Skip to content

Course home

1.9 Numerical Methods (A-level only)

1.9 Numerical Methods (A-level only)

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106
Question 97

A researcher is monitoring the concentration of a specialized catalyst, PPP mg/L, within a chemical bioreactor. The concentration ttt minutes after the reaction commences is modelled by the equation

P=480e0.12t2e0.12t+3,t≥0, t∈R P = \frac{480e^{0.12t}}{2e^{0.12t} + 3}, \quad t \ge 0, \ t \in \mathbb{R} P=2e0.12t+3480e0.12t​,t≥0, t∈R

According to this model:

a.

Determine the concentration of the catalyst at the instant the reaction begins.

[2]
b.

Calculate the time ttt at which the concentration reaches 160 mg/L, giving your answer to 2 decimal places.

[3]
c.

Explain why, according to this model, the concentration of the catalyst can never reach 250 mg/L.

[2]
Markscheme

1.9 Numerical Methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.9 Numerical Methods (A-level only)

125 exam-style questions on OCR A Level Maths 1.9 Numerical Methods (A-level only), covering 1.9.1 Locating roots by sign change (A-level only), 1.9.2 Failure of sign change methods (A-level only), 1.9.3 Simple iterative methods (A-level only), 1.9.4 Newton-Raphson method (A-level only), 1.9.5 Failure of iterative methods (A-level only), 1.9.6 Numerical integration (A-level only), and 1.9.7 Numerical methods in context (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank