A-LevelMathematicsDifferentiation9709/22 · Oct/Nov 2021 · Q36 Marks

The curve with equation y = 5x – 2 tan 2x has exactly one stationary point in the interval 0 ≤ x < ¼π. Find the coordinates of this stationary point, giving each coordinate correct to 3 significant figures.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

[*M1] Differentiate to obtain first derivative of form k₁ + k₂ sec² 2x Where k₁k₂ ≠ 0.
[A1] Obtain correct 5 – 4 sec² 2x
[M1] Equate first derivative of form k₁ + k₂ sec² 2x to zero and obtain value for cos² 2x OE Or value for tan² 2x which must be > 0. –1 < cos 2x < 1.
[A1] Obtain cos 2x = 2/√5 or (decimal) equivalent Or tan 2x = 1/2
[A1] Obtain x = 0.232 AWRT
[A1] Obtain y = 0.159 AWRT

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Topic: Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source: A-Level Mathematics, Oct/Nov 2021 Paper 2 Variant 2, question 3.

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