A-LevelMathematicsTrigonometry9709/32 · Feb/Mar 2025 · Q46 Marks

By first expressing the equation tan(x-60°) = 2cotx as a quadratic equation in tanx, solve the equation for 0° ≤ x ≤ 180°.

(a)By first expressing the equation tan(x-60°) = 2cotx as a quadratic equation in tanx, solve the equation for 0° ≤ x ≤ 180°.[6]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2025). The mark or mark type is shown in brackets.

[B1] State (tanx - √3)/(1 + √3 tanx) OE Allow decimals throughout.
[B1] 2 cot x replaced by 2/tanx SOI
[B1] Reduce the equation to tan²x – 3√3 tanx – 2 = 0, or three-term equivalent May be implied by further work.
[M1] FT their 3-term quadratic. Allow tan⁻¹(..).
[A1] Obtain answer, e.g. 79.8° AWRT 79.8.
[A1] Obtain the second answer, e.g. 160.2° and no other in the interval Allow 160, or AWRT 160.2. Treat answers in radians as a misread. Ignore answers outside the given interval.

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Topic: Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source: A-Level Mathematics, Feb/Mar 2025 Paper 3 Variant 2, question 4.

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