Definite Integrals and Total Area

Lecture 55 The Area Between Two Lines

Lecture 56 Improper Integrals

Lecture 57 Volumes of Revolution about the x-axis

Lecture 58 Volumes of Revolution about the y-axis

Lecture 59 Summary

A-level students wishing to write the Cambridge paper 1 pure mathematics exam