OCR C3 2007 June — Question 2 5 marks

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
Year2007
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicModulus function
TypeSolve |linear| < |linear|
DifficultyStandard +0.3 This is a standard modulus inequality requiring squaring both sides to eliminate the absolute values, then solving a quadratic inequality. It's slightly above average difficulty as it involves multiple steps (squaring, rearranging, factorizing, and interpreting the solution) but follows a well-established technique taught in C3 with no novel insight required.
Spec1.02g Inequalities: linear and quadratic in single variable1.02l Modulus function: notation, relations, equations and inequalities
2 Solve the inequality \(| 4 x - 3 | < | 2 x + 1 |\).
AnswerMarks Guidance
Identify critical value \(x = 2\)B1
Attempt process for determining both critical valuesM1
Obtain \(\frac{1}{2}\) and \(2\)A1
Attempt process for solving inequalityM1 table, sketch …; implied by plausible answer
Obtain \(\frac{1}{2} < x < 2\)A1 5 
Identify critical value $x = 2$ | B1 |
Attempt process for determining both critical values | M1 |
Obtain $\frac{1}{2}$ and $2$ | A1 |
Attempt process for solving inequality | M1 | table, sketch …; implied by plausible answer
Obtain $\frac{1}{2} < x < 2$ | A1 | 5

---
2 Solve the inequality $| 4 x - 3 | < | 2 x + 1 |$.

\hfill \mbox{\textit{OCR C3 2007 Q2 [5]}}
This paper (9 questions)
View full paper
Q1 5 Q2 5 Q3 7 Q4 7 Q5 7 Q6 9 Q7 9 Q8 11 Q9 12