O-LevelAdditional MathematicsEquations, inequalities and graphs4037/11 · May/June 2024 · Q15 Marks

1 (a) On the axes, sketch the graph of y=-=(x+2)(2x-1)(x+5), stating the intercepts with the axes. [Figure 1.1 - Graph axes with x and y labels, a cubic graph is shown passing through x-intercepts -5, -2, 0.5 and y-intercept 2]

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

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Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

[3] B1 for correct shape with max and min in the correct quadrant. Ignore labelling of their maximum point if incorrect coordinates. Must have a cubic shape
[3] B1 for -5, -2, 1/2 marked on x-axis.
[3] B1 for 2 marked on the y-axis. Must have a cubic shape
[2] B1 for each
[2] If B0 then SC1 for x<-5, -2<x<=1/2

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Topic: Equations, inequalities and graphs, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source: O-Level Additional Mathematics, May/June 2024 Paper 1 Variant 1, question 1.

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