Summary
In algebra, understanding notation, vocabulary, and manipulation is crucial for solving equations and inequalities. This includes interpreting algebraic notation, using brackets, substitution, and rearranging formulae.
- Algebraic Notation — symbols and letters used to represent numbers and operations. Example: In 3x + 2, 'x' is a variable.
- Brackets — used to group terms and indicate the order of operations. Example: In 2(x + 3), the expression inside the bracket is calculated first.
- Substitution — replacing variables with numerical values. Example: If x = 2, then 3x becomes 3(2) = 6.
- Expressions — combinations of terms without an equality sign. Example: 4x + 5 is an expression.
- Equations — mathematical statements showing equality between two expressions. Example: 2x + 3 = 7 is an equation.
- Inequalities — expressions that use signs like >, <, ≥, and ≤ to show the relationship between expressions. Example: x < 4 is an inequality.
- Rearranging Formulae — changing the subject of a formula. Example: From y = mx + c to x = (y - c) / m.
Exam Tips
Key Definitions to Remember
- Algebraic notation: symbols and letters representing numbers.
- Brackets: used to group terms.
- Substitution: replacing variables with numbers.
Common Confusions
- Mixing up expressions and equations.
- Forgetting to apply operations inside brackets first.
Typical Exam Questions
- What is the value of 3x + 2 when x = 4? Answer: 14
- Solve the inequality 2x - 3 > 5. Answer: x > 4
- Rearrange the formula y = 3x + 2 to make x the subject. Answer: x = (y - 2) / 3
What Examiners Usually Test
- Ability to interpret and use algebraic notation.
- Skill in rearranging formulae to change the subject.
- Understanding of solving linear equations and inequalities.