Equations and formulas

• Construct expressions, equations and formulas from words, including simultaneous equations.
• Solve linear equations, including with brackets and unknowns on both sides.
• Solve fractional equations with numerical and linear algebraic denominators.
• Solve simultaneous linear equations in two unknowns.
• Solve quadratic equations by factorising, completing the square and the quadratic formula (given in the List of formulas); give answers in surd form when asked.
• Change the subject of a formula, including when the subject appears twice or under a power or root.

Turn the words into algebra

Choose a letter, write each quantity in terms of it, then use the fact in the question to make an equation. Consecutive integers are n, n + 1, …; consecutive even numbers are 2n, 2n + 2, …

Expand, collect, divide

Expand any brackets, collect the unknown on the side where it has the larger coefficient, then divide. Answers can be fractions or negative.

Multiply through by every denominator

Multiply every term by the lowest common denominator to clear the fractions. With algebraic denominators this often gives a quadratic. Check that no answer makes a denominator zero.

Eliminate one unknown

Make the coefficients of one unknown equal (multiply one or both equations), then add if the signs are different or subtract if they are the same. Substitute back to find the other unknown, and check in the equation you did not use.

Factorise, complete the square, or use the formula

Rearrange to = 0 first. If it factorises, set each bracket equal to zero. If the answer is wanted in surd form, complete the square. If it is wanted to a number of decimal places, use the formula.