TMUA Graphs and Graphical Solutions
This is a very common topic indeed in TMUA, and a thorough understanding of how to sketch fairly accurately all of the common graphs such as trig graphs, log (x) to various bases, a^x, polynomials (especially quadratics and cubics) and modulus graphs is essential. TMUA also presents graphs that no student is expected to recognise, but is expected to be able to deduce certain facts about. TMUA also frequently tests students’ ability to solve 'algebraically challenging' equations and inequalities graphically, as well as to interpret intersections, transformations, and the impact of parameters on graphs.
For those so interested, we offer both one to one TMUA coaching on graphs and graphical solutions, as well as online group coaching via Zoom - 'TMUA Graphs and Graphical Solutions' is Session #11 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 graphs and graphical solutions - 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 #214 - tests understanding of the graph y=A cos (Bx-C) - Fairly Mild
- Teaser #445 - tests understanding of when a cubic has exactly two distinct roots - Standard
- Teaser #434 - tests ability to draw 5-mod(x-1) and x+3 - Standard
- Teaser #212 - tests how to find number of real solutions of x^2-ln(x)-4=0 - Standard
- Teaser #277 - tests drawing quadratics and straight lines to find a maximum - Standard
- Teaser #25 - tests understanding of linear and non linear transformations - Standard
- Teaser #22 - tests ability to find coordinates of intersection of a parabola and circle - Standard
- Teaser #493 - tests understanding of the various components of logarithms and exponents and their allowed values - Standard
- Teaser #473 - tests understanding of how to apply various transformations to a quadratic's vertex - Standard
- Teaser #447 - tests knowledge of finding point of rotational symmetry from a functional equation - Medium
- Teaser #446 - tests knowledge of which functional equations represent symmetry in the line x=a by using graphs- Medium
- Teaser #430 - tests understanding of how to find point of rotational symmetry on a graph - Medium
- Teaser #197 - tests ability to find number of solutions to e^(2x)+x-3=0 in an interval- Medium
- Teaser #481 - tests ability to transform a parabola and calculate where the original and transformed curves cross - Medium
- Teaser #501 - tests understanding of a well known functional inequality - Medium
- Teaser #484 - tests ability to use symmetry and patterns to sum a tricky looking trigonometric series - Medium
- Teaser #449 - tests how to find A when sin^2(Ax) satisfies f(x)=f(x+2) - Medium
- Teaser #204 - tests ability to solve an equation involving multiple 'tan' taking advantage of graphical symmetry - Medium
- Teaser #171 - tests ability to solve an equation involving multiple 'sin' taking advantage of graphical symmetry - Medium
- Teaser #486 - tests recognition of a well known functional inequality - Medium
- Teaser #79 - tests ability to arrange graphs according to their gradient at a point - 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 #310 - tests knowledge of how to graph the modulus of a quadratic, and find the roots - Medium
- Teaser #488 - tests understanding of log bases and their respective graphs - Medium
- Teaser #24 - tests finding the equation of a circle given its gradient y=mx+c - 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 #393 - tests understanding of how inequalities are represented on a graph - Medium
- Teaser #363 - tests understanding of how inequalities are represented on a graph - Medium
- Teaser #333 - tests understanding of how inequalities are represented on a graph - Medium
- Teaser #420 - tests ability to find number of solutions to x^2 sin(2x)=cos(2x) - Quite Tough
- Teaser #503 - tests understanding of how to find when an integral approximation of y=sin^2(x) underestimates the area - 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 #298 - tests ability to establish when two curves ln(x) and ax^3 do not cross - Quite Tough
- Teaser #491 - tests understanding of all steps required to correctly solve a log = log equation - Tough
TMUA Past Questions on Graphs and Graphical Solutions: SP p1 q10; SP p1 q14; SP p2 q7; SP p2 q10; SP p2 q14; SP p2 q19; 2016 p1 q10; 2016 p1 q13; 2016 p1 q17; 2016 p2 q8; 2016 p2 q11; 2016 p2 q14; 2016 p2 q17; 2017 p1 q3; 2017 p1 q8; 2017 p1 q15; 2017 p1 q17; 2017 p2 q7; 2017 p2 q11; 2017 p2 q12; 2017 p2 q14; 2017 p2 q18; 2018 p1 q6; 2018 p1 q12; 2018 p1 q13; 2018 p1 q18; 2018 p2 q4; 2018 p2 q10; 2018 p2 q11; 2018 p2 q18; 2018 p2 q19; 2018 p2 q20; 2019 p1 q6; 2019 p1 q18; 2019 p1 q20; 2019 p2 q14; 2019 p2 q16; 2019 p2 q18; 2020 p1 q11; 2020 p1 q12; 2020 p1 q14; 2020 p1 q16; 2020 p1 q17; 2020 p1 q18; 2020 p2 q5; 2020 p2 q11; 2021 p1 q9; 2021 p1 q14; 2021 p1 q17; 2021 p1 q20; 2021 p2 q13; 2021 p2 q16; 2021 p2 q17; 2022 p1 q12; 2022 p1 q15; 2022 p1 q18; 2022 p1 q20; 2022 p2 q14; 2022 p2 q18; 2022 p2 q20; 2023 p1 q2; 2023 p1 q9; 2023 p1 q20; 2023 p2 q6; 2023 p2 q7; 2023 p2 q20
Practice makes perfect - good luck in your studies!