Inverse operations
Every arithmetic operation has an inverse — the operation that "undoes" it. OCR J560 expects fluent use of inverses for checking answers, rearranging formulae, and solving equations across all six papers.
The four pairs
| Operation | Inverse |
|---|---|
| Addition (+) | Subtraction (−) |
| Subtraction (−) | Addition (+) |
| Multiplication (×) | Division (÷) |
| Division (÷) | Multiplication (×) |
| Squaring (x²) | Square root (√) |
| Cubing (x³) | Cube root (∛) |
| Power (xⁿ) | nth root |
Why inverses matter
1. Checking answers. If 17 + 28 = 45, then 45 − 28 should give 17. OCR Foundation Paper 1 routinely awards B1 for a verification step.
2. Solving equations. To solve 3x + 5 = 20, undo each operation in reverse:
- Subtract 5: 3x = 15
- Divide by 3: x = 5
3. Rearranging formulae. To make r the subject of A = πr²:
- Divide by π: A/π = r²
- Square root: r = √(A/π)
4. Function machines. Forward: x → ×3 → +5 → output. Reverse: output → −5 → ÷3 → x.
Order matters when undoing
Apply inverses in the reverse order of the original operations. If the forward order is "× 2 then + 7", the inverse is "− 7 then ÷ 2", not "÷ 2 then − 7".
Squaring and square-rooting
x² has TWO inverses: +√ and −√. So x² = 25 gives x = ±5 (both must be stated for full marks on Higher).
But √25 by convention denotes only the positive root: 5.
OCR mark scheme conventions
- M1 for setting up an inverse step (e.g. subtract 5 from both sides).
- A1 cao for the final value.
- "Show your working" is implicit — answers without working can lose method marks even if correct.
- For ± solutions, both roots must be given for full A1.
⚠Common mistakes
- Applying inverses in the wrong order.
- Forgetting the negative root after square-rooting.
- Using division as the inverse of subtraction (it's addition).
- Not "undoing" both sides of an equation symmetrically.
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