O-LevelAdditional MathematicsQuadratic functions4037/21 · May/June 2015 · Q99 Marks

Find the set of values of x for which 4x² + 19x-5 ≤ 0.

(a)Find the set of values of x for which 4x² + 19x-5 ≤ 0.[3]
(b)(i)Express x² + 8x – 9 in the form (x + a)² + b, where a and b are integers.[2]
(b)(ii)Use your answer to part (i) to find the greatest value of 9 – 8x - x² and the value of x at which this occurs.[2]
(b)(iii)Sketch the graph of y = 9 - 8x - x², indicating the coordinates of any points of intersection with the coordinate axes. [Figure 9.1][2]

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Mark scheme

Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.

[M1] Solves quadratic
[A1] critical values 1/4 and -5 soi
[A1] -5 ≤ x ≤ 1/4 Accept: [-5, 1/4]; -5 ≤ x AND x ≤ 0.25
[B1,B1] (x+4)²–25 or a = 4 and b = -25
[B1ft] (Greatest value =) 25 Must be clear
[B1ft] x = -4
[B1] Correct shape with maximum in second quadrant and crossing positive and negative axes correctly
[B1] All 3 intercepts correctly shown on graph

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About this question

Topic

Quadratic functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 9 marks.

Source

O-Level Additional Mathematics, May/June 2015 Paper 2 Variant 1, question 9.

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