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3.5.4 Differentiation (A-level only)

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Question 62

A profile for a streamlined racing drone winglet, symmetric about the $x$ -axis, is designed using a Cartesian coordinate system. The upper boundary of the winglet is defined by the parametric equations:

x = -1.6t^2

y = 16t - 0.8t^2

for $\le t \le 20$ , where $x\,$ and $y\,$ are measured in millimetres.

Determine the total length of the winglet along the $x$ -axis.

[2]

bi.

Find an expression for $dydx\displaystyle \frac{dy}{dx}$ in terms of $t$ .

[2]

bii.

Hence, show that the maximum width of the winglet is exactly one-quarter of its total length.

[3]

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 62

x = -1.6t^2

y = 16t - 0.8t^2

for $\le t \le 20$ , where $x\,$ and $y\,$ are measured in millimetres.

Determine the total length of the winglet along the $x$ -axis.

[2]

bi.

Find an expression for $dydx\displaystyle \frac{dy}{dx}$ in terms of $t$ .

[2]

bii.

Hence, show that the maximum width of the winglet is exactly one-quarter of its total length.

[3]

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.