Algebraic notation

Algebraic notation is precise written maths. WJEC awards method marks for correct notation even when the final answer is wrong — habits matter.

Multiplication conventions

• Numbers before letters: 3a not a3.
• Letters in alphabetical order: 3abc, not 3cba.
• Powers indicate repeated multiplication: a^3 = a × a × a.
• The × sign is omitted between a number and a letter, between two letters, and between a letter and a bracket: 3(x + 2), not 3 × (x + 2).
• Multiplying like letters: a × a = a^2; a × a × a × b = a^3 b.

Division

• Always written as a fraction: x ÷ 4 = x/4. Avoid the ÷ symbol in algebraic working.
• Reciprocal: 1/x can also be written x^{-1} (Higher).

Addition and subtraction — like terms

Like terms have identical letter parts (same variables, same powers).

• 3a + 5a = 8a (like terms)
• 3a + 5b cannot be simplified (unlike terms)
• 3a^2 + 5a is not simplifiable — different powers.

Substituting values

When substituting, write brackets around negative numbers:

• If a = -3, then a^2 = (-3)^2 = 9, not -9.
• If a = 2, b = -4, c = 5, then ab + c = (2)(-4) + 5 = -8 + 5 = -3.

Index laws (preview — fully covered in N7/A4)

• a^m × a^n = a^{m+n}
• a^m ÷ a^n = a^{m-n}
• (a^m)^n = a^{mn}

Identity vs equation

• An equation is true for specific values: 2x + 3 = 11 (only x = 4).
• An identity is true for all values: 2(x + 3) ≡ 2x + 6 (the ≡ symbol).

Exam tip

WJEC penalises sloppy notation. Writing "3 × x × x" instead of 3x^2 may lose A1 in a "simplify" question. Always tidy expressions to standard form before circling the answer.