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Topic 1: Surds and quadratic functions

Surds

4 hours

• Understand the concept of a surd as an irrational number represented using a square root or a radical sign.
• Simplify square roots of natural numbers which contain perfect square factors, e.g. √45 = √9 × 5 = √9√5 = 3√5
• Rationalise the denominator of fractional expressions involving square roots, e.g. √7 √3 = √7 √3 × √3 √3 = √7×√3 √3×√3 = √21 3
• Use the four operations to simplify surds, e.g. √5 − 2√5 + 4√5 = 3√5 and 2√3 × 5√11 = 10√33

Quadratic functions

7 hours

• Recognise and determine features of the graphs of 𝑦 = 𝑥2, 𝑦 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐, 𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘 and 𝑦 = 𝑎(𝑥 − 𝑥1)(𝑥 − 𝑥2), including their parabolic nature, turning points, axes of symmetry and intercepts. 1 interactive
• Solve quadratic equations algebraically using factorisation, the quadratic formula (both exact and approximate solutions), completing the square and using technology.
• Sketch the graphs of quadratic functions, with or without technology.
• Use the discriminant to determine the number of solutions to a quadratic equation. 1 interactive
• Determine turning points and zeros of quadratic functions, with and without technology.
• Model and solve problems that involve quadratic functions, with and without technology.