O-LevelAdditional MathematicsEquations, inequalities and graphs4037/22 · May/June 2024 · Q16 Marks
On the axes, sketch the graph of y = (2x-5) (x+3)(1-x), stating the intercepts with the coordinate axes.
- (a)On the axes, sketch the graph of y = (2x-5) (x+3)(1-x), stating the intercepts with the coordinate axes.[3]
- (b)(i)solve the inequality (2x-5)(x+3)(1-x) ≤ 0[2]
- (b)(ii)on the axes below, sketch the graph of y = |(2x-5)(x+3)(1-x)|.[1]
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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.
- [B3] B1 for correct shape; the ends must extend above and below the x-axis
- [B3] B1 for correct roots indicated; must have attempted a cubic shape
- [B3] B1 for correct y-intercept indicated; must have attempted a cubic shape
- [B2] -3 ≤ x ≤ 1, x ≥ 2.5 mark final answer
- [B2] FT their (a) providing it is an equivalent cubic shape and has 3 stated or indicated roots for B2, B1 or SC1
- [B2] B1 for one correct inequality out of two
- [B2] If 0 scored then SC1 for -3<x<1,x > 2.5 or -3<x<1, x > 2.5 or -3 < x < 1, x > 2.5
- [B1] FT their (a) providing it is an equivalent cubic shape
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