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1.10 G: Differentiation

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Question 215

The horizontal position x x\,x of a piston in a high-precision engine is modelled by the equation

x=18cos⁡2(2θ)0<θ<π4 x = 18 \cos^2(2\theta) \qquad 0 < \theta < \frac{\pi}{4} x=18cos2(2θ)0<θ<4π​

where θ \theta\,θ is the crankshaft angle in radians.

Show that the rate of change of the angle with respect to the position, dθdx\displaystyle \frac{d\theta}{dx}dxdθ​, can be expressed in the form

dθdx=−1ABx−x2 \frac{d\theta}{dx} = -\frac{1}{A\sqrt{Bx - x^2}} dxdθ​=−ABx−x2​1​

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

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Markscheme

1.10 G: Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.10 G: Differentiation

375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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