A-Level Maths: Pure (Year 2)

Master the pure content from A-level maths (second year), and practice on real past paper exam questions.

4.55 (79 reviews)
Udemy
platform
English
language
Math
category
590
students
19.5 hours
content
Nov 2023
last update
$79.99
regular price

What you will learn

Differentiation: chain rule, product rule, quotient rule and more

Integration: reverse chain rule, integration by parts, integration by substitution, differential equations and more

Partial fractions

Graphs and functions

Binomial expansion

Radians

Advanced trigonometry, including sec, cosec and cot, and trigonometric identities

Parametric equations

Vectors

Numerical methods, including iteration and Newton-Raphson

Description

A-Level Maths: Pure (Year 2) is a course for anyone studying A-Level Maths:

This course covers all the second year pure content in A-Level. The course is suitable for all major exam boards, including Edexcel, OCR, AQA and MEI. It is also a great course for anyone wanting to learn some more advanced pure maths. This course is intended for purchase by adults.

The main sections of the course are:

- Parametric Equations - where we learn how to express algebraic fractions in partial fractions, a trick used to great effect later in the course.

- Functions in Graphs - where we explore modulus functions, graph transformations, and learn about different types of functions, range and domain.

- Binomial Expansion - here we extend the binomial expansion formula covered in my Pure (Year 1 / AS) course to include negative and fractional powers.

- Radians - we learn about a new way to measure angles, and the amazing things that this facilitates.

- Trigonometric Functions - here we learn about three new trig functions (sec, cosec and cot), and explore the numerous ways that these new functions can be used.

- Trigonometric Identities and Modelling - Here we learn about the compound angle formulae, and look at how these can be used. We also explore harmonic form and learn to use this to model real-world scenarios.

- Differentiation - in this chapter we take the differentiation already learned in the Pure (Year 1 / AS) course to a whole new level. We learn how to differentiate pretty much every type of function we can think of, learning about the chain rule, product and quotient rules, as well as connected rates of change.

- Integration - a giant chapter in which we learn many different techniques to integrate increasing advanced functions. We also explore differential equations.

- Parametric Equations - here we learn about a brand new way to represent a curve, and explore how to use calculus with parametric curves.

- Numerical Methods - here we explore various techniques for finding roots of equations, like x = cosx, that are impossible for find exact solutions to.

- Vectors - here we learn how to work with vectors in 3D, extending what was covered in the previous pure course.



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 30 day money-back guarantee.

· 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

Content

Introduction

Introduction

Partial Fractions and Proof

Two Factors
Two Factors - quiz
Three Factors
Three Factors - quiz
Repeated Factors
Repeated Factors - quiz
Top Heavy Fractions
Top Heavy Fractions - quiz
Proof By Contradiction - Part 1
Proof By Contradiction - Part 1 - quiz
Proof By Contradiction - Part 2
Proof By Contradiction - Part 2 - quiz
Classic Proof By Contradiction 1
Classic Proof By Contradiction 2
Partial Fractions and Proof - Exam Questions

Functions and Graphs

The Modulus Function - Graphs - Part 1
The Modulus Function - Graphs - Part 1 - quiz
The Modulus Function - Graphs - Part 2
The Modulus Function - Equations and Inequalities - Part 2
The Modulus Function - Equations and Inequalities - Part 1
The Modulus Function - Equations and Inequalities - Part 1
The Modulus Function - Equations and Inequalities - Part 2
The Modulus Function - Graphs - Part 2 - quiz
Combining Graph Transformations
Combining Graph Transformations
Mappings
Mappings - quiz
Domain and Range
Domain and Range - quiz
Composite Functions
Composite Functions - quiz
Inverse Functions
Inverse Functions - quiz
Piecewise Functions
Piecewise Functions - quiz
Functions and Graphs Exam Questions

Sequences and Series

Arithmetic Sequences
Arithmetic Sequences - quiz
Arithmetic Series
Arithmetic Series - quiz
Geometric Sequences - Part 1
Geometric Sequences - Part 1 - quiz
Geometric Sequences - Part 2
Geometric Sequences - Part 2 - quiz
Geometric Series
Geometric Series - quiz
Sums to Infinity
Sums to Infinity - quiz
Sigma Notation
Sigma Notation - quiz
Partial Sums
Partial Sums - quiz
Recurrence Relations
Recurrence Relations - quiz
Sequences and Series Exam Questions

