# A-Level Maths: Pure (Year 1 / AS)

## What you'll learn

- Solving equations - linear, quadratic, cubic, trigonometric and more!
- Solving inequalities - linear and quadratic
- Circle equations and geometry
- Binomial expansion
- Graphs - polynomials, reciprocals and trigonometric
- Trigonometry - equations, identities, graphs and proofs
- Calculus - differentiation and integration
- Stationary points and applications of differentiation
- Exponentials Logarithms - solving equations, modelling and graphs
- Polynomial division
- Proof

## Requirements

- Good knowledge of GCSE maths or equivalent
- A good scientific calculator (e.g. Casio classwiz fx-991EX or graphical calculator).

## Description

**A-Level Maths: Pure (Year 1 / AS) is a course for anyone studying A-Level Maths:**

This course covers all the pure content in A-Level AS maths, usually covered in the first year of study (Year 12). The course is suitable for all major exam boards, including Edexcel, OCR, AQA and MEI. 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.

- Graphs – we will learn how to sketch and work with graphs, including higher order polynomials, 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.

- Polynomial Division – we learn new and powerful algebraic techniques that allow us to divide, factorise and solve higher order polynomials.

- Proof – we learn a range of different techniques for proving mathematical claims.

- Binomial expansion – here we learn a new algebraic technique for expanding brackets raise to large powers.

- 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.

- Vectors – we extend GCSE vector ideas to much more complex problems, including vector proofs.

- 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.

**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*

## Who this course is for:

- Students taking (or planning to take) A-level maths.
- Anyone interested in working through an introductory course in pure mathematics!

## Course content

- Preview01:13

## Instructor

After finishing my studies at Oxford University I worked for a year in India before moving to London, which is where I have been ever since.

I have taught mathematics in some of the best performing schools in the country for over 10 years, where I have taught all levels of school maths, including GCSE, A-Level, Further Maths and Oxbridge entrance paper preparation. I also have 1000's of hours of tutoring experience working one-to-one with students on A-level maths and further maths.

Alongside this I have worked with businesses to train their staff in mathematical skills, such as statistics, data analysis and mathematical software packages.

Away from my work I love music and long-distance cycling, and recently cycled from London to Istanbul.