Study Notes
In algebra, understanding notation, vocabulary, and manipulation is crucial for solving equations and inequalities. You will learn to interpret algebraic notation, use brackets, substitute values, and simplify expressions.
- 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 operations to be performed first. Example: In 2(x + 3), the expression inside the bracket is calculated first.
- Substitution — replacing variables with numerical values in expressions or equations. Example: If x = 2, then 3x becomes 3(2) = 6.
- Expressions — combinations of numbers, variables, and operations without an equality sign. Example: 4x + 5 is an expression.
- Equations — mathematical statements that assert the equality of two expressions. Example: 2x + 3 = 7 is an equation.
- Inequalities — statements about the relative size or order of two expressions. Example: x < 4 is an inequality.
- Factors — numbers or expressions that multiply together to form another number or expression. Example: Factors of 6 are 1, 2, 3, and 6.
- Simplify Expressions — reducing expressions to their simplest form. Example: 2x + 3x simplifies to 5x.
- Rearrange 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
- Brackets
- Substitution
- Expressions
- Equations
- Inequalities
- Factors
Common Confusions
- Mixing up expressions and equations
- Forgetting to apply operations inside brackets first
- Confusing the direction of inequality signs
Typical Exam Questions
- What is the value of 3x + 2 when x = 4? Substitute x = 4 to get 3(4) + 2 = 14
- Simplify the expression 2x + 3x - 4x. Combine like terms to get x
- Solve the inequality 2x - 3 > 5. Add 3 to both sides and divide by 2 to get x > 4
What Examiners Usually Test
- Ability to correctly use and interpret algebraic notation
- Skill in simplifying expressions and solving equations
- Understanding of how to rearrange formulae to change the subject