Year 10 - Maths
Checking and securing understanding of forming 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 use a letter to represent a generalised number and form a linear equation from a context.
Key Notes
- Quantities that change can be assigned a variable.
- If there is a relationship between these quantities, we can write this algebraically.
- With two quantities, the algebraic statement can form an equation.
Vocabulary To Learn
- Equation: An equation is used to show 2 expressions that are equal to each other.
- Interior angle: An interior angle is an angle formed inside a polygon by two of its edges.
- Vertically opposite angles: Vertically opposite angles are pairs of opposite angles formed when two lines intersect at a point. They are equal.
Common Mistakes To Avoid
- When forming expressions brackets can be missed out or incorrectly used.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Quantities that change can be assigned a variable. If there is a relationship between these quantities, we can write this algebraically.
2. Use this key word in a maths sentence and explain it clearly. 'Equation'
An equation is used to show 2 expressions that are equal to each other. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: When forming expressions brackets can be missed out or incorrectly used. Correction: Review priority of operations. Testing algebraic manipulations with numerical values can be useful when pupils are unsure if things are equivalent. E.g. the difference between 2(x + 4) and 2x + 4 can be shown with 2(5 + 4) and 2(5) + 4.
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 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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