Graphing Inequalities (AQA GCSE Maths: Higher): Exam Questions

The lines $y=x—2$ and $x+y=10$   are drawn on the grid.

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

$$\begin{gathered} y>x-2 \\ x+y<10 \\ x>3 \end{gathered}$$

Write down the three inequalities that define the shaded region.

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

   $$\begin{gathered} x⩽5 \\ y⩾3 \\ y\le x \end{gathered}$$

Label your region $\mathbf{R}$.

On the grid, identify the region represented by

$x⩽5$      $y⩽4$      $x+y>6$

Label the region R.

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

i)   $x=1.5$

ii)   $y=x$

iii)   $x+y=6$

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

$x⩾1.5$             $y⩾x$      $x+y⩽6$

 Label the region $\mathbf{R}$.

The diagram shows two straight lines drawn on a grid.

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

Label the region $\mathbf{R}$.

The region $\mathbf{R}$, shown shaded in the diagram, is bounded by three straight lines.

Write down the three inequalities that define the region $\mathbf{R}$.

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

The region R satisfies these inequalities.

$3y+6x⩾13$      $y⩽x-2$            $x>3$

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

The graphs of $y=x$ and $y=-2$ are drawn on the grid.

The region R satisfies the following inequalities.

$y⩾-2$         $y⩽x$         $y<4-2x$

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

The diagram shows the lines $y=2x+1$ and $7x+4y=28$

The region R satisfies these inequalities.

   $y⩽2x+1$         $7x+4y⩾28$      $y>1$

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

On the grid below, indicate the region $\mathrm{R}$ that satisfies the following inequalities:

$y\ge 4x<6y<x$

Given that $x$ and $y$ are integers such that

$3<x<7$

$4<y<9$

and $x+y=13$

find all the possible values of $x$.

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

$y⩾-1y⩽4-xy⩽3x-1$

Mark this region with the letter $R$.

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

$x+y<4y>x-1y<3x$

Label the region $\mathbf{R}$.

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

$y>1x+y<5y>2x$

Label the region $\mathbf{R}$.

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

$x+y<7y<2xy>3$

Label the region $\mathbf{R}$.

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

Write down three inequalities that define the shaded region.

The region $\mathbf{R}$, shown shaded in the diagram, is bounded by three straight lines. Write down the three inequalities that define $\mathbf{R}$.

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

Write down the three inequalities that define the shaded region.

Region R satisfies these inequalities.

$\begin{array}{rcl}y& >& 3\\ y& ⩾& x\\ x+y& ⩽& 9\end{array}$

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

The diagram below shows a 1cm coordinate grid.

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

Shade the region on the grid given by the inequality $y⩾6.$

A fourth shaded region, given by the inequality

$y⩾kx+2,$

is added to the grid.

The unshaded region now has area 23cm².

Find the value of$k$.

$k$ = .............

Find the three inequalities that define the region $R$.

Find the point $(x,y)$, with integer co-ordinates, inside the region $R$ such that $3x+5y=35$.

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