TMUA Functions
TMUA loves function questions, whether they be directly evaluated, composite, or any number of other wacky possibilities, including recursively defined functions. Certain functions such as 'Even and Odd Functions' and 'Modulus Functions' are so common we list them on a separate page for more efficient revision and study. Characteristics such as domain and range tend not to be directly tested in TMUA, though they are certainly indirectly tested (for example cross checking values found as potential solutions against the domain or range of the original expression). As such it is vital to be familiar with domains and ranges of all the 'usual' functions (trig, log, exponential, fractions etc).
For those so interested, we offer both one to one TMUA coaching on functions, as well as online group coaching via Zoom - 'TMUA Functions (inc Modulus, Even and Odd)' is Session #10 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 functions - 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 #304 - tests knowledge of how to evaluate a composite function - Standard
- Teaser #261 - tests understanding of f(g(x)) and uses a neat trick to disentangle to a quadratic - Standard
- Teaser #59 - tests ability to evaluate composite functions - Standard
- Teaser #413 - tests knowledge of finding undefined values for a quadratic fraction as denominator - Standard
- Teaser #466 - tests ability to spot the type of symmetry of a functional equation - Standard
- Teaser #449 - tests how to find A when sin^2(Ax) satisfies f(x)=f(x+2) - Medium
- Teaser #446 - tests knowledge of which functional equations represent symmetry in the line x=a - Medium
- Teaser #272 - tests knowledge of domains of both logs and square roots - Medium
- Teaser #12 - tests ability to find domain of a log of a polynomial - Medium
- Teaser #487 - tests understanding of the integral of f(|x|) - Medium
- Teaser #430 - tests understanding of how to find point of rotational symmetry for f(2+x)+f(2-x)=10 - Medium
- Teaser #502 - tests ability to split a function into its odd and even components - Medium
- Teaser #213 - tests ability to spot a pattern to evaluate a complex composite function - Medium
- Teaser #501 - tests understanding of a well known functional inequality - Medium
- Teaser #274 - tests how to find the composite function f(f(f(f(f(x))))) by spotting a pattern - Medium
- Teaser #153 - tests how to solve an equation involving the composite function cos(sin(x)) - Medium
- Teaser #500 - tests understanding of when sqrt(x^2) = (sqrt(x))^2 - Medium
- Teaser #486 - tests recognition of a well known functional inequality - Medium
- Teaser #471 - tests which function provides a counterexample to an integral statement - Medium
- Teaser #461 - tests ability to establish which functional equations have solutions and which don't - Quite Tough
- Teaser #479 - tests understanding of which functional equations are sufficient for an integral to hold true - Quite Tough
- Teaser #467 - tests ability to execute transformations in the right order and then recognise a functional equation - Quite Tough
- Teaser #504 - tests advanced manipulation of two log(log) functions to solve an inequality - Quite Tough
- Teaser #480 - tests ability to split a function into its odd and even components to solve a functional equation - Quite Tough
- Teaser #491 - tests understanding of all steps required to correctly solve a log = log equation - Tough
TMUA Past Questions on Functions: 2017 p1 q2; 2017 p1 q17; 2017 p2 q10; 2017 p2 q11; 2017 p2 q15; 2018 p1 q13; 2019 p1 q8; 2019 p1 q16; 2020 p1 q8; 2020 p2 q13; 2020 p2 q20; 2021 p1 q5; 2021 p1 q7; 2021 p1 q11; 2021 p1 q13; 2021 p1 q20; 2021 p2 q17; 2021 p2 q20; 2022 p1 q3; 2022 p1 q9; 2022 p2 q20; 2023 p1 q3; 2023 p1 q14; 2023 p1 q20
Practice makes perfect - good luck in your studies!