A-LevelMathematicsTrigonometry9709/21 · Oct/Nov 2025 · Q36 Marks

Solve the equation |2x-3|=|5x+2|.

(a)Solve the equation |2x-3|=|5x+2|.[3]
(b)Hence solve the equation |2 secθ-3|=|5secθ+2| for π < θ < 2π. Give your answer correct to 3 significant figures.[3]

Mark scheme

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

[B1] (a) Solve 2x-3=5x+2 to obtain -5/3 [Or exact equivalent.]
[M1] (a) Attempt solution of linear equation where 2x and 5x have different signs
[A1] (a) Obtain 1/7 OE
[B1] (a) State or imply non-modulus equation (2x – 3)² = (5x + 2)²
[M1] (a) Attempt complete solution of three-term quadratic equation
[A1] (a) Obtain -5/3 and 1/7 or equivalents [OE]
[B1 FT] (b) State or imply cosθ = -5/3 [Following an appropriate answer from part (a).]
[M1] (b) Attempt correct process for finding third quadrant angle [Condone working in degrees for this mark.]
[A1] (b) Obtain 4.07 [Or greater accuracy 4.0688...]

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Topic: Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source: A-Level Mathematics, Oct/Nov 2025 Paper 2 Variant 1, question 3.

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