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1.7 Differentiation

1.7 Differentiation

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Question 153

The pressure, PPP kPa, inside a vacuum chamber ttt seconds after a suction pump is activated is modelled by the equation

P=15+Ae−kt P = 15 + Ae^{-kt} P=15+Ae−kt

where AAA and kkk are positive constants.

Given that the pressure inside the chamber at the instant the pump was activated was 100100100 kPa,

a.

find the value of AAA.

[2]
b.

Given also that, exactly 15 seconds after the pump was activated, the pressure was 404040 kPa,

find the value of kkk to 3 significant figures.

[4]
c.

Using the values for AAA and kkk,

find, according to the model, the rate of change of the pressure inside the chamber exactly 5 seconds after the pump was activated. Give your answer in kPa s−1\text{kPa}\,\text{s}^{-1}kPas−1 to 3 significant figures.

[3]
d.

Explain why, according to the model, the pressure cannot fall to 101010 kPa.

[2]
Markscheme

1.7 Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.7 Differentiation

425 exam-style questions on OCR A Level Maths 1.7 Differentiation, covering 1.7.1 Derivative as gradient of the tangent, 1.7.2 Gradient of the tangent at a point, 1.7.3 Sketching the gradient function, 1.7.4 Second derivatives, 1.7.5 Second derivative as rate of change of gradient, 1.7.6 Convex, concave and points of inflection (A-level only), 1.7.7 Differentiation from first principles for powers of x, 1.7.8 Differentiation from first principles for sin x and cos x (A-level only), 1.7.9 Differentiating x^n, 1.7.10 Differentiating e^(kx) and a^(kx) (A-level only), 1.7.11 Differentiating trigonometric functions (A-level only), 1.7.12 Derivative of ln x (A-level only), 1.7.13 Tangents and normals, 1.7.14 Stationary points, 1.7.15 Increasing and decreasing functions, 1.7.16 Points of inflection (A-level only), 1.7.17 Product and quotient rules (A-level only), 1.7.18 Chain rule (A-level only), 1.7.19 Parametric and implicit differentiation (A-level only), 1.7.20 Constructing differential equations (A-level only), and 1.7 Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.

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