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3.5.4 Differentiation (A-level only)

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Question 74

A chemical reaction's rate $R$ (measured in units/s) and the concentration $C$ of the substrate (measured in mmol/L) are related by the equation

R^3 + 5C^2 - 30RC = 0

The graph of this relationship for $\ge 0$ forms a loop in the first quadrant with a stationary point at $P$ , where the rate of change of $R$ with respect to $C$ is zero.

Show that at the point $P$ , the rate $R$ satisfies the equation

R^2(R - 45) = 0

[5]

Hence, find the coordinates of $P$ in the form $(C, R)$ .

[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 74

A chemical reaction's rate $R$ (measured in units/s) and the concentration $C$ of the substrate (measured in mmol/L) are related by the equation

R^3 + 5C^2 - 30RC = 0

The graph of this relationship for $\ge 0$ forms a loop in the first quadrant with a stationary point at $P$ , where the rate of change of $R$ with respect to $C$ is zero.

Show that at the point $P$ , the rate $R$ satisfies the equation

R^2(R - 45) = 0

[5]

Hence, find the coordinates of $P$ in the form $(C, R)$ .

[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.