Quadratic Equations

Scheme of work: GCSE Higher: Year 11: Term 1: Quadratic Equations

Simplify and manipulate algebraic expressions by:
Expanding products of two or more binomials
Factorising quadratic expressions of the form x² + bx + c, including the difference of two squares
Simplifying expressions involving sums, products and powers, including the laws of indices
Factorising quadratic expressions of the form ax² + bx + c.

Know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent and use algebra to support and construct arguments and proofs.
Simplify and manipulate algebraic expressions by factorising quadratic expressions of the form ax² + bx + c.
Understand and use standard mathematical formulae; rearrange formulae to change the subject
Identify and interpret roots, intercepts, turning points of quadratic functions graphically
Deduce roots algebraically and turning points by completing the square
Recognise, sketch and interpret graphs of quadratic functions
Solve quadratic equations (including those that require rearrangement) algebraically by factorising, by completing the square and by using the quadratic formula; find approximate solutions using a graph
Solve two simultaneous equations in two variables linear/quadratic algebraically; find approximate solutions using a graph

Check brackets have been factorised correctly by multiplying them back out.
To solve quadratics by factorising, students must identify two numbers with a product of c and a sum of b.
When a quadratic cannot be solved by factorising students should use completing the square or the quadratic formula.
Students should be able to derive the quadratic formula from the method of completing the square.
A sketched graph is drawn freehand, including the roots, turning point and intercept values.
Quadratic and linear simultaneous equations should be sketched before solved algebraically to ensure students know to find and the x and y values.

The trial and improvement method is often incorrectly used to try and solve quadratics.
When solving quadratic and linear simultaneous equations students often forget to find the y values as well the x.
When using the formula to solve quadratics students often forget to evaluate the negative solution. Some students also incorrectly apply the division by reducing the terms it covers.
Students tend to struggle deriving quadratic equations from geometrical facts.