CAIE P3 2016 June — Question 1 4 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2016
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicModulus function
TypeSolve k|linear| compared to |linear|
DifficultyStandard +0.3 This is a standard modulus inequality requiring case-by-case analysis based on critical points x = 2 and x = -1/3. While it involves multiple cases and careful algebraic manipulation, the technique is routine for P3 students and follows a well-practiced method with no conceptual surprises.
Spec1.02g Inequalities: linear and quadratic in single variable1.02l Modulus function: notation, relations, equations and inequalities

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

AnswerMarks Guidance
State or imply non-modular inequality \(2(x-2)^2 > (3x+1)^2\), or corresponding quadratic equation, or pair of linear equations \(2(x-2) = \pm(3x+1)\)B1
Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations for \(x\)M1
Obtain critical values \(x = -5\) and \(x = \frac{2}{5}\)A1
State final answer \(-5 < x < \frac{2}{5}\)A1 [4]
OR:
AnswerMarks Guidance
Obtain critical value \(x = -5\) from a graphical method, or by inspection, or by solving a linear equation or inequalityB1
Obtain critical value \(x = \frac{2}{5}\) similarlyB2
State final answer \(-5 < x < \frac{2}{5}\)B1 [4]
*[Do not condone \(\leq\) for \(<\)]*
State or imply non-modular inequality $2(x-2)^2 > (3x+1)^2$, or corresponding quadratic equation, or pair of linear equations $2(x-2) = \pm(3x+1)$ | B1 | 

Make reasonable solution attempt at a 3-term quadratic, or solve two linear equations for $x$ | M1 | 

Obtain critical values $x = -5$ and $x = \frac{2}{5}$ | A1 | 

State final answer $-5 < x < \frac{2}{5}$ | A1 | [4]

**OR:**

Obtain critical value $x = -5$ from a graphical method, or by inspection, or by solving a linear equation or inequality | B1 | 

Obtain critical value $x = \frac{2}{5}$ similarly | B2 | 

State final answer $-5 < x < \frac{2}{5}$ | B1 | [4]

*[Do not condone $\leq$ for $<$]*

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

\hfill \mbox{\textit{CAIE P3 2016 Q1 [4]}}