TMUA Modulus Maths
TMUA loves testing on modulus maths (aka using the absolute/positive value of 'x' in functions, or the absolute value of the function f(x) - or both), whether it be solving modulus equations (algebraically or graphically), comparing integrals of functions and their absolute value cousins, or noting various symmetries between modulus functions.
For those so interested, we offer both one to one TMUA coaching on modulus maths, 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 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 modulus maths - 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 #415 - tests basic understanding of moduli - Fairly Mild
- Teaser #434 - tests ability to draw 5-mod(x-1) and x+3 - Standard
- Teaser #474 - tests ability to solve two modulus inequalities and deduce a maximum of mod(y-x) - Standard
- Teaser #437 - tests which statements are necessary for x>2 to be true - Standard
- Teaser #456 - tests how to find the minimum value of abs(x) given a trig equation - Medium
- Teaser #454 - tests how to solve a modulus equation involving a quadratic - Medium
- Teaser #422 - tests ability to solve modulus equation by splitting into regions - Medium
- Teaser #310 - tests knowledge of how to graph the modulus of a quadratic, and find the roots - Medium
- Teaser #470 - tests sufficiency of various inequality and modulus statements, often using counterexamples to disprove - 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 #494 - tests understanding of how to find positive solutions to a modulus equation - Medium
- Teaser #500 - tests understanding of when sqrt(x^2) = (sqrt(x))^2 - Medium
- Teaser #280 - tests knowledge of how to graph the modulus of a quadratic, and find the product of roots using the fact the amended function is even - Medium
- Teaser #489 - tests ability to integrate a product of two modulus - Quite Tough
- Teaser #492 - tests ability to use graphical methods and a symmetry trick to solve a tough looking modulus equation - Quite Tough
- Teaser #417 - tests ability to sketch the graph of the modulus of (ax+b)/(cx+d) - Quite Tough
- Teaser #282 - tests noticing even and odd functionality to massively simplify an integral - Quite Tough
TMUA Past Questions on Modulus Maths: 2017 p2 q19; 2018 p1 q10; 2019 p1 q10; 2019 p2 q18; 2020 p1 q18; 2021 p1 q7; 2021 p1 q9; 2021 p2 q16; 2021 p2 q19; 2021 p2 q20; 2022 p1 q7; 2022 p1 q20; 2022 p2 q14; 2023 p1 q19; 2023 p2 q20
Practice makes perfect - good luck in your studies!