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3.8 Numerical Methods (A-level only)

3.8 Numerical Methods (A-level only)

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Question 67

A chemical engineer monitors the rate of a reaction, R(t)R(t)R(t), measured in mmol L−1^{-1}−1 min−1^{-1}−1, at regular intervals during the first 8 minutes of a process. The following table records the measured rate at various times t t\,t in minutes. The values of R(t)R(t)R(t) are rounded to 3 decimal places.

ttt02468
R(t)R(t)R(t)0.4501.2822.9141.8450.312
a.

Using the trapezium rule with all the values of R(t)R(t)R(t) in the given table, obtain an estimate for the total yield of the substance, given by

∫08R(t) dt \int_{0}^{8} R(t) \, dt ∫08​R(t)dt

giving your answer to 2 decimal places.

[4]
b.

Use your answer to part (a) to estimate (i)

[∫08(R(t)−0.2) dt [\int_{0}^{8} (R(t) - 0.2) \, dt [∫08​(R(t)−0.2)dt

(ii)

[∫311R(t−3) dt [\int_{3}^{11} R(t-3) \, dt [∫311​R(t−3)dt
[4]
Markscheme

3.8 Numerical Methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.8 Numerical Methods (A-level only)

129 exam-style questions on WJEC A Level Maths 3.8 Numerical Methods (A-level only), covering 3.8.1 Numerical Methods (A-level only), 3.8.2 Numerical Methods (A-level only), 3.8.3 Numerical Methods (A-level only), 3.8.4 Numerical Methods (A-level only), and 3.8.5 Numerical Methods (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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