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1.9 Calculus

1.9 Calculus

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Question 284
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

1.9 Calculus Questions

  1. A Level
  2. /Maths
  3. /1.9 Calculus

825 exam-style questions on OCR (MEI) A Level Maths 1.9 Calculus, covering 1.9.1 Gradient of a curve at a point, 1.9.2 Gradient as limit of chord gradient, 1.9.3 Derivative as gradient of tangent, 1.9.4 Sketch the gradient function, 1.9.5 Differentiate y = kx^n, 1.9.6 Second derivative as rate of change of gradient, 1.9.7 Stationary points: maxima and minima, 1.9.8 Increasing and decreasing functions, 1.9.9 Tangent and normal at a point, 1.9.10 Differentiate e^kx, a^kx and ln x (A-level only), 1.9.11 Differentiate trigonometric functions (A-level only), 1.9.12 Product rule (A-level only), 1.9.13 Quotient rule (A-level only), 1.9.14 Chain rule (A-level only), 1.9.15 Rates of change with the chain rule (A-level only), 1.9.16 Implicit differentiation (A-level only), 1.9.17 Concavity and the second derivative (A-level only), 1.9.18 Points of inflection (A-level only), 1.9.19 Integration as reverse of differentiation, 1.9.20 Integrate kx^n, 1.9.21 Constant of integration, 1.9.22 Indefinite and definite integrals, 1.9.23 Area between a graph and the x-axis, 1.9.24 Integrate e^kx, 1/x, sin kx, cos kx (A-level only), 1.9.25 Integration as the limit of a sum (A-level only), 1.9.26 Area between two curves (A-level only), 1.9.27 Integration by substitution (reverse chain rule) (A-level only), 1.9.28 Integration by substitution (other cases) (A-level only), 1.9.29 Integration by parts (A-level only), 1.9.30 Integration using partial fractions (A-level only), 1.9.31 Formulate first order differential equations (A-level only), 1.9.32 Solve first order differential equations (A-level only), and 1.9.33 Interpret solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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