Quadratic Equations

Worksheets that build up the quadratic equation step by step, before the quadratic function. Students first solve a garden area problem by guessing and find that an equation with a squared unknown can have two solutions. Then they solve incomplete equations: x² = a, discussing when there are two solutions, one or none, and equations where a product equals zero. Only then comes the definition of a quadratic equation and its coefficients. Then they learn four methods: factorising, completing the square, the quadratic formula derived by completing the square, and choosing the quickest method. They practise the methods with a tangram of equations in different forms. Next they use the discriminant to tell how many solutions an equation has, and discover and apply Vieta’s formulas. Then come equations with a parameter: the number of solutions, a given relation between the solutions and the signs of the solutions. Finally they solve equations that become quadratic and word problems, look for mistakes in other people’s work and check what they have learned. The worksheets have tasks for working in pairs and alone, and most end with an exit card.