GCSE Mathematics · Edexcel 1MA1 · Topic A.3

Solving equations and inequalities

Key points

Linear equations: do the same to both sides, e.g. $3x - 4 = 11 \Rightarrow 3x = 15 \Rightarrow x = 5$ .
Quadratics: set equal to zero, then factorise, use the formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , or complete the square: $x^2 + bx + c = \left(x + \frac{b}{2}\right)^2 - \left(\frac{b}{2}\right)^2 + c$ .
Simultaneous equations: eliminate one variable (match coefficients, then add or subtract) or substitute. Check in both equations.
Linear and quadratic simultaneous equations (higher): substitute the linear one into the quadratic.
Inequalities: solve like equations, but reverse the sign when multiplying or dividing by a negative. Show on a number line (open circle for $<$ , filled for $\le$ ).
Quadratic inequalities (higher): find the roots, sketch the graph and read off the region.
Iteration (higher): use $x_{n+1} = g(x_n)$ repeatedly to approximate a solution.

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Solving means finding the values that make a statement true. This sub-topic covers linear and quadratic equations, simultaneous equations and inequalities, plus graphical and, at Higher tier, iterative methods. Setting up an equation from…

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