An inequality is used to show that one expression may not be equal to another.

A quadratic is an equation, graph or sequence where the highest exponent of the variable is 2. The general form for a quadratic is ax^2 + bx + c

Solving quadratic inequalities in one variable graphically

Maths

Checking and securing understanding of simultaneous equations

Non-solutions to simultaneous linear equations

Inequalities on number lines

Solving simple linear inequalities

Solving more complicated linear inequalities

Linear inequalities in context

A single solution set

Solution set notation

Solving a linear inequality graphically

Solving a set of linear inequalities graphically

Relating graphical solutions to algebraic solutions for inequalities

Solving quadratic inequalities algebraically

Advanced problem solving with linear inequalities

In this unit, pupils will learn how to extend their understanding of solving equations and extend this to consider inequalities. Pupils will consider a variety of inequalities and ways that their solutions can be represented.

In this unit, pupils extend their understanding of inequalities and consider a range of contextual inequalities and ways to find and represent their solutions.

Inequalities

$$-5<x<5$$ is the __________ the quadratic inequality $$x^2-25<0$$.

This is the curve $$y=x^2-9$$ Use the graph to solve $$x^2-9<0$$.

This is the curve $$y=x^2-9$$. Use the graph to solve $$x^2-9>0$$.

This is the curve $$y=x^2-9$$. Use the graph to solve $$x^2-9<-9$$.

This is the curve $$y=x^2-4x+4$$. The solution to the inequality $$1<x^2-4x+4<4$$ is $$0<x<1$$ or {{}}.

Rearrange and sketch to solve $$100-x^2<64$$.

When graphed, a quadratic equation forms...

This could be the sketch of which one of these quadratics?

What is the minimum value of this quadratic?

The solution to $$2x^2-14=x^2-3x+14$$ is $$x=4$$ and $$x=$${{}}.

Solving quadratic inequalities in one variable graphically

Lesson outcome