Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/12) | Q#1

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A curve is such that . The point (2,5) lies on the curve. Find the equation of the curve.


We are given that;

We can find equation of the curve from its derivative through integration;


Rule for integration of  is:

If a point   lies on the curve , we can find out value of . We substitute values of  and    in the equation obtained from integration of the derivative of the curve i.e. .

We are also given that curve passes through the point (2,5).

Substitution of x and y coordinates of point in above equation;

Therefore equation of the curve is;