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Students learn how to solve a range of quadratic equations using factorisation, applying the formula and completing the square. Learning progresses from solving equations to deriving and sketching quadratics as a graph.

This unit takes place in Year 11 Term 1 and follows on from solving linear and simultaneous equations.

- Simplify and manipulate algebraic expressions by:
- Expanding products of two or more binomials
- Factorising quadratic expressions of the form x
^{2}+ 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 ax
^{2}+ 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 ax
^{2}+ 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 need to identify two numbers that have a product of c and a sum of b. Roots are found when each bracket is made to equal zero and are solved for x.
- 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 and includes the roots, turning point and intercept values.
- Quadratic identities in the form (x + a)
^{2}+ b ≡ ax^{2}+ bx + c can be solved either through completing the square to RHS = LHS or by expanding the brackets to LHS = RHS and equating the unknowns. - Quadratic and linear simultaneous equations should be sketched before solved algebraically to ensure students know to find and the x and y values.

- The method of trial and improvement 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.

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