Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2016  OctNov  (P19709/12)  Q#2
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Question
i. Express the equation in the form , where k is a constant.
ii. Hence solve the equation for .
Solution
i.
We are given that;
We know that , therefore;
Comparison with given yields;
ii.
We are required to solve for .
From (i) we know that can be written in the form;
Therefore, we solve for .
To solve this equation for , we can substitute . Hence,
Since given interval is , for interval can be found as follows;
Multiplying the entire inequality with 2;
Since ;
Hence the given interval for is .
To solve equation for interval ,
Using calculator we can find the value of .
Properties of are listed below.
Properties of 

Domain 

Range 

Periodicity 



Odd/Even 

Translation/ Symmetry 


We utilize the periodic property of to find other solutions (roots) of .
Therefore;
For;















Only following solutions (roots) are within the given interval ;


Since ;


Therefore;




Hence, all the solutions of the equation within the interval for are;


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