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Year 11
Higher

Solving quadratic inequalities algebraically

I can solve a quadratic inequality algebraically.

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New
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Year 11
Higher

Solving quadratic inequalities algebraically

I can solve a quadratic inequality algebraically.

Download all resources
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Share activities with pupils
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These resources will be removed by end of Summer Term 2025.

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Lesson details

Key learning points

  1. The solutions to the quadratic equation can be found using one of your known methods
  2. By sketching the graph, it is easy to define the solution set
  3. By studying the features of the quadratic, it is easy to define the solution set

Keywords

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

  • Quadratic - 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

Common misconception

All inequalities are graphed with solid lines.

When graphed, strict inequalities are indicated with a dashed line. This is important as it visually tells us that values on the line will not satisfy the inequality.


To help you plan your year 11 maths lesson on: Solving quadratic inequalities algebraically, download all teaching resources for free and adapt to suit your pupils' needs...

Encourage pupils to identify the region that satisfies multiple inequalities in different ways: graphically, testing a point, algebraically.
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This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
$$(x+8)(x-2)$$ is the quadratic $$x^2+6x-16$$ in __________ form.
Correct answer: factorised
solution
expression
equation
inequality
Q2.
Match the quadratics to their factorised form.
Correct Answer:$$x^2+15x+54$$,$$(x+9)(x+6)$$
tick

$$(x+9)(x+6)$$

Correct Answer:$$x^2+3x-54$$,$$(x+9)(x-6)$$
tick

$$(x+9)(x-6)$$

Correct Answer:$$x^2-3x-54$$,$$(x-9)(x+6)$$
tick

$$(x-9)(x+6)$$

Correct Answer:$$x^2-15x+54$$,$$(x-9)(x-6)$$
tick

$$(x-9)(x-6)$$

Correct Answer:$$2x^2+24x+54$$,$$(x+9)(2x+6)$$
tick

$$(x+9)(2x+6)$$

Correct Answer:$$2x^2+21x+54$$,$$(2x+9)(x+6)$$
tick

$$(2x+9)(x+6)$$

Q3.
If $$x^2-7x-30=0$$ factorises to $$(x-10)(x+3)=0$$, where are its roots?
Correct answer: $$x=10$$
$$x=-10$$
$$x=3$$
Correct answer: $$x=-3$$
$$x=-30$$
Q4.
Which of the below is the quadratic formula?
Correct answer: $$x={{-b\pm{\sqrt{b^2-4ac}}}\over{2a}}$$
$$x={{b\pm{\sqrt{b^2-4ac}}}\over{2a}}$$
$$x=-b\pm{{\sqrt{b^2-4ac}}\over{2a}}$$
$$x=-b+{{\sqrt{b^2-4ac}}\over{2a}}$$
$$x={{-b+{\sqrt{b^2-4ac}}}\over{2a}}$$
Q5.
This is a sketch of $$y=x^2-10x+24$$. Use it to solve this inequality: $$x^2-10x+24<0$$.
An image in a quiz
$$x<6$$
Correct answer: $$4<x<6$$
$$10<x<24$$
$$x<4$$ or $$x>6$$
$$x>4$$ or $$x>6$$
Q6.
Which of these is a rearrangement of $$x^2-10x-87=0$$ when completing the square?
$$(x-5)^2=87$$
$$(x-5)^2=-87$$
$$(x-5)^2=62$$
$$(x-5)^2=-112$$
Correct answer: $$(x-5)^2=112$$

Exit quiz

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6 Questions

Q1.
The curve $$y=x^2+2x-15$$ has __________ at $$x=-5$$ and $$x=3$$.
solutions
equations
Correct answer: roots
turning points
Q2.
Solve $$x^2+2x-15<0$$.
$$x<3$$
$$x<-5$$
Correct answer: $$-5<x<3$$
$$x<-5$$ and $$x>3$$
There is no solution to this inequality.
Q3.
Solve $$x^2+2x-15>0$$.
$$x>0$$
Correct answer: $$x<-5$$ or $$x>3$$
$$-5<x<3$$
$$x<-5$$ or $$x<3$$
There is no solution to this inequality.
Q4.
Solve $$x^2-9<16$$.
Correct answer: $$-5<x<5$$
$$x<-5$$ and $$x>5$$
$$-3<x<3$$
$$x<-3$$ and $$x>3$$
There is no solution to this inequality.
Q5.
Solve $$-x^2-2x+15>0$$.
$$x<-5$$ and $$x>3$$
$$x<-3$$ and $$x>5$$
$$x>-5$$ and $$x>3$$
Correct answer: $$-5<x<3$$
$$-3<x<5$$
Q6.
The solution to $$2x^2-5x+20<x^2+8x-10$$ is $$3<x<$$ .
Correct Answer: 10