Notation, vocabulary and manipulation: •• use and interpret algebraic notation, including: •• ab in place of a × b •• 3y in place of y + y + y and 3× y •• a² in place of a × a, a³ in place of a × a × a, a²b in place of a × a × b •• a/b in place of a ÷ b •• coefficients written as fractions rather than as decimals •• brackets

The idea

Algebraic notation is a compact language: juxtaposition means multiplication, so ab means a × b and 3y means y + y + y or 3 × y. Indices record repeated multiplication: a² means a × a, a³ means a × a × a, and a²b means a × a × b. A fraction bar means division, so a/b means a ÷ b. Coefficients should be written as fractions rather than decimals, for example (1/2)x rather than 0.5x, and brackets group terms so the whole group is treated as one quantity.

What earns the marks

• Recognise that ab is the product a × b, not a + b.
• Interpret 3y as y + y + y and as 3 × y.
• Interpret a² as a × a, a³ as a × a × a and a²b as a × a × b.
• Interpret a/b as a ÷ b.
• Write coefficients as fractions rather than decimals, for example (1/2)x not 0.5x.
• Use brackets to group terms so the grouped quantity is treated as a single unit.

Common mistakes and how to put them right

• Reading ab as a + b.

  Put it right by treating juxtaposition as multiplication, so ab = a × b.

• Reading a² as a × 2.

  Put it right by treating the index as repeated multiplication, so a² = a × a.

• Writing a coefficient as a decimal such as 0.5x.

  Put it right by writing it as a fraction such as (1/2)x.

• Ignoring brackets and applying an operation to only part of a grouped expression.

  Put it right by treating the bracketed group as one quantity.

Exam tips

• Check indices by counting how many identical factors are multiplied, not by multiplying the base by the index.
• When a coefficient is a decimal, convert it to a fraction and compare with the options.