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3.5.4 Differentiation (A-level only)

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Question 70

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

\cos^2(2\theta) \qquad 0 < \theta < \frac{\pi}{4}

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

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

\frac{d\theta}{dx} = -\frac{1}{A\sqrt{Bx - x^2}}

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

[6]

Markscheme

3.5.4 Differentiation (A-level only) Questions

A Level
Maths
3.5.4 Differentiation (A-level only)

82 exam-style questions on CCEA A Level Maths 3.5.4 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

3.5.4 Differentiation (A-level only)

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3.5.4 Differentiation (A-level only)

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Question 70

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

\cos^2(2\theta) \qquad 0 < \theta < \frac{\pi}{4}

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

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

\frac{d\theta}{dx} = -\frac{1}{A\sqrt{Bx - x^2}}

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

[6]

Markscheme

3.5.4 Differentiation (A-level only) Questions

A Level
Maths
3.5.4 Differentiation (A-level only)

82 exam-style questions on CCEA A Level Maths 3.5.4 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.