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1.11 H: Integration

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Question 25

The volume of excess reagent, VVV (in litres), produced in a chemical reaction is modelled by the probability density function

f(v)={kv(25−v2)0≤v≤50otherwise f(v) = \begin{cases} kv(25 - v^2) & 0 \le v \le 5 \\ 0 & \text{otherwise} \end{cases} f(v)={kv(25−v2)0​0≤v≤5otherwise​
a.

Show that k=4625k = \frac{4}{625}k=6254​.

[4]
b.

Using integration, determine:

the mean volume of excess reagent produced per reaction,

[3]
c.

the probability that a reaction produces more than 3 litres of excess reagent.

[3]
d.

Three independent reactions are carried out.

Find the probability that at least 2 of these reactions produce more than 3 litres of excess reagent.

[3]
Markscheme

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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