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

#### Prerequisite Knowledge

• 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 ax2Â + bx + c.
• Understand and use standard mathematical formulae; rearrange formulae to change the subject

#### Success Criteria

• 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

#### Key Concepts

• 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.

#### Common Misconceptions

• 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.

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