OCR H240/03 2019 June — Question 3 7 marks

Exam BoardOCR
ModuleH240/03 (Pure Mathematics and Mechanics)
Year2019
SessionJune
Marks7
PaperDownload PDF ↗
TopicModulus function
TypeSolve |linear| < |linear|
DifficultyModerate -0.3 Part (a) requires solving an absolute value inequality by considering cases (x < 2, 2 ≤ x < 3, x ≥ 3), which is a standard A-level technique but involves careful algebraic manipulation. Part (b) tests understanding of transformations of modulus functions, requiring recognition that |2x - 6| = 2|x - 3| and identifying the horizontal translation and vertical stretch. Both parts are routine applications of core techniques with no novel insight required, making this slightly easier than average.
Spec1.07k Differentiate trig: sin(kx), cos(kx), tan(kx)1.07n Stationary points: find maxima, minima using derivatives1.08i Integration by parts1.09d Newton-Raphson method1.09f Trapezium rule: numerical integration

  1. In this question you must show detailed reasoning. Solve the inequality \(|x - 2| \leqslant |2x - 6|\). [4]
  2. Give full details of a sequence of two transformations needed to transform the graph of \(y = |x - 2|\) to the graph of \(y = |2x - 6|\). [3]

\begin{enumerate}[label=(\alph*)]
\item In this question you must show detailed reasoning.

Solve the inequality $|x - 2| \leqslant |2x - 6|$. [4]

\item Give full details of a sequence of two transformations needed to transform the graph of $y = |x - 2|$ to the graph of $y = |2x - 6|$. [3]
\end{enumerate}

\hfill \mbox{\textit{OCR H240/03 2019 Q3 [7]}}