Year 10 - Maths
Advanced problem solving with algebraic manipulation
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 use your knowledge of algebraic manipulation to solve problems.
Key Notes
- Quadratic equations can model real-life situations.
- Solutions would need to be interpreted in context.
- The difference of two squares is not only used in algebra, but can be used to quickly calculate numerical expressions.
- Where there is a choice of method, you will decide the most efficient method to use.
Vocabulary To Learn
- Partial product: A partial product refers to any of the multiplication results that lead up to an overall multiplication result.
- Binomial: A binomial is an algebraic expression representing the sum or difference of exactly two unlike terms.
- 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
- Including solutions which are not valid in the context of the question.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Quadratic equations can model real-life situations. Solutions would need to be interpreted in context.
2. Use this key word in a maths sentence and explain it clearly. 'Partial product'
A partial product refers to any of the multiplication results that lead up to an overall multiplication result. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Including solutions which are not valid in the context of the question. Correction: Pupils should finish every problem by substituting their solutions back into the original problem. This will help them check their answers but also make them think about whether their solutions are valid in context.
More Lessons In This Unit
- 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 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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