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**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 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 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.

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