Introduction to Advanced Mathematics

Algebra skills review, coordinate geometry, polynomials, uncertainty, indices.
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  • Lectures 37
  • Length 1.5 hours
  • Skill Level Intermediate Level
  • Languages English
  • Includes Lifetime access
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About This Course

Published 2/2016 English

Course Description

Do you want to gain confidence and fluency in maths, to the equivalent of AS-level in the UK?  It is also appropriate for anyone making the transition to more comlicated maths. Through this course of videos, I will illuminate various topics in core mathematics. 

Learn, Reinforce and Master Advanced Maths Techniques with Theo

  • Make algebra much less confusing
  • Deal with any sort of coordinate geometry with ease
  • Learn how to sketch any curve given its equation
  • Transition smoothly from GCSE-equivalent level maths to maths appropriate for any AS or A2 maths exam board

What really makes this course different is that you can see me the entire time. 
Too many maths course have zero human interaction, they simply display a blank screen on which the instructor writes. Not so here. I will interact with you by looking directly into the camera, as you would expect from a private tutor in a classroom setting. 

I base my lessons on the OCR MEI exam topics, which in turn are covered in all the other exam boards. So you can be sure that what you will learn here, you can apply on exam day. Let me help you become a real success at maths, and open doors for yourself in terms of exam grades and getting a really good career in the years to come. 

A complete summary of the skills and techniques needed to ace the C1 - Introduction to Advanced Mathematics module at A-level, for the guidance-seeking student to the adult brushing up on once-known skills. The course will take to complete from 2 to 4 hours. The course is structured very conveniently to ensure smooth transition from one topic to another.

What are the requirements?

  • Students should be familiar with the content of GCSE or equivalent level mathematics.

What am I going to get from this course?

  • Answer questions concerning basic algebra, coordinate geometry, polynomials, uncertainty, indices, and using the language of advanced mathematics. Students will be able to understand the C1 module of A-Level Maths, especially the difficult OCR MEI Examination syllabus.

Who is the target audience?

  • These videos are for students taking A-level maths or a similar level of maths, who are unsure of techniques that they need to answer problems correctly. You will enjoy these videos as I explain mathematical concepts in a personal, face-to-face way as you would with your own teacher. These videos are not appropriate for anyone below A-level standard, but they may also be handy for people who need to brush up their maths skills.

What you get with this course?

Not for you? No problem.
30 day money back guarantee.

Forever yours.
Lifetime access.

Learn on the go.
Desktop, iOS and Android.

Get rewarded.
Certificate of completion.


Section 1: Recap essential algebra

Theo McCausland of Carfax Education Baku hosts this series of introductory videos into A-level Mathematics.


Brush up on essential algebra. 


Get all of your a's with the rest of your a's, rinse and repeat!


You will find that this is a necessary step in many advanced calculations. 


Sometimes we need to do the reverse of what's in lecture 4. 


How do algebraic terms behave when we multiply them or divide them by one another?

Dealing with algebraic fractions, which follow the same rules as in arithmetics

You should be familiar with how to deal with fractions, another essential in advanced maths. 


The easiest type of quadratic factorisation. This requires practice and some intuition to get right every time.

Such equations can be approached with a graphical method to find approximate roots.

Using the completing the square method to derive the Quadratic Formula, which is an immensely useful formula that allows the factorisation of any quadratic equation.


The quadratic formula tells us much more than you may think!


In terms of being able to sketch a quadratic function, nothing saves you time like knowing how to complete the square.


More practice - this will save you so much time in sketching accurate curves. 

Section 2: Coordinate geometry

You are probably familiar with (x, y) coordinates, and soon you will also be with (x, y, z). 


Knowing the difference lets you understand how much detail you need to include in the exam. 


The gradient of a line is one of its most important quantities. 


We can say that m=0.


First m = second m


First m x second m = -1


Remember Pythagoras'? 


Using the arithmetic mean of the coordinates of the two points which the midpoint lies between


Starting with lines parallel to the x-axis or the y-axis.


These lines always go through the origin O(0,0). So the only other key is to know the gradient. 


These go through a y-intercept, where y=c. The gradient is still m. 


As you might guess, the y-intercept is where x=0; the x-intercept where y=0.


We aren't limited to good old y = mx + c! 


But how do we find the equation if we don't know it already? How do we know if a point lies on the line? 


We can find the equation of any line that satisfies two points. The line cuts both those points and goes on for infinity past them in either direction.


This lecture illustrates what many general curves of x in increasing powers look like. 


Reciprocal curves look a bit different. They are quite pleasing to the eye (even with my horrible drawing). 


Circular functions, in coordinates? You bet. 


Circles needn't be centred on the origin.


You might have encountered all of these theorems in higher level GCSE maths. They are a bunch of facts to remember, so don't skip this one. Time to review. 


Interesting points often occur when curves and lines meet each other. This could represent the solution to a real-world problem. 


This time by proving that a line is the tangent to a curve. This method gave us a repeated solution, so the line touches the curve at only one point. This implies that the line is a tangent.


We wrap up this section by taking a look at the intersection of a quadratic curve and a circular function. 

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Instructor Biography

Carfax Education, Top-level private tutor services

Carfax Education, an international group, originating from Oxford and headquartered in London, specializes in providing guidance and support to individuals and institutions who seek to access the best educational opportunities available in Britain, Switzerland, the USA, the UAE, and Azerbaijan. Carfax opened its first office in Azerbaijan in 2012 and plans to expand to other countries throughout the Caspian Sea region.

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