Evaluating Expressions – Substitution Method
Evaluating an expression means finding its numerical value by substituting given values in place of the variables.
How to Evaluate
- Write down the expression.
- Replace each variable with its given value.
- Follow BODMAS/PEMDAS to calculate.
Worked Examples
Easy: Evaluate 3x + 5 when x = 4
3(4) + 5 = 12 + 5 = 17
Medium: Evaluate 2a² − 3b when a = 3, b = 2
2(3)² − 3(2) = 2(9) − 6 = 18 − 6 = 12
Advanced: Evaluate (x + y)/(x − y) when x = 7, y = 3
(7 + 3)/(7 − 3) = 10/4 = 2.5
Negative Substitution
Evaluate x² − 4x + 3 when x = −2: (−2)² − 4(−2) + 3 = 4 + 8 + 3 = 15
Key Takeaways
- Replace each variable with its value before calculating.
- Use brackets when substituting negative values: −2² ≠ (−2)².
- Follow order of operations after substituting.
Practice Questions
- Evaluate 4x − 7 when x = 5.
- Evaluate a + 2b when a = 3, b = 4.
- Evaluate m² + n when m = 5, n = 8.
- Evaluate 3(p + q) − 2p when p = 4, q = 2.
- Evaluate 2x² − x − 6 when x = −1.