Edexcel IGCSE Maths (4MA1) · Unit 4: Graphs & Functions
Edexcel IGCSE 4MA1 Inequalities on Graphs: Exam 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 8 exam-style questions yourself and check your working against the mark scheme.
Regions on Graphs 1: Linear Inequalities on a Grid: Showing and describing regions defined by linear inequalities on a grid.
Regions on Graphs 2: Harder Inequalities: Shading regions defined by several inequalities.
Inequalities on Graphs worked examples
Worked example 1: Linear inequalities on a grid
The region R is given by , and . Find its vertices and decide whether is in R.
Solution
Vertices: , , and gives .
Test : ✓, ✓, ✓.
So is in R (on the boundary, which is included).
Answer: Vertices ; yes
4 steps
Tip: Solid lines for ≤ and ≥, dashed for < and >.
Worked example 2: Vertices of a region
Find the vertices of the region , , .
Solution
and : .
and : .
and : , .
Answer:
4 steps
Tip: Each vertex is where two boundary lines meet.
Where students lose marks on inequalities on graphs
Examiner's noteQuadratic inequalities: the final answer
Where marks are lost: Most factorise correctly but cannot write the final inequality (or write two separate conditions that contradict).
Examiners flagged this in 2 exam series (November 2024, June 2025). Summarised in our own words from Pearson Edexcel examiner reports. Read the full note →
Inequalities on Graphs exam-style questions
Try each question before you open the answer (one has its full worked solution open). 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 , including points on the line. Write down the inequality that describes the region.
Show the answer and mark scheme
B1 x ≤ 3
Answer:
Question 2 · easy · 1 mark
Does the point lie in the region ? Give a reason for your answer.
Show the answer and mark scheme
B1 No, since 2 × 2 + 1 = 5 and 5 is not greater than 5 (the point is on the boundary, which is not included)
Answer: No (it lies on the boundary line, which is not included)
Question 3 · easy · 2 marks
The region R is defined by , and . How many points with integer coordinates lie in R?
Show the answer and mark scheme
M1 lists at least 6 correct points or a correct count for one value of x
A1 10
Answer: 10
Question 4 · medium · 3 marks
Find the coordinates of the vertices of the region defined by , and .
Show the answer and mark scheme
B1 (0, 0)
B1 (8, 0)
B1 (4, 4)
Answer:
Question 5 · medium · 3 marks
A region is the triangle with vertices , and , including its edges. Write down the three inequalities that define the region.
Show the answer and mark scheme
B1 x ≥ 0
B1 y ≥ 0
B1 x + 2y ≤ 6 oe
Answer:
Question 6 · medium · 2 marks
The lines and form part of the boundary of a region. Find the coordinates of the point where they meet.
Full worked solution Free, no sign-in
M1 x + 2x = 6
A1 (2, 4)
Answer:
Every question here has a full worked solution.See them all →
Question 7 · hard · 3 marks
The region R is defined by , and . 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
Question 8 · hard · 3 marks
A region is the triangle with vertices , and , including its edges. Write down three inequalities that define the region.
Show the answer and mark scheme
B1 x ≥ 1
B1 y ≥ 1
B1 x + y ≤ 6
Answer:
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.
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.
Practise inequalities on graphs with your progress saved
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