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 algebraically

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 in one variable graphically

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

The curve $$y=x^2+2x-15$$ has __________ at $$x=-5$$ and $$x=3$$.

The solution to $$2x^2-5x+20<x^2+8x-10$$ is $$3<x<$${{}}.

$$(x+8)(x-2)$$ is the quadratic $$x^2+6x-16$$ in __________ form.

Match the quadratics to their factorised form.

If $$x^2-7x-30=0$$ factorises to $$(x-10)(x+3)=0$$, where are its roots?

Which of the below is the quadratic formula?

This is a sketch of $$y=x^2-10x+24$$. Use it to solve this inequality: $$x^2-10x+24<0$$.

Which of these is a rearrangement of $$x^2-10x-87=0$$ when completing the square?

Solving quadratic inequalities algebraically

Lesson outcome