TMUA Binomial Expansions
Binomial expansions are a recurring theme in TMUA, and it is essential to know the Binomial Theorem and how to use it to find various coefficients and powers. The questions either tend to test an expansion directly (finding the coefficient of a certain term or disentangling some given relationship between expansion coefficients) or indirectly (multiplying out various powers of brackets for example).
For those so interested, we offer both one to one TMUA coaching on Binomial Expansions, as well as online group coaching via Zoom - 'TMUA Binomial Expansions, Series and Sequences' is Session #15 of 20. Check our TMUA Group Coaching Schedule page for dates when this session is available - details of what we cover in each group session can be found on our TMUA Coaching Sessions Overview page. For more general information on our online sessions check out our 'Online Coaching FAQ'.
Feel free to contact us if you require more information regarding any of the above.
Free Revision Resources
The below list of questions links to short videos (teasers) on our YouTube channel which directly or indirectly test elements of what is required to succeed in answering TMUA questions on binomial expansions - they also provide a detailed solution to the question posed, together with tips and tricks and are arranged roughly in increasing order of difficulty. All the videos are taken from the Gresty Academy YouTube podcast 'A Crash Course in TMUA Must Know Maths' which contains hundreds of TMUA style questions and is great for revision.
- Teaser #16 - tests ability to spot a series sum is a line of Pascals Triangle - Standard
- Teaser #362 - tests whether you know a great trick to find the sum of all coefficients of an expansion - Medium
- Teaser #505 - tests ability to find the coefficient where powers of a and b are the same in a binomial expansion - Medium
- Teaser #279 - tests knowledge of a useful trick to find coefficient of x^3 in a binomial expansion - Quite Tough
[Note: We also have a 'Binomial Expansion' playlist on our YouTube channel however the videos in this playlist are not all relevant to TMUA (some are too easy, some are too hard, and many cover topics not tested in TMUA).]
TMUA Past Questions on Binomial Expansions: SP p1 q20; 2016 p1 q19; 2017 p1 q13; 2018 p1 q7; 2018 p2 q2; 2019 p1 q3; 2019 p2 q1; 2020 p1 q13; 2021 p1 q16; 2022 p2 q2; 2023 p1 q6
Practice makes perfect - good luck in your studies!