Algebraic notation
Algebraic notation is a shorthand language. OCR J560 expects fluency from the very first questions on Foundation Paper 1: ax, x², 2x + 3, etc., must all be read and written correctly.
Letters as numbers
A letter (variable) stands for an unknown or general number. We use letters because:
- The number is unknown (we want to find it).
- The number can vary (a formula valid for many values).
Conventions
- Multiplication is implied: 3x means 3 × x. We never write 3 × x in algebra.
- Coefficient first, letter second: write 3x, not x3.
- Letters in alphabetical order: write 4ab, not 4ba.
- Powers: x² means x × x; x³ means x × x × x.
- Division is written as a fraction: x/2 or x ÷ 2.
- 1 as coefficient is omitted: write x, not 1x. Write −x, not −1x.
Reading expressions
| Expression | What it means |
|---|---|
| 5x | 5 multiplied by x |
| x + 5 | 5 added to x |
| x − 5 | 5 subtracted from x |
| 5 − x | x subtracted from 5 (different from x − 5!) |
| x/5 | x divided by 5 |
| 5/x | 5 divided by x |
| x² | x squared (x × x) |
| 2x² | 2 × x × x (only x is squared, not the 2) |
| (2x)² | 4x² (the whole 2x is squared) |
The brackets matter enormously: 2x² ≠ (2x)².
Substitution
To substitute is to replace each letter with its value, then evaluate using BIDMAS.
Example: evaluate 3x² − 2x + 5 when x = 4.
- 3(4)² − 2(4) + 5
- = 3 × 16 − 8 + 5
- = 48 − 8 + 5 = 45
Negative numbers in substitution are a common source of error — always use brackets.
- x = −2 in x²: (−2)² = +4 (positive, since negative × negative = positive).
- x = −2 in −x²: −(−2)² = −4 (the squaring binds tighter than the negation).
Forming expressions from words
OCR loves "Write an expression for…" questions. Common phrases:
- "n more than": n + …
- "n less than": − n
- "n times": ×n
- "Twice n": 2n
- "n squared": n²
- "Sum of": +
- "Difference between": − (usually larger − smaller)
- "Product of": ×
OCR mark scheme conventions
- Most algebraic-notation questions are 1–2 marks. B1 for a correct expression, A1 for a correct value after substitution.
- "Show that" questions need every step visible — algebraic shortcuts that skip a line lose method marks.
- Equivalent algebraic forms are usually accepted (oe = "or equivalent") unless the question specifies a form.
⚠Common mistakes
- Writing 3 × x instead of 3x (loses style marks but usually no method).
- Forgetting brackets when substituting negatives.
- Misreading 2x² as (2x)².
- Adding instead of multiplying when "of" or coefficient is implied.
AI-generated · claude-opus-4-7 · v3-ocr-maths-leaves