1.02g Inequalities: linear and quadratic in single variable

420 questions

Sort by: Default | Easiest first | Hardest first
Edexcel FP2 2004 June Q6
7 marks Standard +0.8
6. Find the complete set of values of \(x\) for which $$\left| x ^ { 2 } - 2 \right| > 2 x$$
Edexcel FP2 2007 June Q5
7 marks Standard +0.3
5. Find the set of values of \(x\) for which $$\frac { x + 1 } { 2 x - 3 } < \frac { 1 } { x - 3 }$$
Edexcel FP2 2009 June Q7
12 marks Challenging +1.2
  1. Sketch the graph of \(y = \left| x ^ { 2 } - a ^ { 2 } \right|\), where \(a > 1\), showing the coordinates of the points where the graph meets the axes.
  2. Solve \(\left| x ^ { 2 } - a ^ { 2 } \right| = a ^ { 2 } - x , a > 1\).
  3. Find the set of values of \(x\) for which \(\left| x ^ { 2 } - a ^ { 2 } \right| > a ^ { 2 } - x , a > 1\).
Edexcel FP2 2010 June Q3
7 marks Standard +0.8
3.
  1. Find the set of values of \(x\) for which $$x + 4 > \frac { 2 } { x + 3 }$$
  2. Deduce, or otherwise find, the values of \(x\) for which $$x + 4 > \frac { 2 } { | x + 3 | }$$
Edexcel FP2 2011 June Q1
7 marks Standard +0.3
  1. Find the set of values of \(x\) for which
$$\frac { 3 } { x + 3 } > \frac { x - 4 } { x }$$
Edexcel FP2 2013 June Q2
7 marks Standard +0.3
2. Use algebra to find the set of values of \(x\) for which $$\frac { 6 x } { 3 - x } > \frac { 1 } { x + 1 }$$
Edexcel FP2 2014 June Q2
5 marks Standard +0.3
2. Using algebra, find the set of values of \(x\) for which $$3 x - 5 < \frac { 2 } { x }$$
Edexcel FP2 2014 June Q2
6 marks Standard +0.8
2. Use algebra to find the set of values of \(x\) for which $$\left| 3 x ^ { 2 } - 19 x + 20 \right| < 2 x + 2$$
Edexcel FP2 2015 June Q1
7 marks Standard +0.3
  1. Use algebra to find the set of values of \(x\) for which $$x + 2 > \frac { 12 } { x + 3 }$$
  2. Hence, or otherwise, find the set of values of \(x\) for which $$x + 2 > \frac { 12 } { | x + 3 | }$$
Edexcel FP2 2016 June Q1
6 marks Standard +0.3
  1. Use algebra to find the set of values of \(x\) for which
$$\frac { x } { x + 1 } < \frac { 2 } { x + 2 }$$
Edexcel FP2 2017 June Q2
9 marks Standard +0.3
2. Use algebra to find the set of values of \(x\) for which $$\frac { x - 2 } { 2 ( x + 2 ) } \leqslant \frac { 12 } { x ( x + 2 ) }$$ "
Edexcel FP2 Specimen Q1
7 marks Standard +0.3
  1. Find the set of values of \(x\) for which
$$\frac { x } { x - 3 } > \frac { 1 } { x - 2 }$$
Edexcel F2 2021 October Q2
8 marks Standard +0.3
2. Use algebra to determine the set of values of \(x\) for which $$\frac { x } { 2 - x } \leqslant \frac { x + 3 } { x }$$ (Solutions relying entirely on graphical methods are not acceptable.)
(8)
Edexcel C1 2006 June Q2
4 marks Moderate -0.8
Find the set of values of \(x\) for which $$x ^ { 2 } - 7 x - 18 > 0 .$$
OCR C1 2005 January Q8
8 marks Moderate -0.8
8 The length of a rectangular children's playground is 10 m more than its width. The width of the playground is \(x\) metres.
  1. The perimeter of the playground is greater than 64 m . Write down a linear inequality in \(x\).
  2. The area of the playground is less than \(299 \mathrm {~m} ^ { 2 }\). Show that \(( x - 13 ) ( x + 23 ) < 0\).
  3. By solving the inequalities in parts (i) and (ii), determine the set of possible values of \(x\).
OCR C1 2007 January Q3
5 marks Easy -1.2
3 Solve the inequalities
  1. \(3 ( x - 5 ) \leqslant 24\),
  2. \(5 x ^ { 2 } - 2 > 78\).
OCR C1 2008 January Q6
8 marks Moderate -0.3
6
  1. Solve the equation \(x ^ { 2 } + 8 x + 10 = 0\), giving your answers in simplified surd form.
  2. Sketch the curve \(y = x ^ { 2 } + 8 x + 10\), giving the coordinates of the point where the curve crosses the \(y\)-axis.
  3. Solve the inequality \(x ^ { 2 } + 8 x + 10 \geqslant 0\).
OCR C1 2005 June Q1
4 marks Moderate -0.8
1 Solve the inequality \(x ^ { 2 } - 6 x - 40 \geqslant 0\).
OCR C1 2007 June Q8
9 marks Moderate -0.8
8
  1. Express \(x ^ { 2 } + 8 x + 15\) in the form \(( x + a ) ^ { 2 } - b\).
  2. Hence state the coordinates of the vertex of the curve \(y = x ^ { 2 } + 8 x + 15\).
  3. Solve the inequality \(x ^ { 2 } + 8 x + 15 > 0\).
OCR C1 2008 June Q7
7 marks Moderate -0.8
7 Solve the inequalities
  1. \(8 < 3 x - 2 < 11\),
  2. \(y ^ { 2 } + 2 y \geqslant 0\).
OCR MEI C1 2008 January Q11
12 marks Moderate -0.8
11
  1. Write \(x ^ { 2 } - 5 x + 8\) in the form \(( x - a ) ^ { 2 } + b\) and hence show that \(x ^ { 2 } - 5 x + 8 > 0\) for all values of \(x\).
  2. Sketch the graph of \(y = x ^ { 2 } - 5 x + 8\), showing the coordinates of the turning point.
  3. Find the set of values of \(x\) for which \(x ^ { 2 } - 5 x + 8 > 14\).
  4. If \(\mathrm { f } ( x ) = x ^ { 2 } - 5 x + 8\), does the graph of \(y = \mathrm { f } ( x ) - 10\) cross the \(x\)-axis? Show how you decide.
OCR MEI C1 2009 January Q3
3 marks Easy -1.8
3 Solve the inequality \(7 - x < 5 x - 2\).
OCR MEI C1 2007 June Q1
3 marks Easy -2.0
1 Solve the inequality \(1 - 2 x < 4 + 3 x\).
OCR MEI C1 2008 June Q1
2 marks Easy -1.8
1 Solve the inequality \(3 x - 1 > 5 - x\).
OCR MEI C1 2015 June Q4
3 marks Easy -1.8
4 Solve the inequality \(\frac { 4 x - 5 } { 7 } > 2 x + 1\).