Year 10 - Maths
Checking and securing understanding of solving and interpreting linear equations
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 complex linear equations involving brackets.
Key Notes
- With linear equation involving brackets, there are two methods for addressing the brackets.
- You can expand the bracket (multiply out).
- You can divide each term.
- If there is a common factor across all terms, then division may be best.
Vocabulary To Learn
- Additive inverse: The additive inverse of a number is a number that, when added to the original number, gives the sum of 0.
- Reciprocal: The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1
- Like terms: Like terms are terms that have the same set of variables and corresponding exponents.
Common Mistakes To Avoid
- If a linear equation involves brackets, these always have to be expanded first.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
With linear equation involving brackets, there are two methods for addressing the brackets. You can expand the bracket (multiply out).
2. Use this key word in a maths sentence and explain it clearly. 'Additive inverse'
The additive inverse of a number is a number that, when added to the original number, gives the sum of 0. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: If a linear equation involves brackets, these always have to be expanded first. Correction: Get pupils to use knowledge of factors and collecting like terms to simplify problems.
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 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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