AS level

Pure Maths C1
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Co-ordinates
This is all about the points on a graph, curves, tangents, gradients and normals.
A Revision Aid

Be careful with the co-ordinates question.
It is usually the first queston and you need you to remember a lot of formulas.
 If you are not careful you can get bogged down and the time will run away with you.
I got in a tangle in the mocks and before I knew it I had spent over 30 minutes on the first question.
A disaster !!

What you need to know is how to calculate the following
The distance between two points - this is based on pythagorus
If you have the co-ordinates of two points (x1,y1) and (x2,y2)
then the line between them is the hypotenuse of a right-angled triangle and is therefor equal to

√(x2-x1)2 + (y2-y1)2
Example
Find the length of line AB with co-ordinates (-3,0) and (1,3)
length AB = √ ((1--3)2 + (3-0)2)
= √ (16 +9) = √ (25) = 5
To calculate the gradient of two points of a line you would use
y2-y1/x2-x1
To calculate the equation of a line when you know 1 point and the gradient
you would use
y-y1=m(x-x1)
To calculate the equation of a line when you know both points but not the gradient
you would use
y-y1/x-x1 = y2-y1/x2-x1
notes
A "normal" is another name for a perpendicular line from a tangent.
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www.lawrencejohn.net