O-LevelAdditional MathematicsEquations, inequalities and graphs4037/12 · Oct/Nov 2025 · Q15 Marks

On the axes, sketch the graph of y = (1-x)(x - 5)(2x-5), stating the intercepts with the axes.

(a)On the axes, sketch the graph of y = (1-x)(x - 5)(2x-5), stating the intercepts with the axes.[3]
(b)Hence solve the inequality (1-x)(x-5)(2x−5) ≤ 0.[2]

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Mark scheme

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

[3] B1 for the correct shape with a distinct minimum in 4th quadrant and a distinct maximum in the first quadrant. No turning over at end points, suggesting further stationary points.
B1 for 1, 2.5 and 5 on the x-axis or stated. Independent mark for critical values seen correctly marked on the x-axis or stated with no contradiction and no other critical x-values
B1 for 25 marked correctly on the y-axis or stated with no contradiction. Independent mark.
[2] B1 Mark final answer for 1≤x≤2.5
B1 Mark final answer for x≥5

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Topic: Equations, inequalities and graphs, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2025 Paper 1 Variant 2, question 1.

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