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1.7 Differentiation

1.7 Differentiation

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Question 173

The concentration of a chemical reactant in a solution, CCC mg/L, after ttt minutes is modeled by the equation:

log⁡10C=1.84−0.072t \log_{10} C = 1.84 - 0.072t log10​C=1.84−0.072t
a.

Show that this equation can be written in the form C=km−tC = km^{-t}C=km−t, where kkk and mmm are constants. Give the value of kkk to the nearest whole number and the value of mmm to 2 significant figures.

[3]
b.

With reference to the equation in part (a), interpret the value of the constant kkk.

[1]
c.

When the reaction temperature is increased, the concentration CCC after ttt minutes satisfies the equation:

C=560×1.15−t C = 560 \times 1.15^{-t} C=560×1.15−t

Use calculus to find, to 2 significant figures, the value of dCdt\frac{dC}{dt}dtdC​ when t=4t = 4t=4.

[3]
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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