TMUA Transformations
It is very important to be familiar with all of the basic transformations, including linear translations up, down, left and right, stretches in both directions, reflections (usually in vertical or horizontal lines) and rotations. TMUA likes testing this topic, not only directly, but also mixed in with other topics such as integrals, differentiation and general polynomials.
For those so interested, we offer both one to one TMUA coaching on transformations, as well as online group coaching via Zoom - 'TMUA Transformations' is Session #4 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 transformations - 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 #411 - tests transforming a cubic's roots from a, b, c to 2a-1, 2b-1 and 2c-1 - Standard
- Teaser #19 - tests finding equation of a reflection of a parabola in the y-axis - Standard
- Teaser #268 - tests how to find a quadratic whose roots are the square of another quadratic using a neat trick - Standard
- Teaser #473 - tests understanding of how to apply various transformations to a quadratic's vertex - Standard
- Teaser #25 - tests understanding of linear and non linear transformations - Standard
- Teaser #446 - tests knowledge of which functional equations represent symmetry in the line x=a - Medium
- Teaser #430 - tests understanding of how to find point of rotational symmetry for f(2+x)+f(2-x)=10 - Medium
- Teaser #252 - tests how to find a quadratic with transformed roots - Medium
- Teaser #26 - tests following sequences of transformations on a curve - Medium
- Teaser #481 - tests ability to transform a parabola and calculate where the original and transformed curves cross - Medium
- Teaser #495 - tests how to rotate a quadratic about a non-origin point - Medium
- Teaser #487 - tests understanding of the integral of f(|x|) - Medium
- Teaser #502 - tests ability to split a function into its odd and even components - Medium
- Teaser #417 - tests ability to sketch the graph of the modulus of (ax+b)/(cx+d) by noting a transformation of a standard graph - Quite Tough
- Teaser #467 - tests ability to execute transformations in the right order and then recognise a functional equation - Quite Tough
- Teaser #492 - tests ability to use graphical methods, transformations and a symmetry trick to solve a tough looking modulus equation - Quite Tough
- Teaser #479 - tests understanding of which functional equations are sufficient for an integral to hold true - Quite Tough
TMUA Past Questions on Transformations: SP p1 q10; SP p2 q19; 2016 p1 q9; 2016 p2 q11; 2017 p1 q12; 2017 p1 q15; 2017 p1 q18; 2017 p2 q10; 2017 p2 q11; 2017 p2 q14; 2018 p2 q10; 2018 p2 q15; 2019 p1 q8; 2019 p1 q16; 2019 p2 q20; 2020 p1 q10; 2021 p1 q18; 2022 p1 q10; 2023 p1 q11
Practice makes perfect - good luck in your studies!