TMUA Geometry and Shapes
This is a very common topic indeed in TMUA, testing everything from properties of shapes such as rhombus, kites and parallelograms, to their areas, volumes, centres etc.
TMUA occasionally tests on polygons and it is vital to be proficient in matters such as interior/exterior angles, and what defines (and doesn't define) a regular/irregular polygon.
Certain topics are so commonly tested on TMUA we have separated them for more efficient study and revision, namely 'Circles and Circle Equations', and 'Triangles and Congruency'. Vectors are rarely (if ever) tested in TMUA, though there is no reason that vector techniques can't be used to solve certain TMUA geometry questions (after all the exam is multiple choice).
For those so interested, we offer both one to one TMUA coaching on geometry and shapes, as well as online group coaching via Zoom - 'TMUA Geometry and Shapes' is Session #12 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 geometry and shapes (excluding 'Circles and Circle Equations', and 'Triangles and Congruency') - 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 #378 - tests finding the distance between two points on a composite shape - Standard
- Teaser #41 - tests finding area of triangle given rhombus and square - Standard
- Weekend Workout #7 - tests finding the area of triangle inscribed in a circle inscribed in a square - Standard
- Teaser #135 - tests ability to extract ratio and surface area of cuboid information to answer the word problem - Standard
- Teaser #22 - tests ability to find coordinates of intersection of a parabola and circle - Standard
- Teaser #95 - tests knowledge of how to split a pyramid in two by volume - Standard
- Teaser #103 - tests understanding of symmetry of a quadratic to find the area of a triangle - Standard
- Teaser #121 - tests how to find the radius of a reduced sphere - Standard
- Teaser #99 - tests ability to apply Heron's Formula to a triangle word problem (the final calculation is beyond TMUA) - Standard
- Teaser #43 - tests knowledge of ellipse and circle characteristics - Standard
- Teaser #218 - tests using vector cross product to find the area of a triangle in 3D space - Standard
- Teaser #425 - tests ability to spot two sets of similar triangles to find a length within a trapezium - Medium
- Teaser #93 - tests finding expected score on a dartboard based on probability of landing in certain areas - Medium
- Teaser #498 - tests how to establish when both axes are tangent to a circle - Medium
- Teaser #393 - tests how to find the area bound by inequalities on a graph - Medium
- Teaser #172 - tests how to find the area of a square inside multiple circles using symmetry - Medium
- Teaser #143 - tests how to find the maximum area of a rectangle inscribed in a semicircle - Medium
- Teaser #185 - tests manipulation of position vectors to see when two particles reach their closest point - Medium
- Teaser #496 - tests criteria for which a triangle is described uniquely - Medium
- Teaser #389 - tests how to find the centre of a composite of basic shapes - Medium
- Teaser #203 - tests how to find the radius of a circle inscribed in an equilateral triangle - Medium
- Teaser #363 - tests how to find the area bound by inequalities on a graph - Medium
- Teaser #361 - tests how to find the centre of a composite of basic shapes - Medium
- Teaser #333 - tests how to find the area bound by inequalities on a graph - Medium
- Teaser #408 - tests how to find the centre of solid and wire triangles - Quite Tough
TMUA Past Questions on Geometry and Shapes (excluding 'Circles and Circle Equations', and 'Triangles and Congruency'): SP p1 q12; 2016 p1 q12; 2016 p1 q20; 2016 p2 q16; 2017 p1 q3; 2017 p1 q6; 2017 p1 q9; 2017 p1 q17; 2017 p2 q2; 2018 p1 q19; 2018 p2 q5; 2019 p2 q10; 2020 p1 q16; 2020 p2 q7; 2021 p2 q2; 2021 p2 q7; 2022 p1 q4; 2022 p1 q14; 2022 p1 q15; 2022 p2 q11; 2022 p2 q19; 2023 p1 q5; 2023 p2 q9
Practice makes perfect - good luck in your studies!