TMUA Pattern Finding
A great number of TMUA questions look very daunting at first glance and the way to begin to solve them is to find some sort of pattern and extrapolate to find the 'general rule'.
Frequently, pattern finding is linked to disentangling bizarrely defined sequences, series or integrations, and equally frequently it is linked to a word problem or puzzle, which could literally be on any topic under the sun.
For those so interested, we offer both one to one TMUA coaching on pattern finding, as well as online group coaching via Zoom - 'TMUA Pattern Finding and Word Problems' is Session #16 of 20. Check our TMUA Group Coaching Schedule page for dates when these sessions are 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 pattern finding - 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 #178 - tests ability to find a pattern to simplify and sum a series of powers - Fairly Mild
- Teaser #436 - tests ability to find smallest value of x satisfying cos (ax+b) = y - Standard
- Teaser #59 - tests ability to evaluate composite functions - Standard
- Teaser #304 - tests knowledge of how to evaluate a composite function quickly by spotting a pattern - Standard
- Teaser #233 - tests adding numbers in different bases by spotting a pattern - Standard
- Teaser #466 - tests ability to spot the pattern of symmetry of a functional equation - Standard
- Teaser #483 - tests ability to discover which of five options is the only possible first term of an arithmetic progression - Standard
- Teaser #274 - tests how to find f(f(f(f(f(x))))) by spotting a pattern - Medium
- Teaser #213 - tests ability to spot a pattern to evaluate a complex composite function - Medium
- Teaser #240 - tests ability to spot pattern to find a(100) given a(1) and a(n) - Medium
- Teaser #484 - tests ability to use symmetry and patterns to sum a tricky looking trigonometric series - Medium
- Teaser #322 - tests finding a pattern to sum a series of powers of a root of a cubic - Quite Tough
- Teaser #467 - tests ability to execute transformations in the right order and then recognise a functional equation pattern - Quite Tough
- Teaser #86 - tests ability to solve a crossword puzzle of sequences - Quite Tough
TMUA Past Questions involving Pattern Finding: SP p2 q16; 2016 p1 q4; 2016 p2 q6; 2016 p2 q19; 2016 p2 q20; 2017 p1 q11; 2017 p1 q17; 2017 p2 q6; 2017 p2 q15; 2018 p2 q7; 2018 p2 q8; 2018 p2 q16; 2019 p1 q4; 2019 p1 q19; 2019 p2 q9; 2020 p2 q11; 2021 p1 q5; 2021 p1 q13; 2021 p1 q15; 2021 p2 q19; 2021 p2 q20; 2022 p1 q5; 2022 p1 q11; 2022 p2 q16; 2022 p2 q19; ; 2022 p2 q20; 2023 p1 q3; 2023 p1 q4; 2023 p1 q6; 2023 p1 q17; 2023 p2 q15; 2023 p2 q16; 2023 p2 q17
Practice makes perfect - good luck in your studies!