Inequalities (Edexcel IGCSE Further Pure Maths): Exam Questions

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 $\mathbf{both}3+x<2x–1\mathbf{and}x(x–1)>6$

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

$3x+4y⩽242x-5y+10⩾0y⩽5x⩾-1$

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

$y⩽2x+54y⩾x-85y+3x⩽30$

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

$y⩾-x-1$ and $y⩾3x-8$ and $2y⩽x+8$

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 $3x^2-8x-3<0$