Quadratics

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 ax² + bx + c.
Understand and use standard mathematical formulae; rearrange formulae to change the subject

Graphically identifies and interprets quadratic functions’ 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 x² 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.