GCSE›AQA GCSE Maths›Mind mapsEquations and InequalitiesAQA GCSE Maths: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsLinear equationsUnknown appears only to the power 1Expand brackets firstCollect unknowns on one sideDivide to leave the unknown alone3(x+2)=x+103(x+2) = x+103(x+2)=x+10 gives x=2x = 2x=2QuadraticsRearrange into ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0Factorise, then solve each bracket =0= 0=0Complete the square: (x+p)2+q=0(x+p)^2 + q = 0(x+p)2+q=0x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=2a−b±b2−4acSimultaneousTwo equations, same two unknownsLinear/linear: elimination or substitutionLinear/quadratic: substitute the linear into the quadraticGraph solutions are where lines intersectEquationsand inequalities=<≥Problems and iterationForm an equation from the problemInterpret the answer in contextIteration: xn+1=f(xn)x_{n+1} = f(x_n)xn+1=f(xn)Repeat from a start value until it convergesInequalitiesSolve like equationsFlip the sign when multiplying by a negativeStrict <<< or >>>: open circle≤\leq≤ or ≥\geq≥: closed circleGraphs: dashed line for strict, solid if includedExam tipsCheck if it factorises before the formulaLinear/quadratic can give two solutionsReverse the sign for a negative divisor