Topic 2: Binomial expansion and cubic functions — Maths Interactives

Binomial expansion

3 hours

Understand the notion of a combination as an unordered set of 𝑟 objects taken from a set of 𝑛 distinct objects.
Recognise and use the link between Pascal’s triangle and the notation (𝑛 𝑟)
Use the binomial theorem (𝑥 + 𝑦)𝑛 = 𝑥𝑛 + (𝑛 1)𝑥𝑛−1𝑦+... + (𝑛 𝑟)𝑥𝑛−𝑟𝑦𝑟+... + 𝑦𝑛 to expand expressions, e.g.(2𝑥 − 1)3

Cubic functions

9 hours

Identify the coefficients and the degree of a polynomial.
Expand quadratic and cubic polynomials from factors.
Recognise and determine features of the graphs of 𝑦 = 𝑥3, 𝑦 = 𝑎(𝑥 − ℎ)3 + 𝑘 and 𝑦 = 𝑎(𝑥 − 𝑥1)(𝑥 − 𝑥2)(𝑥 − 𝑥3), including shape, intercepts, and behaviour as 𝑥 → ∞ and 𝑥 → − ∞. 1 interactive
Solve cubic equations using technology, and algebraically in cases where the equation is factorised.
Sketch the graphs of cubic functions, with and without technology.
Model and solve problems that involve cubic functions, with and without technology.