Plug in and calculate
To evaluate an expression, you:
- Substitute: replace each variable with its value.
- Calculate, following the order of operations.
Example: Evaluate 4x + 7 when x = 3.
- 4(3) + 7
- 12 + 7 = 19
Use brackets when substituting
Put each substituted value in brackets. This keeps multiplication clear and avoids sign errors.
Example: 5a − 2b when a = 4 and b = −3
- 5(4) − 2(−3)
- 20 + 6 = 26
Without brackets, you might write 5 × 4 − 2 − 3 = 15. Wrong!
Exponents with negatives
Example: x² when x = −5
- (−5)² = 25 ✓
- Writing −5² gives −25 ✗
Example: −x² when x = 3 → −(3²) = −9
More examples
| Expression | Values | Work | Result |
|---|---|---|---|
| 3m − 8 | m = 2 | 3(2) − 8 | −2 |
| 2x² + 1 | x = 4 | 2(16) + 1 | 33 |
| (a + b)/2 | a = 7, b = 11 | 18/2 | 9 |
| 6 − 2y | y = −4 | 6 − 2(−4) | 14 |
| xy − y | x = 3, y = 5 | 15 − 5 | 10 |
Evaluating formulas
A formula is an expression set equal to a quantity.
Area of a triangle: A = ½bh. Find A when b = 10 cm and h = 7 cm.
A = ½(10)(7) = 35 cm².
Temperature: F = 1.8C + 32. Convert C = 25.
F = 1.8(25) + 32 = 45 + 32 = 77 °F.
Simple interest: I = Prt. P = $500, r = 0.04, t = 3.
I = 500(0.04)(3) = $60.
Making a table of values
Evaluating for several values builds a table:
| n | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| 2n + 3 | 5 | 7 | 9 | 11 |
Worked examples
Example 1: Evaluate 10 − 3k for k = 4.
10 − 12 = −2.
Example 2: Evaluate a² − 2a for a = −3.
9 − 2(−3) = 9 + 6 = 15.
Example 3: Evaluate (p + q)² for p = 2, q = 3.
5² = 25 (not 2² + 3² = 13).
Common mistakes
- Writing 3x with x = 4 as 34 instead of 3 × 4.
- Not using brackets for negative values.
- Ignoring order of operations after substituting.
Try it yourself
- 7y − 5 for y = 3
- 2a + 3b for a = −1, b = 4
- x² + x for x = −2
- P = 2(l + w) for l = 8, w = 5
- d = vt for v = 60 and t = 2.5
Answers: 1) 16 2) 10 3) 2 4) 26 5) 150
Quick recap
- Substitute, then evaluate using the order of operations.
- Put substituted values in brackets, especially negatives.
- Formulas are evaluated the same way.