Year 10 - Maths
Solving quadratic equations by factorising where rearrangement is required
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 where rearrangement is required.
Key Notes
- In order for factorising to be a valid method, the quadratic must equal zero.
- To achieve a product of zero, one of the binomial expressions evaluate to zero.
- Either expression could be zero so you must find the solution for each expression.
- If the quadratic were not equal to zero, you would have uncertainty about what each expression must equal.
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.
Common Mistakes To Avoid
- Pupils may try to factorise and solve without rearranging first.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
In order for factorising to be a valid method, the quadratic must equal zero. To achieve a product of zero, one of the binomial expressions evaluate to zero.
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: Pupils may try to factorise and solve without rearranging first. Correction: Being able to put the factors equal to zero only makes sense if we are using the property that if two values multiply to zero, one of them is zero.
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 Study Guide
- Solving quadratic equations by using the formula Study Guide
- The product of three binomials Study Guide
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