OCR C3 2005 June — Question 2 4 marks

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
Year2005
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicModulus function
TypeSolve |linear| = |linear| (both linear inside)
DifficultyModerate -0.8 This is a straightforward modulus equation requiring students to consider cases where expressions inside the modulus are positive or negative. The method is standard (square both sides or consider sign cases), and the algebra is simple with linear expressions only, making it easier than average but not trivial since it requires systematic case analysis.
Spec1.02l Modulus function: notation, relations, equations and inequalities

2 Find the exact solutions of the equation \(| 6 x - 1 | = | x - 1 |\).

AnswerMarks Guidance
Either obtain \(x = 0\)B1 [ignoring errors in working]
Form linear equation with signs of \(6x\) and \(x\) differentM1 [ignoring other sign errors]
State \(6x - 1 = -x + 1\)A1 [or correct equiv with or without brackets]
Obtain \(\frac{2}{7}\) and no other non-zero valueA1 Total: 4 marks [or exact equiv]
Or: Obtain \(36x^2 - 12x + 1 = x^2 - 2x + 1\)B1 [or equiv]
Attempt to solve quadratic equationM1 [as far as factorisation or subn into formula]
Obtain \(\frac{2}{7}\) and no other non-zero valueA1 [or exact equiv]
Obtain 0B1 Total: 4 marks [ignoring errors in working]
Either obtain $x = 0$ | B1 | [ignoring errors in working]

Form linear equation with signs of $6x$ and $x$ different | M1 | [ignoring other sign errors]

State $6x - 1 = -x + 1$ | A1 | [or correct equiv with or without brackets]

Obtain $\frac{2}{7}$ and no other non-zero value | A1 | Total: 4 marks [or exact equiv]

Or: Obtain $36x^2 - 12x + 1 = x^2 - 2x + 1$ | B1 | [or equiv]

Attempt to solve quadratic equation | M1 | [as far as factorisation or subn into formula]

Obtain $\frac{2}{7}$ and no other non-zero value | A1 | [or exact equiv]

Obtain 0 | B1 | Total: 4 marks [ignoring errors in working]
2 Find the exact solutions of the equation $| 6 x - 1 | = | x - 1 |$.

\hfill \mbox{\textit{OCR C3 2005 Q2 [4]}}