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Question 74

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

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

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