TMUA Differentiation and Applications
Differentiation is a very common topic indeed in TMUA, though most directly asked differentiations tend to be right at the beginning of a TMUA paper and involve differentiating nothing more complex than various powers of 'x'. However, a familiarity with differentiation is essential as it is often used to answer other questions such as finding gradients, turning points, maxima and minima, and convexity or concavity of a curve (ie the second derivative) - especially with regards to the Trapezium Rule. The derivative of a function is also frequently tested in a more abstract sense (ie what properties might f'(x) have given some properties of the function f(x)).
For those so interested, we offer both one to one TMUA coaching on Differentiation and Applications, as well as online group coaching via Zoom - 'TMUA Differentiation and Applications' is Session #5 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 differentiation and applications - 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 #126 - tests how to find the equation of the gradient of a fairly complex function at the origin - Medium
- Teaser #400 - tests how to find the gradient of a curve - Medium
- Teaser #130 - tests finding maximum value of xy^2 given constraints - Medium
- Teaser #143 - tests how to find the maximum area of a rectangle inscribed in a semicircle - Medium
- Teaser #498 - tests how to establish when both axes are tangent to a circle - Medium
- Teaser #24 - tests finding the equation of a circle given its gradient y=mx+c - Medium
- Teaser #79 - tests ability to arrange graphs according to their gradient at a point - Medium
- Teaser #486 - tests recognition of a well known functional inequality related to calculus - Medium
- Teaser #478 - tests ability to find the maximum of an exponential expression - Medium
- Teaser #490 - tests ability to find a maximum of an exponential trigonometric expression - Medium
- Teaser #298 - tests ability to differentiate and compare results to find a common tangent - Quite Tough
- Teaser #503 - tests understanding of how to find when an integral approximation of y=sin^2(x) underestimates the area - Quite Tough
[Note: We also have a 'Differentiation' 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 Differentiation and Applications: SP p1 q13; SP p2 q2; SP p2 q14; 2016 p1 q3; 2016 p1 q12; 2016 p1 q13; 2016 p1 q15; 2016 p1 q18; 2016 p2 q2; 2016 p2 q6; 2017 p1 q1; 2017 p1 q2; 2017 p1 q6; 2017 p1 q10; 2017 p1 q15; 2017 p1 q16; 2017 p2 q1; 2017 p2 q2; 2017 p2 q16; 2017 p2 q19; 2018 p1 q9; 2018 p1 q11; 2018 p1 q13; 2018 p1 q16; 2018 p2 q1; 2018 p2 q6; 2018 p2 q18; 2019 p1 q1; 2019 p1 q7; 2019 p1 q18; 2019 p2 q14; 2020 p1 q1; 2020 p1 q16; 2020 p2 q1; 2020 p2 q12; 2020 p2 q16; 2021 p1 q2; 2021 p1 q11; 2021 p2 q6; 2021 p2 q8; 2021 p2 q9; 2021 p2 q12; 2022 p1 q3; 2022 p1 q12; 2022 p1 q15; 2022 p2 q1; 2022 p2 q17; 2023 p1 q11; 2023 p1 q14; 2023 p1 q19; 2023 p2 q19; 2023 p2 q20
Practice makes perfect - good luck in your studies!