Sketch y=|linear| and y=linear with unknown constants, then solve

Sketch and solve problems involving modulus of linear expression compared to a linear expression where one or more unknown constants (e.g. a, b, k) are present.

9 questions · Standard +0.2

Sort by: Default | Easiest first | Hardest first
CAIE P3 2024 June Q1
3 marks Moderate -0.8
1
  1. Sketch the graph of \(\mathrm { y } = | \mathrm { x } - 2 \mathrm { a } |\), where \(a\) is a positive constant.
  2. Solve the inequality \(2 \mathrm { x } - 3 \mathrm { a } < | \mathrm { x } - 2 \mathrm { a } |\).
Edexcel C3 2014 January Q6
10 marks Moderate -0.3
  1. Given that \(a\) and \(b\) are constants and that \(0 < a < b\),
    1. on separate diagrams, sketch the graph with equation
      1. \(y = | 2 x + a |\),
      2. \(y = | 2 x + a | - b\).
    Show on each sketch the coordinates of each point at which the graph crosses or meets the axes.
  2. Solve, for \(x\), the equation $$| 2 x + a | - b = \frac { 1 } { 3 } x$$ giving any answers in terms of \(a\) and \(b\).
Edexcel C3 2017 June Q6
8 marks Standard +0.3
  1. Given that \(a\) and \(b\) are positive constants,
    1. on separate diagrams, sketch the graph with equation
      1. \(y = | 2 x - a |\)
      2. \(y = | 2 x - a | + b\)
    Show, on each sketch, the coordinates of each point at which the graph crosses or meets the axes. Given that the equation $$| 2 x - a | + b = \frac { 3 } { 2 } x + 8$$ has a solution at \(x = 0\) and a solution at \(x = c\),
  2. find \(c\) in terms of \(a\).
Edexcel FP2 2005 June Q1
5 marks Standard +0.8
  1. Sketch the graph of \(y = | x - 2 a |\), given that \(a > 0\).
  2. Solve \(| x - 2 a | > 2 x + a\), where \(a > 0\).
    (3)(Total 5 marks)
Edexcel C34 2016 June Q6
9 marks Standard +0.3
6. Given that \(a\) and \(b\) are constants and that \(a > b > 0\)
  1. on separate diagrams, sketch the graph with equation
    1. \(y = | x - a |\)
    2. \(y = | x - a | - b\) Show on each sketch the coordinates of each point at which the graph crosses or meets the \(x\)-axis and the \(y\)-axis.
  2. Hence or otherwise find the complete set of values of \(x\) for which $$| x - a | - b < \frac { 1 } { 2 } x$$ giving your answer in terms of \(a\) and \(b\).
Edexcel PMT Mocks Q1
5 marks Standard +0.3
  1. Given that \(a\) is a positive constant,
    a. Sketch the graph with equation
$$y = | a - 2 x |$$ Show on your sketch the coordinates of each point at which the graph crosses the \(x\)-axis and \(y\)-axis.
b. Solve the inequality \(| a - 2 x | > x + 2 a\)
Edexcel Paper 2 2021 October Q11
10 marks Standard +0.8
11. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6c32000f-574f-473c-bd04-9cfe2c1bd715-30_630_630_312_721} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} Figure 4 shows a sketch of the graph with equation $$y = | 2 x - 3 k |$$ where \(k\) is a positive constant.
  1. Sketch the graph with equation \(y = \mathrm { f } ( x )\) where $$f ( x ) = k - | 2 x - 3 k |$$ stating
    $$k - | 2 x - 3 k | > x - k$$ giving your answer in set notation.
  2. Find, in terms of \(k\), the coordinates of the minimum point of the graph with equation $$y = 3 - 5 f \left( \frac { 1 } { 2 } x \right)$$
Edexcel FP2 Q36
5 marks Moderate -0.3
  1. Sketch the graph of \(y = |x - 2a|\), given that \(a > 0\). [2]
  2. Solve \(|x - 2a| > 2x + a\), where \(a > 0\). [3]
SPS SPS SM Mechanics 2022 February Q10
10 marks Standard +0.3
\includegraphics{figure_4} Figure 4 Figure 4 shows a sketch of the graph with equation $$y = |2x - 3k|$$ where \(k\) is a positive constant.
  1. Sketch the graph with equation \(y = f(x)\) where $$f(x) = k - |2x - 3k|$$ stating • the coordinates of the maximum point • the coordinates of any points where the graph cuts the coordinate axes [4]
  2. Find, in terms of \(k\), the set of values of \(x\) for which $$k - |2x - 3k| > x - k$$ giving your answer in set notation. [4]
  3. Find, in terms of \(k\), the coordinates of the minimum point of the graph with equation $$y = 3 - 5f\left(\frac{1}{2}x\right)$$ [2]