O-LevelAdditional MathematicsEquations, inequalities and graphs4037/11 · May/June 2017 · Q811 Marks

On the axes below sketch the graphs of y = |2x – 5| and 9y = 80x – 16x².

(i)On the axes below sketch the graphs of y = |2x – 5| and 9y = 80x – 16x².[5]
(ii)Solve |2x – 5|= 4.[3]
(iii)Hence show that the graphs of y = |2x – 5| and 9y = 80x – 16x² intersect at the points where y = 4.[1]
(iv)Hence find the values of x for which 9|2x – 5| ≤ 80x – 16x².[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

[B5] B1 for shape of modulus function
B1 for y intercept = 5 (for modulus graph only)
B1 for x intercept = 2.5 at the V of a modulus graph
B1 for shape of quadratic function for -1 ≤ x ≤ 6
B1 for intercepts at x = 0 and x = 5 for a quadratic graph
[B1] one correct answer
[M1] solution of two different correct linear equations or solution of an equation obtained from squaring both sides or use of symmetry from first solution.
[A1] second correct solution x=9/2, x=1/2
[B1] verification using both x values or for forming and solving 16x² −80x+36=0
[M1] using their values from (ii) in an equality of the form a≤x≤b or a<x<b
[A1] 1/2 <x< 9/2 cao

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