Algebra - Solving equations and inequalities: translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution

The idea

Translate worded problems into algebra. This can mean creating an expression (e.g. the cost of 3 pens at x pence each is 3x), a formula from a procedure (e.g. a taxi fare F for m miles at £2 per mile plus a £1.50 fixed charge is F = 1.5 + 2m), or an equation by setting two expressions equal. For an equation, define your unknown (e.g. 'let c be the cost of a coffee in pounds'). Write other quantities in terms of it. If two facts relate two unknowns, derive a pair of simultaneous equations. After solving, always reread the question. It might ask for a derived value, like a total cost, not just your variable. Finally, check your answer makes sense in the context and state units clearly.

What earns the marks

• Deriving a correct formula from a described procedure, with all variables clearly defined.
• Forming a correct expression, equation, or pair of simultaneous equations from the information given.
• Solving the derived equation(s) correctly, with marks available for method even if the set-up was flawed.
• Interpreting the solution back in the original context, with correct units and sensible rounding.

Common mistakes and how to put them right

• Confusing the fixed and variable parts when creating a formula, for example swapping a standing charge with a per-unit cost.

• Mixing units within an equation, such as pounds on one side and pence on the other, without conversion.

• Solving correctly but giving the value of the variable (e.g. x) when the question asked for a related quantity (e.g. 2x + 5).

Exam tips

• When creating a formula, identify what changes (the variable) and what stays the same (the constant or fixed charge).
• Before writing an equation, state what your letter stands for and its units (e.g., 'let t be the time in hours').
• After solving, reread the last line of the question to ensure you are answering what was actually asked.