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1.11 H: Integration

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Question 205

The concentration of a specific contaminant in a groundwater sample, C C\,C mg/L, h h\,h hours after a purification agent is added, is modelled by the equation

C=250e−0.12h+15,h≥0 C = 250e^{-0.12h} + 15, \quad h \ge 0 C=250e−0.12h+15,h≥0
a.

Find the initial concentration of the contaminant in the sample.

[1]
b.

Sketch the graph of C C\,C against hhh. On your sketch, state the equation of any asymptote to the curve.

[3]
c.

Find the value of h h\,h for which C=50C = 50C=50, giving your answer to 2 decimal places.

[3]
d.

Show by differentiation that

dCdh=A+BC \frac{\mathrm{d}C}{\mathrm{d}h} = A + BC dhdC​=A+BC

where A A\,A and B B\,B are constants to be determined.

[3]

1.11 H: Integration Questions

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

Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions 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), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

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