TMUA Integration and Areas
Integration as a standalone direct question is not frequently tested, and if it is then the integrals tend to be fairly standard (polynomials) and the question sits right at the beginning of the paper (it is unlikely skills such as integration by parts or substitution will be required). Integration is also tested as a part of other questions such as finding areas between curves etc (one aspect of finding areas under curves which is frequently tested is use of the Trapezium Rule, and whether it under or overestimates areas). Integration is also tested increasingly frequently on a more abstract level, given a general function rather than a specific one, and understanding how certain transformations or other operations might affect the integral.
For those so interested, we offer both one to one TMUA coaching on integration and areas, as well as online group coaching via Zoom - 'TMUA Integration and Areas' is Session #6 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 integration and areas - 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 #405 - tests ability to find the area enclosed between a curve and the x-axis - Medium
- Teaser #501 - tests understanding of a well known functional inequality - Medium
- Teaser #459 - tests understanding of 'necessary' logical conditions for an integral - Medium
- Teaser #486 - tests recognition of a well known functional inequality related to integration - Medium
- Teaser #487 - tests understanding of the integral of f(|x|) - Medium
- Teaser #471 - tests which function provides a counterexample to an integral statement - Medium
- Teaser #262 - tests noticing even and odd functionality to massively simplify an integral - Quite Tough
- Teaser #489 - tests ability to integrate a product of two modulus - Quite Tough
- Teaser #282 - tests noticing even and odd functionality to massively simplify an integral - Quite Tough
- Teaser #503 - tests understanding of how to find when an integral approximation of y=sin^2(x) underestimates the area - Quite Tough
- Teaser #479 - tests understanding of which functional equations are sufficient for an integral to hold true - Quite Tough
TMUA Past Questions on Integration and Areas: SP p1 q15; 2016 p1 q5; 2016 p2 q1; 2016 p2 q11; 2016 p2 q18; 2017 p1 q1; 2017 p1 q3; 2017 p1 q12; 2017 p1 q15; 2017 p1 q17; 2017 p2 q6; 2017 p2 q10; 2017 p2 q11; 2018 p1 q1; 2018 p1 q12; 2018 p2 q18; 2019 p1 q8; 2019 p1 q9; 2019 p1 q10; 2019 p1 q12; 2019 p1 q16; 2019 p2 q13; 2020 p1 q11; 2020 p1 q14; 2020 p2 q6; 2020 p2 q12; 2020 p2 q13; 2020 p2 q16; 2021 p1 q2; 2021 p1 q7; 2021 p1 q10; 2021 p1 q13; 2021 p1 q15; 2021 p2 q1; 2021 p2 q12; 2021 p2 q20; 2022 p1 q3; 2022 p1 q6; 2022 p1 q7; 2022 p2 q12; 2023 p1 q1; 2023 p1 q3; 2023 p1 q10; 2023 p1 q19; 2023 p2 q2; 2023 p2 q5; 2023 p2 q17; 2023 p2 q20
Practice makes perfect - good luck in your studies!