Study Notes
Substitution involves replacing letters with numbers to find the value of an expression, ensuring the correct order of operations is applied.
- Substitution — replacing variables in an expression with given numbers. Example: Find the value of 3m - 5 when m = 6: 3 x 6 - 5 = 18 - 5 = 13.
- Order of Operations — the sequence in which operations are performed in a mathematical expression. Example: Evaluate 2x² + 3x + 8 when x = 4: (2 x 4 x 4) + (3 x 4) + 8 = 32 + 12 + 8 = 52.
Exam Tips
Key Definitions to Remember
- Substitution: Replacing variables with numbers in an expression.
- Order of Operations: The rules that define the correct sequence to evaluate a mathematical expression.
Common Confusions
- Forgetting to apply the correct order of operations (BODMAS/BIDMAS).
- Mixing up which numbers to substitute for which variables.
Typical Exam Questions
- What is the value of 3m - 5 when m = 6? 13
- Evaluate 3x + 4y when x = 10 and y = 2. 38
- Find the perimeter of a rectangle with length 12 cm and breadth 9 cm using P = 2(l + b). 42 cm
What Examiners Usually Test
- Correct substitution of numbers into expressions.
- Application of the order of operations after substitution.
- Ability to solve problems involving substitution in formulas.