Binomial Expansion

The Binomial Expansion Formula
The Binomial Expansion Formula - quiz
Using Binomial Expansion
Using Binomial Expansion - quiz
When The First Term Is Not 1
When The First Term Is Not 1 - quiz
Approximations
Approximations - quiz
Binomial Expansion With Algebraic Fractions
Binomial Expansion With Algebraic Fractions - quiz
Binomial Expansion With Partial Fractions
Binomial Expansion With Partial Fractions - quiz
Binomial Expansion Exam Questions

Radians

Radians - Introduction
Radians - Introduction - quiz
Arc Length
Arc Length - quiz
Sector Area
Sector Area - quiz
Solving Trigonometric Equations In Radians
Solving Trigonometric Equations In Radians - quiz
Small Angle Approximations
Small Angle Approximations - quiz
Using Small Angle Approximations
Using Small Angle Approximations - quiz
Radians Exam Questions

Trigonometric Functions

Sec, Cosec and Cot
Graphs of Sec, Cosec and Cot
Graphs of Sec, Cosec and Cot - quiz
Sec, Cosec and Cot - Proving Simple Identities
Sec, Cosec and Cot - Simple Equations
Sec, Cosec and Cot - Simple Equations - quiz
The Pythagorean Identities
The Pythagorean Identities - quiz
The Pythagorean Identities - Proving Identities
The Pythagorean Identities - Proving Identities - quiz
The Pythagorean Identities - Solving Equations
The Pythagorean Identities - Solving Equations - quiz
The Pythagorean Identities - Exam Style Problems
The Pythagorean Identities - Exam Style Problems - quiz
Inverse Trig Functions - Graphs
Inverse Trig Functions - Graphs - Quiz
Inverse Trig Functions - Calculations
Inverse Trig Functions - Calculations - quiz
Trigonometric Functions Exam Questions

Trigonometry, Identities and Modelling

The Addition Formulae
Using the Addition Formulae
Using the Addition Formulae - quiz
The Double Angle Formulae
The Double Angle Formulae - Solving Equations - Part 1
The Double Angle Formulae - Solving Equations - Part 1
The Double Angle Formulae - Solving Equations - Part 2
The Double Angle Formulae - Solving Equations - Part 2
The Double Angle Formulae - Proving Identities
The Double Angle Formulae - Proving Identities - quiz
The Double Angle Formulae - Exam-Style Problems
The Double Angle Formulae - Exam-Style Problems - quiz
Harmonic Form: acosx + bsinx
Harmonic Form: acosx + bsinx
Harmonic Form - Solving Equations
Harmonic Form - Solving Equations - quiz
Harmonic Form - Minimum and Maximum - Part 1
Harmonic Form - Minimum and Maximum - Part 1 - quiz
Harmonic Form - Minimum and Maximum - Part 2
Harmonic Form - Minimum and Maximum - Part 2 - quiz
Modelling With Trig Equations
Modelling With Trig Equations - quiz
Trigonometry, Identities and Modelling Exam Questions

Differentiation

Differentiating Sinx and Cosx
Differentiating Sinx and Cosx - quiz
Using the Derivatives of Sinx and Cosx
Using the Derivatives of Sinx and Cosx
Differentiating Exponential Functions
Differentiating Exponential Functions - quiz
Differentiating lnx
Differentiating lnx - quiz
The Chain Rule - f(x)^n
The Chain Rule - f(x)^n - quiz
The Chain Rule - Trigonometric Functions
The Chain Rule - Trigonometric Functions - quiz
The Chain Rule - Exponential Functions
The Chain Rule - Exponential Functions - quiz
The Chain Rule - Logarithmic Functions
The Chain Rule - Logarithmic Functions - quiz
The Product Rule
The Product Rule - quiz
The Quotient Rule
The Quotient Rule - quiz
Derivatives of Tan, Sec, Cosec and Cot
Derivatives of Tan, Sec, Cosec and Cot - quiz
Using the Derivatives of Tan, Sec, Cosec and Cot
Using the Derivatives of Tan, Sec, Cosec and Cot - quiz
Implicit Differentiation
Implicit Differentiation - quiz
Implicit Differentiation - Stationary and Critical Points
Implicit Differentiation - Stationary and Critical Points - quiz
Second Derivatives - Convex and Concave Functions
Second Derivatives - Convex and Concave Functions - quiz
Connected Rates of Change - Part 1
Connected Rates of Change - Part 2
Connected Rates of Change - quiz
Differentiation Exam Questions

