# 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;

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