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1.11.3 Definite integrals and areas

Question 8

The rate of a chemical reaction, $r$ grams per minute, is modelled by the function

t^{1.5}, \quad t \ge 0

where $t$ is the time in minutes since the reaction began. A plot of this rate shows a curve starting at the origin, reaching a peak production rate at the point $M$ , and then falling back to zero at the point $P$ .

Using calculus, find the coordinates of the maximum point $M$ .

[4]

The reaction concludes when the rate returns to zero at point $P$ . Use algebra to find the $t$ -coordinate of $P$ .

[2]

The finite region $R$ is bounded by the curve, the horizontal line passing through $M$ , and the vertical line passing through $P$ .

Use algebraic integration to find the area of $R$ , giving your answer to two decimal places.

[5]

Markscheme

1.11.3 Definite integrals and areas Questions

A Level
Maths
1.11.3 Definite integrals and areas

26 exam-style questions on AQA A Level Maths 1.11.3 Definite integrals and areas. Each one has a worked solution and a mark scheme showing where the marks go.

1.11.3 Definite integrals and areas

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1.11.3 Definite integrals and areas

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Question 8

The rate of a chemical reaction, $r$ grams per minute, is modelled by the function

t^{1.5}, \quad t \ge 0

Using calculus, find the coordinates of the maximum point $M$ .

[4]

The reaction concludes when the rate returns to zero at point $P$ . Use algebra to find the $t$ -coordinate of $P$ .

[2]

The finite region $R$ is bounded by the curve, the horizontal line passing through $M$ , and the vertical line passing through $P$ .

Use algebraic integration to find the area of $R$ , giving your answer to two decimal places.

[5]

Markscheme

1.11.3 Definite integrals and areas Questions

A Level
Maths
1.11.3 Definite integrals and areas

26 exam-style questions on AQA A Level Maths 1.11.3 Definite integrals and areas. Each one has a worked solution and a mark scheme showing where the marks go.