Year 10 - Maths
Solving quadratic equations by factorising
Algebraic manipulation
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In algebraic manipulation, pupils use apply knowledge of the distributive law to find the product of two binomaials in order to factorise quadratics.
Lesson Summary
You will learn to solve quadratic equations algebraically by factorising.
Key Notes
- The graph of a quadratic equation can show if there are solutions when the equation is equal to zero.
- A quadratic might be the product of two binomial expressions.
- If you find the two binomial expressions then you can find the values for x
- The product is equal to zero, meaning that one of the two binomial expressions must equal zero.
- You can set each expression to zero to find the value for x
Vocabulary To Learn
- Factorise: To factorise is to express a term as the product of its factors.
- Solution (equality): A solution to an equality with one variable is a value for the variable which, when substituted, maintains the equality between the expressions.
- Parabola: A parabola is a curve where any point on the curve is an equal distance from: a fixed point (the focus ), and a fixed straight line (the directrix ).
Common Mistakes To Avoid
- That the solutions are just the constants in the binomials.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The graph of a quadratic equation can show if there are solutions when the equation is equal to zero. A quadratic might be the product of two binomial expressions.
2. Use this key word in a maths sentence and explain it clearly. 'Factorise'
To factorise is to express a term as the product of its factors. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: That the solutions are just the constants in the binomials. Correction: After factorising, pupils should be writing the one step equations, equal to zero, before writing the solutions.
More Lessons In This Unit
- Advanced problem solving with algebraic manipulation Study Guide
- Checking and securing understanding of changing the subject Study Guide
- Checking and securing understanding of expanding a single bracket Study Guide
- Checking and securing understanding of factorising Study Guide
- Checking and securing understanding of forming linear equations Study Guide
- Checking and securing understanding of simplifying Study Guide
- Checking and securing understanding of solving and interpreting linear equations Study Guide
- Checking and securing understanding of substitution Study Guide
- Checking and securing understanding of the product of two binomials Study Guide
- Factorising a quadratic expression Study Guide
- Factorising quadratics of the form ax^2 + bx + c Study Guide
- Factorising using the difference of two squares Study Guide
- Further algebraic terminology Study Guide
- Problem solving with algebraic manipulation Study Guide
- Solving complex quadratic equations by completing the square Study Guide
- Solving quadratic equations by completing the square Study Guide
- Solving quadratic equations by factorising where rearrangement is required Study Guide
- Solving quadratic equations by using the formula Study Guide
- The product of three binomials Study Guide
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