Binomial Expansion

Binomial Expansion – Extension Homework (IGCSE Further Maths, Chapter 6)

This homework stretches your understanding of binomial expansion beyond the core questions. It is worth 83 marks and is split into colour-coded sections that get harder as you go:

Questions 1–3 (red): past exam questions. Expanding expressions with fractional and negative powers, finding unknown constants, and using an expansion to estimate a square root.
Questions 4–6 (blue): exam-style questions. Rewriting an expression in the form (1 + bx)ⁿ before expanding, finding unknown powers and constants from given coefficients, stating when an expansion is valid, and using a suitable value of x to estimate a value.
Questions 7–8 (green, TIF): problem solving. Finding unknown constants by comparing coefficients, and multiplying two expansions together to estimate √51.
Question 9 (purple, TIEF): the hardest question. Expanding an expression in x² and using it to estimate √101.