CAIE P2 2016 March — Question 2 4 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2016
SessionMarch
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicModulus function
TypeSolve |linear| < |linear|
DifficultyStandard +0.3 This is a standard modulus inequality requiring consideration of critical points (x = 5 and x = -3/2) and testing regions, but follows a routine algorithmic approach taught in P2. It's slightly above average difficulty due to the need to square both sides or systematically consider cases, but remains a textbook exercise with no novel insight required.
Spec1.02l Modulus function: notation, relations, equations and inequalities
2 Solve the inequality \(| x - 5 | < | 2 x + 3 |\).
AnswerMarks Guidance
Either: State or imply non-modular inequality \((x-5)^2 < (2x+3)^2\) or corresponding pair of linear equationsB1
Attempt solution of 3-term quadratic equation or of 2 linear equationsM1
Obtain critical values \(-8\) and \(\frac{2}{3}\)A1
State answer \(x < -8, \quad x > \frac{2}{3}\)A1
Or: Obtain critical value \(-8\) from graphical method, inspection, equationB1
Obtain critical value \(\frac{2}{3}\) similarlyB2
State answer \(x < -8, \quad x > \frac{2}{3}\)B1 [4] 
Either: State or imply non-modular inequality $(x-5)^2 < (2x+3)^2$ or corresponding pair of linear equations | B1 |
Attempt solution of 3-term quadratic equation or of 2 linear equations | M1 |
Obtain critical values $-8$ and $\frac{2}{3}$ | A1 |
State answer $x < -8, \quad x > \frac{2}{3}$ | A1 |

Or: Obtain critical value $-8$ from graphical method, inspection, equation | B1 |
Obtain critical value $\frac{2}{3}$ similarly | B2 |
State answer $x < -8, \quad x > \frac{2}{3}$ | B1 | [4]
2 Solve the inequality $| x - 5 | < | 2 x + 3 |$.

\hfill \mbox{\textit{CAIE P2 2016 Q2 [4]}}
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Q1 3 Q2 4 Q3 5 Q4 5 Q5 5 Q6 8 Q7 9 Q8 11