Year 11 - Maths
Solving quadratic inequalities in one variable graphically
Inequalities
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Study Guides
This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, pupils extend their understanding of inequalities and consider a range of contextual inequalities and ways to find and represent their solutions.
Lesson Summary
You will learn to solve a quadratic inequality graphically.
Key Notes
- A quadratic equation can be represented graphically
- The solutions are where the graph cross the x axis
- By studying the graph, you can see where the equation is greater than 0
- By studying the graph, you can see where the equation is less than 0
- The solution set can be represented algebraically or using set notation
Vocabulary To Learn
- 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 Mistakes To Avoid
- All inequalities are graphed with solid lines.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A quadratic equation can be represented graphically. The solutions are where the graph cross the x axis.
2. Use this key word in a maths sentence and explain it clearly. 'Inequality'
An inequality is used to show that one expression may not be equal to another. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: All inequalities are graphed with solid lines. Correction: 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.
More Lessons In This Unit
- A single solution set Study Guide
- Advanced problem solving with linear inequalities Study Guide
- Checking and securing understanding of simultaneous equations Study Guide
- Inequalities on number lines Study Guide
- Linear inequalities in context Study Guide
- Non-solutions to simultaneous linear equations Study Guide
- Problem solving with linear inequalities Study Guide
- Relating graphical solutions to algebraic solutions for inequalities Study Guide
- Solution set notation Study Guide
- Solving a linear inequality graphically Study Guide
- Solving a set of linear inequalities graphically Study Guide
- Solving more complicated linear inequalities Study Guide
- Solving quadratic inequalities algebraically Study Guide
- Solving simple linear inequalities Study Guide
Browse all guides in the Year 11 Maths guide library.