CAIE P2 2010 November — Question 1 3 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2010
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicModulus function
TypeSolve |linear| > |linear|
DifficultyStandard +0.3 This is a straightforward modulus inequality requiring students to consider critical points at x = -1 and x = 4, then test regions or square both sides. It's slightly above average difficulty as it involves systematic case analysis, but the technique is standard and well-practiced in P2, with no conceptual surprises beyond applying the definition of modulus.
Spec1.02l Modulus function: notation, relations, equations and inequalities

1 Solve the inequality \(| x + 1 | > | x - 4 |\).

AnswerMarks Guidance
State or imply non-modular inequality \((x+1)^2 > (x-4)^2\), or corresponding equation or pair of linear equationsM1
Obtain critical value \(\frac{3}{2}\)A1
State correct answer \(x > \frac{3}{2}\)A1 [3]
OR:
AnswerMarks Guidance
State a correct linear equation for the critical value, e.g. \(x+1 = -x+4\), or corresponding correct linear inequality, e.g. \(x+1 > -(x-4)\)M1
Obtain critical value \(\frac{3}{2}\)A1
State correct answer \(x > \frac{3}{2}\)A1 [3]
State or imply non-modular inequality $(x+1)^2 > (x-4)^2$, or corresponding equation or pair of linear equations | M1 |

Obtain critical value $\frac{3}{2}$ | A1 |

State correct answer $x > \frac{3}{2}$ | A1 | [3]

OR:

State a correct linear equation for the critical value, e.g. $x+1 = -x+4$, or corresponding correct linear inequality, e.g. $x+1 > -(x-4)$ | M1 |

Obtain critical value $\frac{3}{2}$ | A1 |

State correct answer $x > \frac{3}{2}$ | A1 | [3]
1 Solve the inequality $| x + 1 | > | x - 4 |$.

\hfill \mbox{\textit{CAIE P2 2010 Q1 [3]}}