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C1 TANGENTS AND NORMALS

Page history last edited by Steph Richards 15 years, 4 months ago

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?                               y-y_1=m\left(x - x_1\right)

 

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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