O-LevelAdditional MathematicsEquations, inequalities and graphs4037/21 · May/June 2021 · Q36 Marks

Solve the inequality |4x-1|> 9.

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

[M1] 4x-1*9 oe and 4x-1*-9 oe OR 16x²-8x-80*0 oe soi (where * could be = or any inequality sign)
[A2] x > 5/2, x < -2 only; mark final answer (not from wrong working)
[A1] for CV 5/2, -2 oe
[SC1] If M0 then SC1 for any correct inequality with at most one extra inequality
[M1] (2√x−3)(√x−4) or x = u² and (2u – 3)(u – 4) oe soi
[A1] √x = 3/2, √x = 4 oe
[B1] x = 9/4, x = 16 (FT their √x)
[M1] (Alternative) (2x+12)² = (11√x)² simplified to 4x²-73x+144 = 0
[M1] (Alternative) solves 3 term quadratic in x
[A1] (Alternative) x = 9/4, x = 16

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Topic: Equations, inequalities and graphs, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source: O-Level Additional Mathematics, May/June 2021 Paper 2 Variant 1, question 3.

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