CAIE P3 2017 June — Question 2 4 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2017
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicInequalities
TypeSolve absolute value inequality
DifficultyStandard +0.3 This is a straightforward absolute value inequality requiring consideration of two cases based on the sign of (x-3), followed by solving linear inequalities and checking validity of solutions. It's slightly above average difficulty due to the need to handle cases systematically and reject invalid solutions, but remains a standard textbook exercise with no novel insight required.
Spec1.02l Modulus function: notation, relations, equations and inequalities

Solve the inequality \(|x - 3| < 3x - 4\). [4]

Question 2:
AnswerMarks
2EITHER:
State or imply non-modular inequality(x−3) 2 <(3x−4) 2 , or corresponding equation(B1
Make reasonable attempt at solving a three term quadraticM1
Obtain critical valuex= 7
AnswerMarks
4A1
State final answerx> 7 only
AnswerMarks
4A1)
OR1:
AnswerMarks
State the relevant critical inequality 3−x<3x−4, or corresponding equation(B1
Solve for xM1
Obtain critical valuex= 7
AnswerMarks
4A1
State final answerx> 7 only
AnswerMarks
4A1)
OR2:
AnswerMarks
Make recognizable sketches of y= x−3 andy=3x−4 on a single diagram(B1
Find x-coordinate of the intersectionM1
Obtainx= 7
AnswerMarks
4A1
State final answerx> 7 only
AnswerMarks Guidance
4A1)
Total:4
QuestionAnswer Marks
Question 2:
2 | EITHER:
State or imply non-modular inequality(x−3) 2 <(3x−4) 2 , or corresponding equation | (B1
Make reasonable attempt at solving a three term quadratic | M1
Obtain critical valuex= 7
4 | A1
State final answerx> 7 only
4 | A1)
OR1:
State the relevant critical inequality 3−x<3x−4, or corresponding equation | (B1
Solve for x | M1
Obtain critical valuex= 7
4 | A1
State final answerx> 7 only
4 | A1)
OR2:
Make recognizable sketches of y= x−3 andy=3x−4 on a single diagram | (B1
Find x-coordinate of the intersection | M1
Obtainx= 7
4 | A1
State final answerx> 7 only
4 | A1)
Total: | 4
Question | Answer | Marks
Solve the inequality $|x - 3| < 3x - 4$. [4]

\hfill \mbox{\textit{CAIE P3 2017 Q2 [4]}}