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 brackets 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 that assert the equality of two expressions. Example: 2x + 3 = 7 is an equation.
- Inequalities — expressions that show the relationship of one expression being greater or less than another. Example: x > 4 is an inequality.
- Terms — parts of an expression separated by plus or minus signs. Example: In 3x + 2, 3x and 2 are terms.
- Factors — numbers or expressions that multiply together to form another number or expression. Example: In 6x, 2 and 3x are factors.
- Simplifying Expressions — reducing expressions to their simplest form. Example: 2x + 3x simplifies to 5x.
- 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
- Brackets
- Substitution
- Expressions, equations, inequalities
- Terms and factors
Common Confusions
- Mixing up expressions and equations
- Forgetting to apply the distributive law correctly
- Misplacing terms when rearranging formulae
Typical Exam Questions
- What is the solution to the inequality x < 4? x can be any number less than 4.
- How do you simplify the expression 3x + 2x? Combine like terms to get 5x.
- How do you make y the subject in the equation m(y + n) = n(n - y)? y = (n^2 - mn) / (m + n)
What Examiners Usually Test
- Ability to interpret and use algebraic notation
- Skill in simplifying and manipulating expressions
- Understanding of solving equations and inequalities
- Competence in rearranging formulae to change the subject