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1.7 Integration

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Question 67

A chemical reaction produces a foam whose volume $V$ (in $cm3\text{cm}^3$ ) changes at a rate $V^{'} (t)$ where $t\,$ is the time in seconds since the start of observation, for $t > 0$ .

Given that

$\dfrac{(t - 9)^2}{t\sqrt{t}}$
the observation point $P (4, 10)$ lies on the curve $V = g (t)$

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

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

[4]

Find $g (t)$ , simplifying your answer.

[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 67

A chemical reaction produces a foam whose volume $V$ (in $cm3\text{cm}^3$ ) changes at a rate $V^{'} (t)$ where $t\,$ is the time in seconds since the start of observation, for $t > 0$ .

Given that

$\dfrac{(t - 9)^2}{t\sqrt{t}}$
the observation point $P (4, 10)$ lies on the curve $V = g (t)$

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

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

[4]

Find $g (t)$ , simplifying your answer.

[5]

Markscheme

1.7 Integration Questions

A Level
Maths
1.7 Integration