Edexcel IGCSE 4MA1 Inequalities on Graphs: Exam Questions and Answers

The region R is given by $x\ge 0$, $y\ge 1$ and $2x+y\le 6$. Find its vertices and decide whether $(2,2)$ is in R.

Find the vertices of the region $y\le 3$, $y\ge x-1$, $x+y\ge 1$.

A region on a coordinate grid lies to the left of the line $x=3$, including points on the line. Write down the inequality that describes the region.

Does the point $(2,5)$ lie in the region $y>2x+1$? Give a reason for your answer.

The region R is defined by $x\ge 1$, $y\ge 2$ and $x+y\le 6$. How many points with integer coordinates lie in R?

Find the coordinates of the vertices of the region defined by $y\ge 0$, $y\le x$ and $x+y\le 8$.

A region is the triangle with vertices $(0,0)$, $(6,0)$ and $(0,3)$, including its edges. Write down the three inequalities that define the region.

The region R is defined by $y\ge 1$, $y\le 2x$ and $x+y<7$. Find the number of points with integer coordinates in R.

A region is the triangle with vertices $(1,1)$, $(5,1)$ and $(1,5)$, including its edges. Write down three inequalities that define the region.