Edexcel GCSE Maths

Topic Questions

GCSEMathsEdexcelTopic Questions2. AlgebraGraphing Inequalities

Graphing Inequalities

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1
Sme Calculator3 marks

q1-easy-2-22-graphing-inequalities-edexcel-gcse-maths

Write down inequalities to fully define the shaded region.

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2
Sme Calculator3 marks

Show, by shading on the grid, the region defined by all three of the inequalities

x space less-than or slanted equal to space 6 y space greater-than or slanted equal to space 2 y space less-than or slanted equal to space x space plus space 1

Label the region bold R

q7b-4ma1-2hr-qp-jan22-paper2-igcse-maths

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3
Sme Calculator3 marks

Show, by shading on the grid, the region that satisfies all three of the inequalities

x space less or equal than space 4 space space space space space space space and space space space space space space space space y space greater or equal than space – 2 space space space space space space space and space space space space space space space y space less or equal than space x

Label the region bold R bold.

q11-paper2hr-nov2020-edexcel-igcse-maths

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4
Sme Calculator2 marks

q10b-paper2h-june2019-edexcel-igcse-maths-1

The region bold R,  shown shaded in the diagram, is bounded by four straight lines.

Write down the inequalities that define bold R.

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5
Sme Calculator3 marks

The diagram shows two straight lines drawn on a grid.

q12-paper1h-june2018-edexcel-igcse-maths

Show, by shading on the grid, the region defined by all five of the inequalities

x space greater-than or slanted equal to space 0 y space greater-than or slanted equal to space 0 x space plus space y space greater-than or slanted equal to space 4 3 y space less-than or slanted equal to space 2 x space plus space 6 4 x space plus space 3 y space less-than or slanted equal to space 24

Label the region bold R.

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6
Sme Calculator1 mark

The sketch shows the lines x space equals space 1 and y space equals space – 3

q19-paper-3h-nov-2020-aqa-gcse-maths

Which pair of inequalities describes the shaded region?
Tick one box.

square x space less than space 1 space and space y space less than space – 3
square x space less than space 1 space and space y space greater than space – 3
size 28px square x space greater than space 1 space and space y space greater than space – 3
size 28px square x space greater than space 1 space and space y space less than space – 3

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7
Sme Calculator2 marks

Joe draws this graph to identify the region straight R represented by

y space less-than or slanted equal to space x space plus space 2    and    y space greater than space 3 space – space x    and    x space less than space 3

q23-paper3h-nov2017-aqa-gcse-maths

Make two criticisms of his graph.

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8
Sme Calculator2 marks

cie-igcse-2020-oct-nov-p2-tz1-q11

The diagram shows a rectangle with a line of symmetry at x space equals space 2.
Two vertices of the rectangle are at left parenthesis negative 1 comma space 1 right parenthesis and left parenthesis negative 1 comma space 4 right parenthesis.

The shaded region is defined by the inequalities a less or equal than space x less or equal than space b and c less or equal than space y less or equal than space d .
Find the values of a comma space b comma space c and d.


a space equals ................................................      

b space equals ................................................      

c space equals ................................................      

d space equals ................................................      

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9
Sme Calculator5 marks

cie-igcse-2019-may-jun-p2-tz3-q24

By shading the unwanted regions of the grid, draw and label the region R which satisfies the following three inequalities.

y less or equal than 2 x less than 3 y less or equal than x plus 4

 

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10
Sme Calculator3 marks

cie-igcse-2018-oct-nov-p2-tz2-q14
 

By shading the unwanted regions of the grid, find and label the region R that satisfies the following four inequalities.

x less or equal than 3 space space space space space space space space space space x greater or equal than 2 space space space space space space space space space space y less or equal than 2 x plus 1 space space space space space space space space space space y greater or equal than 4 minus x
 

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1a
Sme Calculator2 marks

Given that x and y are integers such that

3 less than x less than 7

4 less than y less than 9

and x plus y space equals space 13

find all the possible values of x.

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1b
Sme Calculator4 marks

On the grid below show, by shading, the region defined by the inequalities

y greater-than or slanted equal to negative 1 space space space space space space space space space space space space space space space space space space space space space space space space space space space space y less-than or slanted equal to 4 minus x space space space space space space space space space space space space space space space space space space space space space space space space y less-than or slanted equal to 3 x minus 1

Mark this region with the letter R.

q1-hard-2-22-graphing-inequalities-edexcel-gcse-maths

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2
Sme Calculator4 marks

On the grid, shade the region that satisfies all these inequalities.

x plus y space less than space 4 space space space space space space space space space space space space space space space space y greater than x minus 1 space space space space space space space space space space space space space space space space space space y less than 3 x


Label the region bold R.

q2-hard-2-22-graphing-inequalities-edexcel-gcse-maths

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3
Sme Calculator3 marks

On the grid, shade the region that satisfies all these inequalities.

y greater than 1 space space space space space space space space space space space space space space space space x plus y less than 5 space space space space space space space space space space space space space space space space space y greater than 2 x


Label the region bold R.

ycZkh2GP_q3-hard-2-22-graphing-inequalities-edexcel-gcse-maths

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4
Sme Calculator4 marks

On the grid show, by shading, the region that satisfies all three of the inequalities

x plus y less than 7 space space space space space space space space space space space space space space space space space space y less than 2 x space space space space space space space space space space space space y greater than 3

Label the region bold R.

q4-hard-2-22-graphing-inequalities-edexcel-gcse-maths

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5
Sme Calculator3 marks

The shaded region in the diagram is bounded by three lines.
The equation of one of the lines is given.

q13-4ma1-2h-qp-jan22-paper2-igcse-maths

Write down three inequalities that define the shaded region.

