Representing inequalities graphicallyEdexcel International A Level Maths: Flashcards

What these 12 flashcards ask

On a sketch, which kind of line goes with < or ?
Which kind of line goes with \le or \ge?
Which side of y=x+r is yx+r?
Which side of x=a is xa?
Which side of the curve is yx^2+bx+c?
How do you check you have shaded the correct side?
What is the boundary of an inequality?
What shape is the graph of y=ax^2+bx+c for a0?
How do you find the turning point of y=x^2-2x-3 without calculus?
How do you find where a line and a curve boundary meet?
Is the point where a solid and a dotted boundary meet in the region?
The region y\le5 and yx+1: which line is solid?

Exam questions on Representing inequalities graphically

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).