1.02l Modulus function: notation, relations, equations and inequalities

395 questions

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CAIE P2 2010 June Q3
4 marks Standard +0.3
3 Solve the inequality \(| 2 x - 1 | < | x + 4 |\).
CAIE P2 2011 June Q1
3 marks Moderate -0.5
1 Solve the equation \(| 3 x + 4 | = | 2 x + 5 |\).
CAIE P2 2012 June Q1
4 marks Moderate -0.3
1 Solve the equation \(\left| x ^ { 3 } - 14 \right| = 13\), showing all your working.
CAIE P2 2012 June Q1
4 marks Standard +0.3
1 Solve the inequality \(| x + 3 | < | 2 x + 1 |\).
CAIE P2 2013 June Q1
5 marks Moderate -0.3
1 Solve the equation \(\left| 2 ^ { x } - 7 \right| = 1\), giving answers correct to 2 decimal places where appropriate.
CAIE P2 2013 June Q2
4 marks Standard +0.3
2 Solve the inequality \(| x - 8 | > | 2 x - 4 |\).
CAIE P2 2014 June Q1
4 marks Standard +0.3
1 Solve the inequality \(| 3 x - 2 | \geqslant | x + 4 |\).
CAIE P2 2014 June Q1
4 marks Moderate -0.3
1
  1. Solve the equation \(| x + 2 | = | x - 13 |\).
  2. Hence solve the equation \(\left| 3 ^ { y } + 2 \right| = \left| 3 ^ { y } - 13 \right|\), giving your answer correct to 3 significant figures.
CAIE P2 2015 June Q1
5 marks Moderate -0.3
1
  1. Solve the equation \(| 3 x + 4 | = | 3 x - 11 |\).
  2. Hence, using logarithms, solve the equation \(\left| 3 \times 2 ^ { y } + 4 \right| = \left| 3 \times 2 ^ { y } - 11 \right|\), giving the answer correct to 3 significant figures.
CAIE P2 2016 June Q3
5 marks Standard +0.3
3
  1. Solve the equation \(| 3 u + 1 | = | 2 u - 5 |\).
  2. Hence solve the equation \(| 3 \cot x + 1 | = | 2 \cot x - 5 |\) for \(0 < x < \frac { 1 } { 2 } \pi\), giving your answer correct to 3 significant figures.
CAIE P2 2017 June Q2
4 marks Standard +0.3
2 Solve the inequality \(| 4 - x | \leqslant | 3 - 2 x |\).
CAIE P2 2017 June Q1
3 marks Standard +0.3
1 Solve the equation \(| x + a | = | 2 x - 5 a |\), giving \(x\) in terms of the positive constant \(a\).
CAIE P2 2018 June Q1
4 marks Standard +0.3
1 Solve the inequality \(| 3 x - 2 | < | x + 5 |\).
CAIE P3 2003 June Q3
4 marks Standard +0.3
3 Solve the inequality \(| x - 2 | < 3 - 2 x\).
CAIE P3 2004 June Q2
4 marks Standard +0.3
2 Solve the inequality \(| 2 x + 1 | < | x |\).
CAIE P3 2008 June Q1
4 marks Standard +0.8
1 Solve the inequality \(| x - 2 | > 3 | 2 x + 1 |\).
CAIE P3 2010 June Q1
4 marks Challenging +1.2
1 Solve the inequality \(| x + 3 a | > 2 | x - 2 a |\), where \(a\) is a positive constant.
CAIE P3 2011 June Q1
3 marks Standard +0.3
1 Solve the inequality \(| x | < | 5 + 2 x |\).
CAIE P3 2012 June Q1
3 marks Moderate -0.3
1 Solve the equation \(\left| 4 - 2 ^ { x } \right| = 10\), giving your answer correct to 3 significant figures.
CAIE P3 2013 June Q4
6 marks Standard +0.3
4
  1. Solve the equation \(| 4 x - 1 | = | x - 3 |\).
  2. Hence solve the equation \(\left| 4 ^ { y + 1 } - 1 \right| = \left| 4 ^ { y } - 3 \right|\) correct to 3 significant figures.
CAIE P3 2013 June Q1
4 marks Standard +0.3
1 Solve the inequality \(| 4 x + 3 | > | x |\).
CAIE P3 2015 June Q2
4 marks Moderate -0.5
2 Use the trapezium rule with three intervals to find an approximation to $$\int _ { 0 } ^ { 3 } \left| 3 ^ { x } - 10 \right| \mathrm { d } x$$
CAIE P3 2015 June Q2
4 marks Moderate -0.5
2 Solve the inequality \(| x - 2 | > 2 x - 3\).
CAIE P3 2016 June Q1
5 marks Moderate -0.3
1
  1. Solve the equation \(2 | x - 1 | = 3 | x |\).
  2. Hence solve the equation \(2 \left| 5 ^ { x } - 1 \right| = 3 \left| 5 ^ { x } \right|\), giving your answer correct to 3 significant figures.
CAIE P3 2016 June Q1
4 marks Standard +0.3
1 Solve the inequality \(2 | x - 2 | > | 3 x + 1 |\).