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Curve Sketching is an incredibly useful tool in mathematical problem solving, as well as an opportunity to improve and test your algebraic understanding.
As you study mathematics through school and college to degree level, your algebraic skills will be increasingly tested. In order to become a strong mathematician, you need to understand what the algebra is telling you. Curve Sketching is often examinable and can be a challenging topic to master due to the multitude of techniques that need to be learnt. This course is here to help.
Computer programs like Autograph, Desmos, Maple and Matlab can all plot curves, but understanding why a curve behaves the way it does relies on your understanding of algebra and calculus. Using techniques that we will learn on this course, you will be able to successfully sketch complicated functions and learn about the behaviour of different graphs.
The course is structured so that you will learn about Graph Transformations and Differentiation and its uses in the initial sections. You will not need to have met these concepts before. I go through Differentiation from its basics, through the derivatives of different functions, and up to the Chain Rule, Product Rule and Quotient Rule.
We then start Sketching, and within this we will learn many different techniques along the way.
Linear Graphs:
Quadratic Graphs:
Cubics and Higher Polynomials:
Rational Functions:
Trigonometric Functions:
Exponential and Logarithmic Functions:
Modulus Functions:
Each of these sections is introduced from scratch and involves several worked examples and exercises for you to complete. There are several quizzes to try along the way to test your understanding, and if there are any problems please do not hesitate to start a discussion and ask for help.
With over 100 lectures and 13 hours of content, this course is perfect for anybody studying a Calculus course or A-Level Mathematics, or for those wanting to test and improve their mathematical ability before tackling a Mathematics-related undergraduate degree course at university.
This quiz will go through several different algebra skills that you will want to be good at before continuing with this course. If you find the quiz too challenging, this course will likely not be at the right level for you at the moment.
I am an A-Level Maths teacher from the UK, having achieved a Masters in Mathematics (MMATH) at the University of Southampton. I have taught A-Level Maths and Further Maths, as well as GCSE Maths, for six years. For the last two years, all of my classes have achieved 100% success, and last year my A-Level Maths and Further Maths classes achieved 70% and 100% high grades (As and Bs) respectively. I am a big fan of using teaching videos as part of instruction and have a growing following on YouTube as TLMaths.