Integration

Integrating Standard Functions
Integrating Standard Functions - quiz
Integrating f(ax+b)
Integrating f(ax+b) - quiz
Reverse Chain Rule - f'(x)[f(x)]^n - Part 1
Reverse Chain Rule - f'(x)[f(x)]^n - Part 2
Reverse Chain Rule - f'(x)[f(x)]^n - quiz
Reverse Chain Rule - Exponential Functions
Reverse Chain Rule - Exponential Functions - quiz
Reverse Chain Rule - Logarithmic Functions - Part 1
Reverse Chain Rule - Logarithmic Functions - Part 2
Reverse Chain Rule - Logarithmic Functions - quiz
Mixed Reverse Chain Rule Problems
Trig Identities for Integration - Pythagorean Identities
Trig Identities for Integration - Pythagorean Identities - quiz
Trig Identities for Integration - Double Angle Formulae
Trig Identities for Integration - Double Angle Formulae
Using Partial Fractions for Integration - Part 1
Using Partial Fractions for Integration - Part 2
Using Partial Fractions for Integration - quiz
Integration by Parts - Polynomial x Exponential
Integration by Parts - Polynomial x Exponential - quiz
Integration by Parts - Polynomial x Trigonometric
Integration by Parts - Polynomial x Trigonometric - quiz
Integration by Parts - Polynomial x Logarithmic
Integration by Parts - Polynomial x Logarithmic - quiz
Integration by Parts - Exponential x Trigonometric
Integration by Parts - Exponential x Trigonometric - quiz
Integration by Substitution 1 - An Alternative to Reverse Chain Rule
Integration by Substitution 1 - An Alternative to Reverse Chain Rule - quiz
Integration by Substitution 2: u = f(x)
Integration by Substitution 2: u = f(x) - quiz
Integration by Substitution 3: x = f(u)
Integration by Substitution 3: x = f(u) - quiz
Integration by Substitution - Definite Integrals
Integration by Substitution - Definite Integrals - quiz
Problem Solving With Integration
Problem Solving With Integration - quiz
The Trapezium Rule
The Trapezium Rule - quiz
Differential Equations - Separating Variables - Part 1
Differential Equations - Separating Variables - Part 2
Differential Equations - Separating Variables - quiz
Forming Differential Equations
Forming Differential Equations - quiz
Modelling with Differential Equations - Part 1
Modelling with Differential Equations - Part 2
Modelling with Differential Equations - quiz
Integration Exam Questions

Parametric Equations

Parametric Equations - Intro
Converting Parametric Equations to Cartesian Form - Substitution
Converting Parametric Equations to Cartesian Form - Substitution - quiz
Converting Parametric Equations to Cartesian Form - Pythagorean Identities
Converting Parametric Equations to Cartesian Form - Pythagorean Identities - qui
Converting Parametric Equations to Cartesian Form - Double Angle Formulae
Converting Parametric Equations to Cartesian Form - Double Angle Formulae - quiz
Intersection of a Parametric Equation with a Line
Intersection of a Parametric Equation with a Line
Differentiating Parametric Equations - Tangents and Normals
Differentiating Parametric Equations - Tangents and Normals
Differentiating Parametric Equations - Stationary and Critical Points
Differentiating Parametric Equations - Stationary and Critical Points - quiz
Integrating Parametric Equations - Part 1
Integrating Parametric Equations - Part 2
Integrating Parametric Equations - quiz
Parametric Equations Exam Questions

Numerical Methods

Locating Roots
Locating Roots - quiz
Iteration - Part 1
Iteration - Part 2
Iteration - quiz
The Newton-Raphson Procedure
The Newton-Raphson Procedure - quiz

3D Vectors

3D Coordinates
3D Coordinates - quiz
Vectors in 3D
Vectors in 3D - quiz
Angles Between Vectors and Coordinate Axes
Angles Between Vectors and Coordinate Axes - quiz
Geometric Problems
Vectors Exam Questions

Screenshots

A-Level Maths: Pure (Year 2) - Screenshot_01A-Level Maths: Pure (Year 2) - Screenshot_02A-Level Maths: Pure (Year 2) - Screenshot_03A-Level Maths: Pure (Year 2) - Screenshot_04

Reviews

Takura
September 11, 2023
Very informative, he explains all the topics clearly in a way that’s easy to understand. I wish I’d gotten the ones suited to Cambridge exams system.
Christopher
August 11, 2023
I am enjoying the course but at I do have to keep going back to fully understand it. I find going over some of it in books helps me to understand more fully and then I can look at the video again and follow it
Thivaharan
August 2, 2023
Could have been better. You should have taken a little more time to show us all the steps while you are doing questions. Especially in year 2. However many thanks for teaching us.
Teresa
August 22, 2021
I have just completed the AS level maths videos, I learnt so much more than just using a textbook. If you want to understand the maths watch these videos.

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3941878
udemy ID
3/27/2021
course created date
4/18/2021
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