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1 Unit 1: Pure Mathematics A

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Question 37

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 Unit 1: Pure Mathematics A Questions

  1. A Level
  2. /Maths
  3. /1 Unit 1: Pure Mathematics A

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