CAIE P2 2009 November — Question 1 4 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2009
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicModulus function
TypeSolve |linear| > |linear|
DifficultyStandard +0.3 This is a straightforward modulus inequality requiring consideration of critical points (x = -3 and x = 0) and testing regions, which is a standard technique taught in P2. While it requires systematic case analysis, it's a routine application of the method with no conceptual surprises, making it slightly easier than average.
Spec1.02l Modulus function: notation, relations, equations and inequalities

1 Solve the inequality \(| x + 3 | > | 2 x |\).

EITHER:
AnswerMarks
Obtain a non-modular inequality from \((x + 3)^2 > (2x)^2\), or corresponding equation, or pair of linear equations \((x + 3) = \pm 2x\)M1
Make reasonable solution attempt at a 3-term quadratic, or solve two linear equationsM1
Obtain critical values \(x = -1\) and \(x = 3\)A1
State answer \(-1 < x < 3\)A1
OR:
AnswerMarks
Obtain critical value \(x = 3\) from a graphical method, or by inspection, or by solving a linear inequality or linear equationB1
Obtain the critical value \(x = -1\) similarlyB2
State answer \(-1 < x < 3\)B1
Total: [4]
**EITHER:**
| Obtain a non-modular inequality from $(x + 3)^2 > (2x)^2$, or corresponding equation, or pair of linear equations $(x + 3) = \pm 2x$ | M1 |
| Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations | M1 |
| Obtain critical values $x = -1$ and $x = 3$ | A1 |
| State answer $-1 < x < 3$ | A1 |

**OR:**
| Obtain critical value $x = 3$ from a graphical method, or by inspection, or by solving a linear inequality or linear equation | B1 |
| Obtain the critical value $x = -1$ similarly | B2 |
| State answer $-1 < x < 3$ | B1 |

**Total: [4]**

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1 Solve the inequality $| x + 3 | > | 2 x |$.

\hfill \mbox{\textit{CAIE P2 2009 Q1 [4]}}