EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Representing inequalities graphically
Representing inequalities graphically · Equations and graphs · Lesson 2 of 6 · 16 marks · 25 minutes
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Instructions
• Answer all the questions.
• Write your answers in the spaces provided.
• The marks for each question are shown in brackets - use this as a guide to how much to write.
• The answers are on separate pages at the back. Attempt every question before you look at them.
• Answer all questions. Show your working.
Question 1 WRITE DOWN (3 marks)
The region R is shown shaded on the grid. Write down the three inequalities that define R.
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(Total for Question 1 = 3 marks)
Question 2 WRITE DOWN (3 marks)
x and y are integers with x ≥ 1, y ≥ 1 and x + y ≤ 4. Write down all the possible pairs (x, y).
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(Total for Question 2 = 3 marks)
Question 3 WRITE DOWN (3 marks)
A region on a grid is bounded by the lines x = 1, y = 1 and x + y = 6, and lies above y = 1, to the right of x = 1 and below x + y = 6. Write down the three inequalities that define the region.
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(Total for Question 3 = 3 marks)
Question 4 EXPLAIN (2 marks)
Explain when you would draw a dashed line rather than a solid line for the boundary of an inequality.
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(Total for Question 4 = 2 marks)
Question 5 DECIDE (2 marks)
Is the point (2, 3) in the region y > 2x − 1? Give a reason.
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(Total for Question 5 = 2 marks)
Question 6 SHADE (3 marks)
On a grid, show by shading the region defined by x ≥ 2, y < 3 and y ≥ 0. Describe the shape you have shaded.
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(Total for Question 6 = 3 marks)
TOTAL FOR PAPER = 16 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (3 marks)
y ≥ 1, x ≤ 4, y ≤ x
• One correct inequality B1
• Two correct B1
• All three correct B1
Question 2 (3 marks)
(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)
• At least 3 correct pairs and none wrong M1
• 5 correct A1
• All 6 correct A1
Question 3 (3 marks)
x ≥ 1, y ≥ 1, x + y ≤ 6
• One correct B1
• Two correct B1
• All three B1
Question 4 (2 marks)
Use a dashed line for < or >, because points on the line are not included in the region. Use a solid line for ≤ or ≥.
• Dashed for < or > M1
• Points on the line not included C1
Question 5 (2 marks)
No. When x = 2, 2x − 1 = 3, and 3 > 3 is false, so the point is on the boundary, which is not included.
• Substitutes M1
• No, with reason A1
Question 6 (3 marks)
A rectangular strip: the region to the right of the line x = 2 (solid), below the dashed line y = 3 and above the x-axis (solid line y = 0).
• x = 2 solid B1
• y = 3 dashed B1
• Correct region B1