Formulae, equations and rearranging — AQA GCSE Maths revision

Solving linear equations

• Keep the equation balanced: whatever you do to one side, do to the other.
• Collect like terms first, then move terms across the equals sign, then divide.
• Solutions can be negative or fractional — don't assume a 'nice' whole number.

Rearranging formulae (changing the subject)

• Treat the subject like the unknown in an equation — isolate it using inverse operations.
• If the subject appears twice, collect those terms and factorise before dividing.
• Square/square-root carefully: to undo x^2, take the square root of both sides (± if needed for pure algebra, but often only positive makes physical sense).

Key terms

Subject of a formula

The single letter alone on one side of the formula, e.g. 'y' in y = mx + c.

Equation

A statement that two expressions are equal, true for specific value(s) of the unknown.

Identity

A statement true for all values of the variable, shown with ≡.

Simultaneous equations

Two or more equations solved together to find values that satisfy all of them.

Coefficient

The number multiplying a variable, e.g. 3 in 3x.

Substitution

Replacing a letter with a given numerical value.

Common exam traps

• Forgetting to apply an operation to every term on both sides of the equation.
• Sign errors when moving terms across the equals sign (should flip sign).
• Not factorising first when the subject appears on both sides of a formula.

Practice questions with answers

1. 1. Solve: 3x + 5 = 20

   Answer: x = 5

   3x = 20 - 5 = 15. x = 15 ÷ 3 = 5.

2. 2. Solve: 2(x - 3) = 10

   Answer: x = 8

   Expand: 2x - 6 = 10. 2x = 16. x = 8.

3. 3. Solve: 5x - 4 = 2x + 11

   Answer: x = 5

   5x - 2x = 11 + 4. 3x = 15. x = 5.

4. 4. Make x the subject of y = x + 7

   • • x = y - 7
   • • x = y + 7
   • • x = 7 - y
   • • x = 7y

   Answer: x = y - 7

   Subtract 7 from both sides: x = y - 7.

5. 5. Make x the subject of y = 4x

   • • x = y/4
   • • x = 4y
   • • x = y - 4
   • • x = y + 4

   Answer: x = y/4

   Divide both sides by 4: x = y/4.

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