TMUA Remainder Theorem
TMUA occasionally tests knowledge of the Remainder Theorem (and its special case the Factor Theorem), as such it needs to be fully understood - see also the topic 'Roots of Equations'. We also include in this topic 'divisibility' (ie under what conditions 'a' divides 'b' etc and divisibility rules).
For those so interested, we offer both one to one TMUA coaching on the remainder theorem, as well as online group coaching via Zoom - 'TMUA Prerequisite Maths One' is Session #1 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 the remainder theorem - 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 #182 - tests knowledge of divisibility rules in a puzzle - Fairly Mild
- Teaser #167 - tests how to find a multiple of various numbers using prime factors - Fairly Mild
- Teaser #428 - tests whether '21=3x7' is a counterexample to a list of statements about primes and divisibility - Medium
- Teaser #33 - tests when a cubic has only one real root - Medium
TMUA Past Questions on the Remainder Theorem: SP p1 q6; SP p2 q8; SP p2 q12; 2016 p1 q2; 2016 p2 q13; 2017 p1 q4; 2017 p2 q17; 2018 p1 q5; 2018 p2 q17; 2019 p2 q2; 2019 p2 q5; 2020 p1 q2; 2021 p2 q4; 2023 p1 q6; 2023 p2 q4
Practice makes perfect - good luck in your studies!