TMUA Necessary and Sufficient
TMUA is obsessed with necessary, sufficient and equivalent questions, which are among the most unfamiliar to most students taking the exam. The basic premise of X being 'necessary', 'sufficient' or 'equivalent' for Y is quite easy to grasp, but many questions twist the wording and frequently invoke 'easy to misinterpret' or 'obviously correct but actually wrong' options. It is clearly necessary to be sufficiently prepared!
For those so interested, we offer both one to one TMUA coaching on necessary/sufficient questions, as well as online group coaching via Zoom - 'TMUA Necessary/Sufficient Questions' is Session #18 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 necessary/sufficient questions - 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 #429 - tests necessary and sufficient logic knowledge in relation to inequalities - Standard
- Teaser #437 - tests which statements are necessary for x>2 to be true - Standard
- Teaser #459 - tests understanding of 'necessary' logical conditions for an integral - Medium
- Teaser #469 - tests understanding of different forms of expressing necessary and sufficient logic - Medium
- Teaser #470 - tests sufficiency of various inequality and modulus statements, often using counterexamples to disprove - Medium
- Teaser #457 - tests equivalence of various logic statements involving necessary and sufficient - Medium
- Teaser #450 - tests which logic inequalities are necessary for y>3 to be true - Medium
- Teaser #439 - tests which Boolean statements are necessary for another Boolean statement - Medium
- Teaser #479 - tests understanding of which functional equations are sufficient for an integral to hold true - Quite Tough
TMUA Past Questions on Necessary/Sufficient: 2016 p2 q10; 2017 p2 q10; 2017 p2 q19; 2018 p2 q5; 2018 p2 q10; 2018 p2 q15; 2018 p2 q18; 2019 p2 q5; 2019 p2 q10; 2019 p2 q13; 2019 p2 q14; 2020 p2 q6; 2020 p2 q7; 2020 p2 q13; 2020 p2 q14; 2020 p2 q15; 2020 p2 q18; 2021 p2 q3; 2021 p2 q6; 2021 p2 q8; 2021 p2 q9; 2021 p2 q15; 2022 p2 q4; 2022 p2 q6; 2022 p2 q8; 2022 p2 q11; 2022 p2 q19; 2023 p2 q5; 2023 p2 q7; 2023 p2 q11; ; 2023 p2 q12; 2023 p2 q13
Practice makes perfect - good luck in your studies!