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Lesson Plan: General Term in the Binomial Theorem Mathematics • Third Year of Secondary School
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find a specific term inside a binomial expansion and find the relation between two consecutive terms.
Objectives
Students will be able to
- recall the formula for a general term in a binomial expansion, ,
- use the formula for a general term in a binomial expansion, , to find a specific term (or its coefficient) for
- a given exponent ,
- the highest or lowest power of in the expansion,
- the middle term(s) in the expansion,
- a given position when terms are arranged by ascending or descending powers of ,
- a specified coefficient,
- two or more terms with the same coefficient as each other,
- understand the relationship between consecutive terms of a binomial expansion,
- use the relationship between consecutive terms in a binomial expansion (and their coefficients) to find
- the ratio between two terms,
- the largest or smallest term,
- find an unknown in a binomial when given information about one or more specific terms.
Prerequisites
Students should already be familiar with
- the binomial theorem,
- combinations and associated notation,
- simplifying factorials.
Exclusions
Students will not cover
- methods involving Pascal’s triangle.
