Representing inequalities graphicallyEdexcel International A Level Maths: Mind map

Exam questions on Representing inequalities graphically

1. A region $R$ of the $x$-$y$ plane contains all the points $(x,y)$ that satisfy both $y>x+1$ and $y\le5$.
   Find the coordinates of the point where the two boundary lines meet, and state, with a reason, whether this point belongs to $R$.2 marks
2. The region $S$ contains all the points $(x,y)$ that satisfy both $y\ge x^2-4$ and $y<2x-1$.
   Show that the point $(3,5)$ lies on the boundary of $S$ but is not in $S$.2 marks
3. The region $T$ contains all the points $(x,y)$ that satisfy both $y>x^2-2x-3$ and $y\le0$.
   Find the coordinates of the points where the curve $y=x^2-2x-3$ crosses the axes, and the coordinates of its minimum point.3 marks