Binomial Expansion Approximations and Estimations
Examples, solutions, videos, activities, and worksheets that are suitable for A Level Maths.
How to answer questions on Binomial Expansion?
Introduction Infinite series expansion (negative & fractions)
Core 4 - Binomial Expansion (1)
Examples of typical questions (approximations & partial fractions)
Core 4 - Binomial Expansion (2)
Binomial Expansion
Edexcel Core Maths C4 June 2010 Q5(b) : ExamSolutions
Revision of A level binomial expansions - questions and answers 1
A rapid review of the definition of a binomial expansion followed with some illustrations of how and why the coefficients are what they are? Demonstrates that the coefficients have a prescribed pattern.
Revision of A level binomial expansions - questions and answers 2
This video gives precise definitions or formulae for the coefficients of a binomial expansion.
Revision of A level binomial expansions - questions and answers 3
This video presents 4 introductory type questions from A level papers and demonstrates a systematic solution methodology for them.
Example:
- Find the first 3 terms in ascending powers of x of the binomial expansion (3 + 2x)5, giving each term in its simplest form.
- Find the first 3 terms in ascending powers of x of the binomial expansion (2 + x)6, giving each term in its simplest form.
- Find the first 3 terms in ascending powers of x of the binomial expansion (3 - 2x)8, giving each term in its simplest form.
Revision of A level binomial expansions - questions and answers 4
This video presents 4 typical questions from A level papers and demonstrates a systematic solution methodology for solving them.
Example:
- a) write down the first 3 terms in ascending powers of x of (1 + px)12, where p is a non-zero constant.
b) Given that in the expansion, the coefficient of x is (-q) and the coefficient of x2 is 11q, find the values of p and q. - a) Find the first 4 terms in ascending powers of x of the binomial expansion (1 + dx)10, where d is a non-zero constant. Give each term in its simplest form.
b) Given that in the expansion, the coefficient of x3 is double that of x2, find the value of d. - a) Find the first 4 terms in ascending powers of x of the binomial expansion (1 + kx)6, where k is a non-zero constant.
b) Given that in the expansion, the coefficients of x and x2 are equal, find (i) the value of k and (ii) the coefficient of x3. - a) Find the first 4 terms in ascending powers of x of the binomial expansion (1 + px)9, where p is a non-zero constant.
b) The first three terms as 1, 36x, qx2, where q is constant. Find the values of p and q.
Revision of A level binomial expansions - questions and answers 5
After a very brief reminder of key formulae which will be used, this video presents 4 less typical questions from A level papers and demonstrates a systematic solution methodology for them. [Minor typo in part b of Q4, should ask for q/p.]
Example:
- a) Write down the first 4 terms in the expansion of (1 + x/10)10, giving each term in its simplest form.
b) Use your expansion to estimate the value of (1.005)10, giving your answer to 4 decimal places. - a) Find the first 4 terms in the expansion of (1 + x/4)8, giving each term in its simplest form.
b) Use your expansion to estimate the value of (1.025)8, giving your answer to 4 decimal places. - In the binomial expansion of (2 - 5x)20, find an expression for the coefficient of x5.
- b) In the binomial expansion of (1 + x)40, the coefficients of x4 and x5 are p and q respectively. Find the value of q/p.
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