Inequalities (Edexcel IGCSE Further Maths): Exam Questions

On the axes below, sketch the lines with equations $2 x + 3 y = 8$ and $2 y = 4 x + 1$

On your sketch, show the coordinates of the points where the lines cross the coordinate axes.

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

$2 x + 3 y \leq 8 2 y \leq 4 x + 1 y \geq 0 x \leq 2$

Find the set of values of $x$ for which $3+x<2x--1$

Find the set of values of $x$ for which $x(x--1)>6$

Find the set of values of $x$ for which $\mathrm{both}3+x<2x--1\mathrm{and}x(x--1)>6$

On the grid below, draw the line with equation

(i) $3x+4y=24$

(ii) $2x-5y+10=0$

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 $R$

The length of rectangle $R$is 2 cm greater than its width.

The area of $R$is greater than 8 cm² and the perimeter of $R$is less than 30 cm.

Given that the width of $R$is $w$ cm,

find the set of possible values of $w$ Give your answer in the form $a<w<b$ where $a$ and $b$are rational numbers.

On the grid opposite draw the line with equation

(i) $y=2x+5$

(ii) $4y=x-8$

(iii) $5y+3x=30$

Show, by shading, the region $R$defined 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

For all points in $R$ with coordinates $\left(x , y\right)$

$P=2x-5y$

Using your graph, find the least value of $P$

On the axes opposite, draw the line with equation

(i) $y=-x-1$

(ii) $y-3x+8=0$

(iii) $2y=x+8$

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

For all points in $R$, with coordinates $\left(x , y\right)$

$P=2y-3x$

Find

(i) the greatest value of $P$

(ii) the least value of $P$

Find the set of values of $x$ for which $2(3x-1)<4-3x$

Find the set of values of $x$ for which $3x^{2}-8x-3<0$

Find the set of values of $x$ for which both $2(3x-1)<4-3x$ and$3x^{2}-8x-3<0$