LINK TO C1 PAST PAPERS
FINDING THE EQUATION OF A TANGENT OR A NORMAL TO A CURVE AT A POINT
Often there are questions set in the C1 examination which link together more than one topic. Questions involving tangents and Normals will use skills of:
DIFFERENTIATION - to find the gradient of a TANGENT to a curve at a general point.
COORDINATE GEOMETRY- A tangent is a strait line and so we often need to use the standard equation of a line in order to find the EQUATION OF A TANGENT to a curve.
Look at a past paper question taken from C1 May 2008
Lets look at the skills involved here.
WHAT DO WE WANT TO FIND? THE EQUATION OF A STRAIGHT LINE
WHAT WILL WE USE?
DO WE KNOW M (The Gradient of the TANGENT) NOT YET!
HOW DO WE FIND M? DIFFERENTIATION
When x=2 (as stated in the question) The GRADIENT OF THE TANGENT WILL BE
Gradient of the TANGENT to the curve when x=2 is 6(2)-8=4
BUT WE WANT THE GRADIENT OF THE NORMAL!
WHAT FACT DO WE KNOW? TANGENT IS PERPENDICULAR TO NORMAL
WHAT ELSE DO WE NEED? X AND Y COORDINATE OF A POINT ON THE LINE
DO WE HAVE THIS? We have that x=2 BUT We do NOT YET have y.
HOW CAN WE FIND Y? BY SUBSTITUTING X=2 INTO THE EQUATION FOR Y
SO (2.3) IS A POINT ON THE LINE!!!
THE EQUATION OF THE NORMAL TO THE CURVE WHEN x=2 IS:
NOW TRY SOME PAST PAPER QUESTIONS FROM A WJEC PAST PAPER WORKSHEET
Comments (2)
Kimberly Northam said
at 8:21 pm on Jan 8, 2009
I cant get the past papers up, the lap top keeps telling me to download something in order to see them :S
Steph Richards said
at 9:12 pm on Jan 8, 2009
You need acrobat reader, Kim. It is free to download from the internet.
Good Luck
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