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1.7 Differentiation

1.7 Differentiation

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Question 125
28%

A specialized coolant storage tank has a depth of 20 cm20\text{ cm}20 cm. The tank is initially empty and a liquid refrigerant is pumped into it. When the depth of the refrigerant is h cmh\text{ cm}h cm, the volume of the liquid in the tank, V cm3V\text{ cm}^3V cm3, is modelled by the equation

V=15h2(h+15)0≤h≤20 V = \frac{1}{5}h^2(h + 15) \quad 0 \le h \le 20 V=51​h2(h+15)0≤h≤20

The refrigerant is pumped into the tank at a constant rate of 350 cm3 s−1350\text{ cm}^3\text{ s}^{-1}350 cm3 s−1. According to the model:

a.

calculate the time taken to fill the tank to its maximum depth.

[2]
b.

determine the rate of change of the depth of the liquid, in cm s−1\text{cm s}^{-1}cm s−1, at the instant when h=10h = 10h=10.

[4]
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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