# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2011 | June | Q#6

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Question

Given that  can be written in the form ,

a.   Write down the value of p and the value of q.

Given that  , and that y=90 when x=4;

b.   find  in terms of x, simplifying the coefficient of each term.

Solution

a.

We are given;

b.

We are required to find y in terms of x, when;

We are also given that y=90 when x=4.

Clearly it is the case of finding equation from its derivative.

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

For the given case;

As demonstrated in (a);

Therefore;

Rule for integration of  is:

Rule for integration of  is:

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 y=90 when x=4.

Therefore, substituting given values of y and x.

Hence, above equation obtained from integration can now be written as;