IGCSEFurther MathsEdexcelExam QuestionsEquations, Identities & InequalitiesInequalities

Inequalities (Edexcel IGCSE Further Pure Maths): Exam Questions

Exam code: 4PM1

31 mins7 questions
1
2 marks

On the axes below, sketch the lines with equations 2 x space plus space 3 y space equals space 8 and 2 y space equals space 4 x space plus space 1 space

Cartesian coordinate system with horizontal x-axis and vertical y-axis meeting at origin marked as O. Arrows indicate positive directions.

Show, by shading on your sketch, the region R defined by the inequalities

2 x space plus space 3 y space less-than or slanted equal to space 8 space space space space space space 2 y space less-than or slanted equal to space 4 x space plus space 1 space space space space y space greater-than or slanted equal to space 0 space space space space x space less-than or slanted equal to space 2

How did you do?

2a
1 mark

Find the set of values of x for which 3 space plus space x space less than space 2 x space – space 1

How did you do?

2b
3 marks

Find the set of values of x for which x left parenthesis x space – space 1 right parenthesis space greater than space 6

How did you do?

2c
1 mark

Find the set of values of x for which bold both space 3 space plus space x space less than space 2 x space – space 1 space bold and space x left parenthesis x space – space 1 right parenthesis space greater than space 6

How did you do?

3
2 marks

Show, by shading on the grid, the region R defined by the inequalities

3 x space plus space 4 y space less-than or slanted equal to space 24 space space space space space 2 x space minus space 5 y space plus 10 space greater-than or slanted equal to space 0 space space space space y space less-than or slanted equal to space 5 space space space space space x space greater-than or slanted equal to space minus 1

Label the region R

A Cartesian grid with x-axis labelled -7 to 9 and y-axis -3 to 8. Axes intersect at origin (0,0). Gridlines form squares in all quadrants.

How did you do?

4
6 marks

The length of rectangle Ris 2 cm greater than its width.

The area of Ris greater than 8 cm2 and the perimeter of Ris less than 30 cm.

Given that the width of Ris w cm,

find the set of possible values of w
Give your answer in the form a less than w less than b where a and bare rational numbers.

How did you do?

5a
1 mark

Show, by shading, the region Rdefined by the inequalities

y less-than or slanted equal to 2 x plus 5      4 y greater-than or slanted equal to x minus 8      5 y plus 3 x less-than or slanted equal to 30

Graph with x-axis from -5 to 11 and y-axis from -5 to 10, both marked at intervals of 1. Grid lines fill the entire graph area.

How did you do?

5b
3 marks

For all points in R with coordinates open parentheses x comma space y close parentheses

P equals 2 x minus 5 y

Using your graph, find the least value of P

Cartesian graph with x-axis from -5 to 11 and y-axis from -5 to 10, marked with gridlines, showing both positive and negative number ranges.

How did you do?

6a
1 mark

Show, by shading on your graph, the region R defined by the inequalities

y greater-than or slanted equal to negative x minus 1 and y greater-than or slanted equal to 3 x minus 8 and 2 y less-than or slanted equal to x plus 8

Graph with x-axis from -6 to 6 and y-axis from -4 to 8, grids marked at each unit. Origin is labelled O, and axes have arrows.

How did you do?

6b
4 marks

For all points in R, with coordinates open parentheses x comma space y close parentheses

P equals 2 y minus 3 x

Find

(i) the greatest value of P

(ii) the least value of P

How did you do?

7a
2 marks

Find the set of values of x for which 2 left parenthesis 3 x space minus space 1 right parenthesis space less than space 4 space minus space 3 x

How did you do?

7b
4 marks

Find the set of values of x for which 3 x squared minus 8 x minus 3 less than 0

How did you do?

7c
1 mark

Find the set of values of x for which both 2 left parenthesis 3 x space minus space 1 right parenthesis space less than space 4 space minus space 3 x and 3 x squared minus 8 x minus 3 less than 0

How did you do?