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1.7.18 Chain rule (A-level only)

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Question 61

The vertical profile of a section of a roller coaster track is modelled by the curve with equation $y = 2x^3 - 24x$ , where $y$ is the vertical displacement in decametres and $x$ is the horizontal distance in decametres from a support pylon.

Point $A$ on the track is located at horizontal distance $x = 2$ .

Point $B$ on the track is located at horizontal distance $x = 2 + h$ .

Show that the gradient of the chord $A B$ is given by $2h^2 + 12h$ .

[4]

Explain how the result of part (a) can be used to show that $A$ is a stationary point on the track section.

[2]

Markscheme

1.7.18 Chain rule (A-level only) Questions

A Level
Maths
1.7.18 Chain rule (A-level only)

74 exam-style questions on OCR A Level Maths 1.7.18 Chain rule (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

1.7.18 Chain rule (A-level only)

Question bank

1.7.18 Chain rule (A-level only)

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Question 61

Point $A$ on the track is located at horizontal distance $x = 2$ .

Point $B$ on the track is located at horizontal distance $x = 2 + h$ .

Show that the gradient of the chord $A B$ is given by $2h^2 + 12h$ .

[4]

Explain how the result of part (a) can be used to show that $A$ is a stationary point on the track section.

[2]

Markscheme

1.7.18 Chain rule (A-level only) Questions

A Level
Maths
1.7.18 Chain rule (A-level only)

74 exam-style questions on OCR A Level Maths 1.7.18 Chain rule (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.