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

Hits: 41

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; 