Introduction to Advanced Mathematics
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Introduction to Advanced Mathematics

Algebra skills review, coordinate geometry, polynomials, uncertainty, indices.
1.0 (1 rating)
Instead of using a simple lifetime average, Udemy calculates a course's star rating by considering a number of different factors such as the number of ratings, the age of ratings, and the likelihood of fraudulent ratings.
14 students enrolled
Created by Carfax Education
Last updated 5/2016
Current price: $10 Original price: $35 Discount: 71% off
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  • 1.5 hours on-demand video
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
What Will I Learn?
  • 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.
View Curriculum
  • Students should be familiar with the content of GCSE or equivalent level mathematics.

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.

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.
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Curriculum For This Course
37 Lectures
Recap essential algebra
14 Lectures 37:45

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

Preview 01:23

Brush up on essential algebra. 

Preview 01:23

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

Preview 01:21

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

Preview 01:36

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

Factorising or "putting brackets in"

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

Algebraic multiplication, and important laws of powers

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. 

Factorising quadratic expressions

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

Quadratic equations which can be factorised by inspection

Such equations can be approached with a graphical method to find approximate roots.
Solving quadratic equations that cannot be factorised

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.

Square method to derive the Quadratic Formula

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

More on the Quadratic Formula, with three examples of quadratic equations

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

More on completing the square.

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

The square in non-factorisable quadratic expressions
Coordinate geometry
23 Lectures 47:57

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

Preview 01:32

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

Preview 02:05

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

Preview 04:21

We can say that m=0.

Horizontal flat lines have a gradient of zero

First m = second m

Parallel lines both have the same gradient

First m x second m = -1

Perpendicular lines, at a right angle, have gradients whose product is -1

Remember Pythagoras'? 

Finding the distance between two points on a line, using Pythagoras' Theorem

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

Finding the midpoint of a line segment

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

How to recognise a straight line from that line's equation

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

Recognising straight lines which have equations of the form y=mx

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

Recognising straight lines with equations of the form y=mx+c

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

Substituting values into our line's equation to find the x- and y-intercepts

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

Writing linear equations in other ways, to be neater or more clear

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? 

Finding the equation of a line and coordinates of a single point 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.

Finding the equation of a line when given coordinates of two points on that line

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). 

Recognising and sketching reciprocal graphs, given their equation

Circular functions, in coordinates? You bet. 

The equations of circular functions which have their centre on the origin

Circles needn't be centred on the origin.

The equations of circles with centre at the general point (h,k) and radius of r

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. 

A review of circle geometry theorems

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

Intersections of curves and lines

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.

Another example of finding intersections between lines and curves

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

A final example of finding intersections
About the Instructor
Carfax Education
1.0 Average rating
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14 Students
1 Course
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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.