TMUA Maximum and Minimum
Finding maximum and/or minimum of 'something' is an essential skill to master in order to succeed in TMUA. Typically there are three methods employed to solve, either a) differentiation (see 'Differentiation and Applications'), b) completing the square (see 'Quadratics (inc Hidden)' or c) putting in extremity values of relevant functions and proceeding from there.
For those so interested, we offer both one to one TMUA coaching on finding maximums and minimums, as well as online group coaching via Zoom - 'TMUA Differentiation and Applications' is Session #5 of 20 and 'TMUA Quadratics (inc Hidden)' is Session #8 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 finding maximums and minimums - 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 #277 - tests drawing quadratics and straight lines to find a maximum - Standard
- Teaser #241 - tests how to calculate minimum value of P(A or B) - Standard
- Teaser #474 - tests ability to solve two modulus inequalities and deduce a maximum of mod(y-x) - Standard
- Teaser #453 - tests how to solve inequalities to find maximum of logs with bases more and less than 1 - Medium
- Weekend Workout #16 - tests understanding of completing the square to find a minimum of a complex function - Medium
- Teaser #456 - tests how to find the minimum value of abs(x) given a trig equation - 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 #478 - tests ability to find the maximum of an exponential expression - Medium
- Teaser #308 - tests manipulation of trig identities and then finding the minimum value using extreme values of sin(2x) - Medium
- Teaser #490 - tests ability to find a maximum of an exponential trigonometric expression - Medium
- Teaser #185 - tests manipulation of position vectors to see when two particles reach their closest point which involves finding the minimum of a square root - Medium
- Teaser #284 - tests knowledge that arithmetic mean >= geometric mean to find a minimum of a complex trig expression - Quite Tough
- Teaser #104 - tests how to find smallest integers that satisfy an equation, uses prime factorisation - Quite Tough
TMUA Past Questions on Finding Maximum and Minimum: SP p1 q15; SP p2 q6; SP p2 q18; 2016 p1 q8; 2016 p1 q12; 2016 p1 q13; 2016 p1 q15; 2016 p1 q18; 2017 p1 q10; 2018 p1 q10; 2018 p1 q13; 2018 p1 q16; 2018 p1 q18; 2019 p1 q7; 2019 p1 q13; 2020 p1 q6; 2020 p1 q8; 2021 p1 q4; 2021 p1 q6; 2021 p1 q12; 2022 p1 q9; 2022 p1 q12; 2022 p1 q13; 2022 p1 q14; 2022 p1 q15; 2022 p1 q18; 2022 p2 q1; 2022 p2 q16; 2022 p2 q20; 2023 p1 q5; 2023 p1 q11; 2023 p1 q15; 2023 p1 q20
Practice makes perfect - good luck in your studies!