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Edexcel IGCSE Maths (4MA1) · Unit 4: Graphs & Functions

IGCSE Maths Inequalities on Graphs Questions and Answers

Inequalities on Graphs questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 2 worked examples first, then try the 3 exam-style questions yourself and check your working against the mark scheme.

Practise inequalities on graphs in Unit 4 →Inequalities on Graphs revision notes

What this topic covers

Inequalities on Graphs worked examples

Worked example 1: Linear inequalities on a grid

The region R is given by \(x\ge0\), \(y\ge1\) and \(2x+y\le6\). Find its vertices and decide whether \((2,\ 2)\) is in R.

Solution

  1. Vertices: \((0,\ 1)\), \((0,\ 6)\), and \(2x+1=6\) gives \((2.5,\ 1)\).
  2. Test \((2,\ 2)\): \(2\times2+2=6\le6\) ✓, \(x\ge0\) ✓, \(y\ge1\) ✓.
  3. So \((2,\ 2)\) is in R (on the boundary, which is included).

Answer: Vertices \((0,1),\ (0,6),\ (2.5,1)\); yes

Tip: Solid lines for ≤ and ≥, dashed for < and >.

Worked example 2: Vertices of a region

Find the vertices of the region \(y\le3\), \(y\ge x-1\), \(x+y\ge1\).

Solution

  1. \(y=3\) and \(y=x-1\): \((4,\ 3)\).
  2. \(y=3\) and \(x+y=1\): \((-2,\ 3)\).
  3. \(y=x-1\) and \(x+y=1\): \(2x=2\), \((1,\ 0)\).

Answer: \((4,3),\ (-2,3),\ (1,0)\)

Tip: Each vertex is where two boundary lines meet.

Inequalities on Graphs exam-style questions

Try each question before you open the answer. The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.

Question 1 · easy · 1 mark

A region on a coordinate grid lies to the left of the line \(x=3\), including points on the line. Write down the inequality that describes the region.

Show the answer and mark scheme
  • B1 x ≤ 3

Answer: \(x\le 3\)

Question 2 · medium · 3 marks

Find the coordinates of the vertices of the region defined by \(y\ge0\), \(y\le x\) and \(x+y\le8\).

Show the answer and mark scheme
  • B1 (0, 0)
  • B1 (8, 0)
  • B1 (4, 4)

Answer: \((0,0),\ (8,0),\ (4,4)\)

Question 3 · hard · 3 marks

The region R is defined by \(y\ge1\), \(y\le2x\) and \(x+y\lt 7\). Find the number of points with integer coordinates in R.

Show the answer and mark scheme
  • M1 correct points for at least two values of x, e.g. x = 1: (1,1), (1,2)
  • M1 systematic count for x = 1 to 5
  • A1 12

Answer: 12

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Revise inequalities on graphs for the exam

Questions students ask

Which Edexcel IGCSE Maths papers test inequalities on graphs?

Either Higher tier paper, 1H or 2H, can test inequalities on graphs: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more inequalities on graphs questions?

In the IGCSE student hub: Unit 4 (Graphs & Functions) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

More Unit 4 topics: Graphs & Functions