Revision notes, worked examples and methods for expressions and substitution.
Notes and quizzes ready · 50 questions · Revision video ready.
Foundation shows shared notes and questions. Higher includes the shared content and labelled Higher extensions. Changing tier starts the notes and a new quiz set.
Revise the key ideas
Algebraic language
A variable represents a number that may be unknown or change. In 5x + 3, 5 is the coefficient of x, 3 is a constant, and 5x and 3 are terms.
An expression has no equality sign; an equation states two expressions are equal; a formula relates quantities; an inequality compares values; an identity is true for all allowed variable values.
Write a × b as ab, y + y + y as 3y, and a × a as a2. 2x means 2 × x, not a two-digit number.
Like terms have the same variable part and powers: 4x + 3x − 2 = 7x − 2. Terms such as x and x2 are not like terms.
Worked example: 3a + 4b − a + 2b = 2a + 6b. Keep the sign with each term when collecting.
Multiplication uses coefficient and index rules: 3x × 4x2 = 12x3. Addition is different: 3x + 4x2 cannot be simplified to 7x3.
Substitution and function machines
Substitution replaces each variable with its given value. Put negative values in brackets before powers or multiplication.
Worked example: If x = −2 and y = 3, then 2x2 − 3y = 2(−2)2 − 3(3) = 8 − 9 = −1.
Worked example: For v = u + at, with u = 5 m/s, a = 2 m/s2 and t = 4 s, v = 5 + 2 × 4 = 13 m/s. Include units and follow the order of operations.
In a function machine, an input undergoes a fixed sequence of operations. Input x, multiply by 3 then add 2 gives output 3x + 2. A two-step function machine
To recover the input, undo the operations in reverse order: output 17 gives (17 − 2) ÷ 3 = 5. Subtracting after division would undo the wrong sequence.
Translating words
Five less than twice a number is 2x − 5. Five minus twice a number is 5 − 2x. Read the wording carefully before writing symbols.
If one ticket costs £p, four tickets cost £4p. If a total charge includes a fixed £3 fee, the formula is C = 4p + 3, not 4(p + 3).
Evaluate and simplify are different instructions. Simplify keeps variables; evaluate finds a numerical value after substitution. Check a simplification by testing a sensible value, although one matching value alone is not a proof.
Test yourself
50 questions · Sets of 10 from the selected tier. For fractions, use / when typing; for powers, use superscripts or ^. Follow each question's answer format. These quick checks support revision; practise full written solutions and proofs too.
Watch M7 · Expressions and substitution
Revise expressions and substitution with this narrated video. Use the player controls to pause, seek, adjust the volume or mute. Turn English captions on or off using the captions menu.
Mr Kidman's Classroom
