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1.7 Integration

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Question 40

The curve $C\,$ has equation $y = f (x)$ where $x > 0$ .

Given that

$\dfrac{(5\sqrt{x} + 2)^2}{x^2\sqrt{x}}$
the point $P (4, - 10)$ lies on $C$

(i) Find the value of the gradient of the curve at $P$ .

(ii) Hence find the equation of the tangent to $C\,$ at $P$ , giving your answer in the form $a x + b y + c = 0$ , where $a$ , $b\,$ and $c\,$ are integers to be found.

[4]

Find $f (x)$ , simplifying your answer.

[6]

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 40

The curve $C\,$ has equation $y = f (x)$ where $x > 0$ .

Given that

$\dfrac{(5\sqrt{x} + 2)^2}{x^2\sqrt{x}}$
the point $P (4, - 10)$ lies on $C$

(i) Find the value of the gradient of the curve at $P$ .

(ii) Hence find the equation of the tangent to $C\,$ at $P$ , giving your answer in the form $a x + b y + c = 0$ , where $a$ , $b\,$ and $c\,$ are integers to be found.

[4]

Find $f (x)$ , simplifying your answer.

[6]

Markscheme

1.7 Integration Questions

A Level
Maths
1.7 Integration