Sketch modulus of linear and non-modulus linear, find intersection

Sketch graphs where one function is modulus of linear expression and the other is a non-modulus linear expression (e.g., y = |2x-9| and y = 5x-3), find intersection points, and possibly solve related equation or inequality.

10 questions · Moderate -0.4

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CAIE P2 2020 June Q5
5 marks Moderate -0.8
5
  1. Sketch, on the same diagram, the graphs of \(y = | 2 x - 3 |\) and \(y = 3 x + 5\).
  2. Solve the inequality \(3 x + 5 < | 2 x - 3 |\).
CAIE P2 2022 June Q2
4 marks Moderate -0.8
2
  1. Sketch, on the same diagram, the graphs of \(y = | 2 x - 9 |\) and \(y = 5 x - 3\).
  2. Solve the equation \(| 2 x - 9 | = 5 x - 3\).
CAIE P2 2024 June Q3
8 marks Standard +0.3
3
  1. Sketch on the same diagram the graphs of \(y = | 3 x - 8 |\) and \(y = 5 - x\).
  2. Solve the inequality \(| 3 x - 8 | < 5 - x\).
  3. Hence determine the largest integer \(N\) satisfying the inequality \(\left| 3 e ^ { 0.1 N } - 8 \right| < 5 - e ^ { 0.1 N }\).
CAIE P2 2021 March Q1
5 marks Moderate -0.8
1
  1. Sketch, on the same diagram, the graphs of \(y = | 3 x - 5 |\) and \(y = x + 2\).
  2. Solve the equation \(| 3 x - 5 | = x + 2\).
CAIE P2 2023 March Q4
7 marks Standard +0.3
4
  1. Sketch, on the same diagram, the graphs of \(y = | 2 x - 11 |\) and \(y = 3 x - 3\).
  2. Solve the inequality \(| 2 x - 11 | < 3 x - 3\).
  3. Find the smallest integer \(N\) satisfying the inequality \(| 2 \ln N - 11 | < 3 \ln N - 3\).
CAIE P2 2020 November Q3
6 marks Moderate -0.3
3
  1. Sketch, on a single diagram, the graphs of \(y = \left| \frac { 1 } { 2 } x - a \right|\) and \(y = \frac { 3 } { 2 } x - \frac { 1 } { 2 } a\), where \(a\) is a positive constant.
  2. Find the coordinates of the point of intersection of the two graphs.
  3. Deduce the solution of the inequality \(\left| \frac { 1 } { 2 } x - a \right| > \frac { 3 } { 2 } x - \frac { 1 } { 2 } a\).
CAIE P2 2021 November Q2
6 marks Moderate -0.8
2
  1. Sketch, on the same diagram, the graphs of \(y = 3 x\) and \(y = | x - 3 |\).
  2. Find the coordinates of the point where the two graphs intersect.
  3. Deduce the solution of the inequality \(3 x < | x - 3 |\).
Edexcel FP2 2003 June Q10
5 marks Moderate -0.3
10. (a) Sketch, on the same axes, the graphs with equation \(y = | 2 x - 3 |\), and the line with equation \(y = 5 x - 1\).
(b) Solve the inequality \(| 2 x - 3 | < 5 x - 1\).
Edexcel FP2 Q1
6 marks Moderate -0.8
  1. (a) Sketch, on the same axes, the graph with equation \(y = | 3 x - 1 |\), and the line with equation \(y = 4 x + 3\).
Show the coordinates of the points at which the graphs meet the \(x\)-axis.
(b) Solve the inequality \(| 3 x - 1 | < 4 x + 3\).
Edexcel FP2 Q13
5 marks Moderate -0.3
13. (a) Sketch, on the same axes, the graphs with equation \(y = | 2 x - 3 |\), and the line with equation \(y = 5 x - 1\).
(b) Solve the inequality \(| 2 x - 3 | < 5 x - 1\).