TMUA Straight Lines
It is vital to be comfortable with every aspect of straight lines (y=mx+c) including finding equations of lines and normals, parallel lines, knowing where lines appear on graphs and cross each other and other graphs, finding tangents etc. This topic is invariably tested as part of a harder question rather than a standalone, for example gradients of curves - see 'Differentiation and Applications' - and graphs - see 'Graphs and Graphical Solutions', where the questions can be quite devious.
For those so interested, we offer both one to one TMUA coaching on straight lines, as well as online group coaching via Zoom - 'TMUA Prerequisite Maths Two' is Session #2 of 20' where we deal with straight line basics and TMUA Graphs and Graphical Solutions' is Session #11 of 20 where we really dive into TMUA straight line specifics. 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 straight lines - 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 #434 - tests ability to draw 5-mod(x-1) and x+3 - Standard
- Teaser #277 - tests drawing quadratics and straight lines to find a maximum - Standard
- Teaser #259 - tests finding a shared surd root of a line, quadratic and cubic - Standard
- Teaser #474 - tests ability to solve two modulus linear inequalities and deduce a maximum of mod(y-x) - Standard
- Teaser #197 - tests ability to find number of solutions to e^(2x)+x-3=0 in an interval by drawing a straight line - Medium
- Teaser #24 - tests finding the equation of a circle given its gradient y=mx+c - Medium
- Teaser #393 - tests understanding of how various straight lines are represented on a graph - Medium
- Teaser #363 - tests understanding of how various straight lines are represented on a graph - Medium
- Teaser #333 - tests understanding of how various straight lines are represented on a graph - Medium
- Teaser #126 - tests how to find the equation of the straight line gradient of a fairly complex function at the origin - Medium
- Teaser #408 - tests how to find the centre of three straight lines weighted by their length - Quite Tough
TMUA Past Questions involving Straight Lines: SP p1 q3; SP p1 q14; 2016 p1 q3; 2016 p2 q8; 2016 p2 q17; 2017 p1 q3; 2018 p1 q11; 2018 p1 q14; 2018 p2 q11; 2019 p1 q18; 2020 p1 q17; 2020 p2 q1; 2021 p1 q1; 2021 p1 q8; 2021 p2 q2; 2021 p2 q7; 2021 p2 q16; 2022 p1 q20; 2022 p2 q5; 2022 p2 q13; 2023 p1 q2; 2023 p1 q13; 2023 p1 q16; 2023 p2 q7; 2023 p2 q14
Practice makes perfect - good luck in your studies!