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1.7 Integration

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Question 94

The profile of a high-precision optical lens is modelled by a curve $C\,$ with equation $y = f (x)$ for $x > 0$ .

Given that

$8x^2 - \dfrac{(x - 4)(2x + 5)}{2\sqrt{x}}$
the point $P (1, 12)$ lies on $C$

find the equation of the normal to $C\,$ at $P$ , giving your answer in the form $y = m x + c$ where $m\,$ and $c\,$ are constants to be found.

[4]

find $f (x)$ , giving each term in simplest form.

[5]

Markscheme

1.7 Integration Questions

A Level
Maths
1.7 Integration

133 exam-style questions on CCEA A Level Maths 1.7 Integration, covering 1.7.1 Integration, 1.7.2 Integration, and 1.7.3 Integration. Each one has a worked solution and a mark scheme showing where the marks go.

1.7 Integration

Question bank

1.7 Integration

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Question 94

The profile of a high-precision optical lens is modelled by a curve $C\,$ with equation $y = f (x)$ for $x > 0$ .

Given that

$8x^2 - \dfrac{(x - 4)(2x + 5)}{2\sqrt{x}}$
the point $P (1, 12)$ lies on $C$

find the equation of the normal to $C\,$ at $P$ , giving your answer in the form $y = m x + c$ where $m\,$ and $c\,$ are constants to be found.

[4]

find $f (x)$ , giving each term in simplest form.

[5]

Markscheme

1.7 Integration Questions

A Level
Maths
1.7 Integration