O-LevelAdditional MathematicsEquations, inequalities and graphs4037/12 · Oct/Nov 2022 · Q28 Marks

On the axes, draw the graph of y = |3x²+13x-10|, stating the coordinates of the points where the graph meets the axes.

(a)On the axes, draw the graph of y = |3x²+13x-10|, stating the coordinates of the points where the graph meets the axes.[4]
(b)Find the set of values of the constant k such that the equation k = |3x²+13x-10| has exactly 2 distinct roots.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

[1] (a) correct basic shape, allow 'construction curve'
[1] (a) (0, 10) must have correct basic shape, must be convinced that this is the vertical intercept
[1] (a) (-5, 0) and (2/3, 0) or (0.667, 0) or better
[1] (a) all previous B marks for all correct with cusps and the correct shape for x < -5 and x > 2/3
[1] (b) Stationary point when x = -13/6 seen or implied
[1] (b) y-value of stationary point is (-)289/12 or (-)24.1 or better (allow +ve or -ve value)
[1] (b) k > 289/12 or k > 24.1 or better
[1] (b) k=0

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Topic: Equations, inequalities and graphs, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2022 Paper 1 Variant 2, question 2.

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