TMUA Cubics and Other Polynomials
TMUA loves testing on cubic equations - everything from their shape on a graph, to sums and products of their roots, to various ways cubics can have exactly 1, 2 or 3 roots. TMUA also tests higher polynomials occasionally (quartics etc) and sometimes it just defines a function as 'a polynomial', and the question proceeds from there. For quadratics, which TMUA loves even more than cubics, see 'Quadratics (inc Hidden)'.
For those so interested, we offer both one to one TMUA coaching on Cubics and other Polynomials, as well as online group coaching via Zoom - 'TMUA Cubics and other Polynomials' is Session #9 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 cubics and other polynomials - 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 #445 - tests understanding of when a cubic has exactly two distinct roots - Standard
- Teaser #411 - tests transforming a cubic's roots from a, b, c to 2a-1, 2b-1 and 2c-1 - Standard
- Teaser #376 - tests comparing coefficients of two cubics to find unknowns - Standard
- Teaser #392 - tests knowledge of the sum and product of the roots of a cubic equation - Standard
- Teaser #259 - tests finding a shared surd root of a line, quadratic and cubic - Standard
- Teaser #129 - tests finding roots of a quartic given two roots - Standard
- Teaser #12 - tests ability to find domain of a log of a polynomial - Medium
- Teaser #215 - tests ability to expand a cubic and compare surd and non surd coefficients - Medium
- Teaser #33 - tests when a cubic has only one real root - Medium
- Teaser #504 - tests ability to find the coefficient where powers of a and b are the same in a binomial expansion - Medium
- Teaser #476 - tests how to solve an inequality involving a polynomial over a polynomial - Medium
- Teaser #130 - tests finding maximum value of xy^2 given constraints (involves a cubic)- Medium
- Teaser #497 - tests knowledge of when a cubic has exactly two distinct roots - Medium
- Teaser #322 - tests finding a pattern to sum a series of powers of a root of a cubic - Quite Tough
- Teaser #477 - tests understanding of when a quartic has exactly two distinct roots - Quite Tough
- Teaser #298 - tests ability to find a common tangent between a cubic and ln(x) - Quite Tough
[Note: We also have a 'Polynomials' 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 Cubics and other Polynomials: SP p1 q4; SP p1 q6; SP p1 q13; SP p2 q12; SP p2 q14; SP p2 q19; 2016 p1 q1; 2016 p1 q2; 2016 p2 q11; 2016 p2 q14; 2017 p1 q4; 2017 p1 q10; 2017 p1 q12; 2017 p1 q16; 2017 p2 q16; 2017 p2 q19; 2018 p1 q5; 2018 p1 q12; 2018 p1 q9; 2018 p2 q6; 2018 p2 q15; 2018 p2 q18; 2019 p1 q7; 2019 p1 q20; 2019 p2 q2; 2019 p2 q14; 2020 p1 q3; 2020 p1 q14; 2020 p1 q20; 2020 p2 q18; 2021 p1 q2; 2021 p2 q6; 2021 p2 q8; 2021 p2 q9; 2021 p2 q12; 2022 p1 q10; 2022 p1 q16; 2022 p1 q18; 2022 p2 q1; 2022 p2 q7; 2022 p2 q17; 2023 p1 q14; 2023 p2 q10; 2023 p2 q18; 2023 p2 q19; 2023 p2 q20
Practice makes perfect - good luck in your studies!