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**Scheme of work: Year 12 A-Level: Pure 1: Quadratics**

- 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 terms of the form ax
^{2}Â + bx + c. - Understand and use standard mathematical formulae; rearrange formulae to change the subject

- Graphically identifies and interprets quadratic functionsâ€™ roots, intercepts, and turning points.
- 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,
- completing the square using the quadratic formula;

- Find approximate solutions using a graph

- Students must understand how the discriminator determines the number and types of roots for a quadratic function.
- When solving quadratic equations involving inequalities arising from the discriminant, students benefit from sketching the quadratic to correctly determine the range of solutions.
- When solving quadratic, ensure students can arrange the coefficients a and b, and constant c term in line with the general form, which helps with the manipulation.
- Students should be able to derive the quadratic formula by completing the square of the general form.

- Students often struggle to manipulate quadratics when the x
^{2}term is negative. - Some students are unclear on the conditions for the number of roots when finding the discriminator.
- Students often resort to using the formula when solving quadratics when it is more appropriate and efficient to use completing the square.
- When sketching quadratic functions with no real roots, students often make mistakes by drawing the curve below y = 0.

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