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9.7 Parametric Differentiation

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Question 27

An aerodynamic profile for a glider wing is designed to be symmetric about the chord line (the $x$ -axis). The upper boundary of the wing's cross-section is modelled by the parametric equations:

x = -1.5t^2

y = 15t - 0.75t^2

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

Determine the total length of the glider wing along the $x$ -axis.

[2]

bi.

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

[3]

bii.

Hence, prove that the maximum thickness (total width) of the wing is exactly one-quarter of its total length.

[4]

Markscheme

9.7 Parametric Differentiation Questions

A Level
Maths
9.7 Parametric Differentiation

35 exam-style questions on Edexcel A Level Maths 9.7 Parametric Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.

9.7 Parametric Differentiation

Question bank

9.7 Parametric Differentiation

Medium Hard

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Question 27

An aerodynamic profile for a glider wing is designed to be symmetric about the chord line (the $x$ -axis). The upper boundary of the wing's cross-section is modelled by the parametric equations:

x = -1.5t^2

y = 15t - 0.75t^2

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

Determine the total length of the glider wing along the $x$ -axis.

[2]

bi.

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

[3]

bii.

Hence, prove that the maximum thickness (total width) of the wing is exactly one-quarter of its total length.

[4]

Markscheme

9.7 Parametric Differentiation Questions

A Level
Maths
9.7 Parametric Differentiation

35 exam-style questions on Edexcel A Level Maths 9.7 Parametric Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.