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6
Sme Calculator3 marks

q13-4ma1-2h-qp-nov21-paper2-igcse-maths

The region bold R, shown shaded in the diagram, is bounded by three straight lines.
Write down the three inequalities that define bold R.

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7
Sme Calculator3 marks

The shaded region in the diagram is bounded by three lines.
The equation of one of the lines is given.

q10-4ma1-1h-qp-jan20-paper1-igcse-maths

Write down the three inequalities that define the shaded region.

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8
Sme Calculator6 marks

Region R satisfies these inequalities.

table row y greater than 3 row y greater-than or slanted equal to x row cell x plus y end cell less-than or slanted equal to 9 end table

By drawing three straight lines on the grid, find and label the region R.

q18-paper4-june2019-ocr-gcse-maths

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9a
Sme Calculator4 marks

The diagram below shows a 1cm coordinate grid.

q18-paper6-nov2017-ocr-gcse-maths

Find an inequality that defines region A and another inequality that defines region B.

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9b
Sme Calculator2 marks

Shade the region on the grid given by the inequality begin mathsize 16px style y space greater-than or slanted equal to space 6. end style

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9c
Sme Calculator5 marks

A fourth shaded region, given by the inequality

y space greater-than or slanted equal to space k x space plus space 2 space comma

is added to the grid.

The unshaded region now has area 23cm2.

Find the value ofspace k.

k = ..............

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10a
Sme Calculator4 marks

cie-igcse-2018-may-jun-3-p4-q9b

Find the three inequalities that define the region R.

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10b
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Find the point left parenthesis x comma space y right parenthesis, with integer co-ordinates, inside the region R such that 3 x plus 5 y equals 35.

( .............. , .............. )

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1
Sme Calculator3 marks

The lines y space equals space x space long dash 2 and x space plus space y space equals space 10 are drawn on the grid.

q1-medium-2-22-graphing-inequalities-edexcel-gcse-maths

On the grid, mark with a cross (x) each of the points with integer coordinates that are in the region defined by

y greater than space x minus 2 x plus y less than 10 x greater than 3

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2
Sme Calculator4 marks

q2-medium-2-22-graphing-inequalities-edexcel-gcse-maths

Write down the three inequalities that define the shaded region.

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3
Sme Calculator3 marks

Show, by shading on the grid, the region defined by all three of the inequalities

   x less-than or slanted equal to space 5 y space greater-than or slanted equal to space 3 y space less or equal than space x

Label your region bold R.

q3-medium-2-22-graphing-inequalities-edexcel-gcse-maths

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4a
Sme Calculator3 marks

q4-4ma1-2h-qp-jan21-paper2-igcse-maths

On the grid, draw and label the straight line with equation

i)
   x equals 1.5
[1]
ii)
   y equals x
[1]
iii)
   x plus y equals 6
[1]

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4b
Sme Calculator1 mark

Show, by shading on the grid, the region that satisfies all three of the inequalities

x greater-than or slanted equal to 1.5             y greater-than or slanted equal to x      x plus y less-than or slanted equal to 6

 Label the region bold R.

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5
Sme Calculator3 marks

The diagram shows two straight lines drawn on a grid.

q12-paper1h-june2018-edexcel-igcse-maths

Show, by shading on the grid, the region defined by all five of the inequalities

x space greater-than or slanted equal to space 0 y space greater-than or slanted equal to space 0 x space plus space y space greater-than or slanted equal to space 4 3 y space less-than or slanted equal to space 2 x space plus space 6 4 x space plus space 3 y space less-than or slanted equal to space 24

Label the region bold R.

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6
Sme Calculator2 marks

The region bold R, shown shaded in the diagram, is bounded by three straight lines.

q11a-ma1-2hr-qp-jan20-paper2-igcse-maths

Write down the three inequalities that define the region bold R.

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7
Sme Calculator3 marks

On the grid, identify the region represented by

x space less-than or slanted equal to space 5      y space less-than or slanted equal to space 4 space      x space plus space y space greater than space 6

Label the region R.

q18-paper-2h-nov-2021-aqa-gcse-maths

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8
Sme Calculator6 marks

The graph of 3y + 6x = 13 is drawn on the grid.

q18-paper5-nov2019-ocr-gcse-maths

The region R satisfies these inequalities.

3 y plus 6 x greater-than or slanted equal to 13      begin mathsize 16px style y less-than or slanted equal to x minus 2 end style            x greater than 3

By drawing two more straight lines, find and label the region R.  

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9
Sme Calculator5 marks

The graphs of y equals x and y space equals negative 2 are drawn on the grid.

q17-paper5-nov2020-ocr-gcse-maths

The region R satisfies the following inequalities.

y greater-than or slanted equal to negative 2         y less-than or slanted equal to x         y less than 4 minus 2 x

By drawing one more line, find and label the region R.

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10
Sme Calculator5 marks

The diagram shows the lines y space equals 2 x plus 1 and 7 x space plus 4 y equals 28

q14-paper5-nov2018-ocr-gcse-maths

The region R satisfies these inequalities.

   y less-than or slanted equal to space 2 x plus 1         7 x space plus 4 y greater-than or slanted equal to 28      y greater than 1

By drawing a third straight line, find and label the region R that satisfies these inequalities.

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