Study Notes
Algebraic expressions are combinations of variables and constants using operations like addition and subtraction. Algebraic equations set two expressions equal to each other, while algebraic formulae use letters to represent variable amounts. Algebraic functions involve only algebraic operations.
- Algebraic Expression — a combination of variables and constants using operations. Example: 3x + 2
- Algebraic Equation — a statement where two expressions are equal. Example: 2x + 3 = 7
- Algebraic Formula — a rule using letters to represent variable amounts. Example: A = πr²
- Algebraic Function — a function involving only algebraic operations. Example: f(x) = x² + 3x + 2
- Commutative Rule of Addition — the order of addition does not matter. Example: a + b = b + a
- Commutative Rule of Multiplication — the order of multiplication does not matter. Example: a × b = b × a
- Associative Rule of Addition — the grouping of addition does not matter. Example: a + (b + c) = (a + b) + c
- Associative Rule of Multiplication — the grouping of multiplication does not matter. Example: a × (b × c) = (a × b) × c
- Distributive Rule of Multiplication — multiplication distributed over addition. Example: a × (b + c) = (a × b) + (a × c)
Exam Tips
Key Definitions to Remember
- Algebraic Expression: combination of variables and constants using operations
- Algebraic Equation: statement where two expressions are equal
- Commutative Rule: order of addition or multiplication does not matter
- Associative Rule: grouping of addition or multiplication does not matter
- Distributive Rule: multiplication distributed over addition
Common Confusions
- Mixing up expressions and equations
- Forgetting to apply the distributive rule correctly
Typical Exam Questions
- What is an algebraic expression? An expression combining variables and constants using operations.
- Solve the equation 2x + 3 = 7. x = 2
- Apply the distributive rule to simplify x(2 + 3). 2x + 3x = 5x
What Examiners Usually Test
- Understanding and application of algebraic rules
- Ability to simplify expressions and solve equations
- Correct use of algebraic operations and rules