TMUA Fractions, Decimals, Percentages, Ratios etc

TMUA rarely tests these topics directly, it is expected that all test takers will be familiar with these areas of maths. Of course pretty much every question indirectly tests knowledge of these topics as part of a bigger question. TMUA occasionally tests other 'basic' areas of maths, such as primes and prime factors, standard form and non decimal bases (binary, hexadecimal) - familiarity is again essential.

For those so interested, we offer both one to one TMUA coaching on Fractions, Decimals, Percentages, Ratios etc, as well as online group coaching via Zoom - 'TMUA Prerequisite Maths One' is Session #1 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 fractions, decimals, percentages, ratios etc - 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 #61 - tests basic understanding of Venn Diagrams given percentages - Mild
• Teaser #316 - tests ability to raise to positive and negative powers, producing fractions - Fairly Mild
• Teaser #15 - tests understanding of converting a recurring decimal to a fraction - Fairly Mild
• Weekend Workout #6 - tests general ability to manipulate percentages and fractions - Fairly Mild
• Teaser #413 - tests knowledge of finding undefined values for a quadratic fraction as denominator of a fraction- Standard
• Weekend Workout #1 - tests ability to evaluate a power tower of fraction exponents - Standard
• Teaser #13 - tests understanding of changing log base from 3.5 and simplifying - Standard
• Teaser #258 - tests a summation of numbers in various bases - Standard
• Teaser #314 - tests hexadecimal subtraction - Standard
• Teaser #233 - tests adding numbers in different bases by spotting a pattern - Standard
• Teaser #44 - tests how to sum a list of binary numbers - Standard
• Teaser #110 - tests understanding of percentage increase and decrease - Standard
• Teaser #94 - tests understanding of percentage increases (calculation too hard for TMUA, method useful) - Standard
• Teaser #135 - tests ability to extract ratio and surface area of cuboid information to answer the word problem - Standard
• Teaser #121 - tests how to find the radius of a reduced sphere using ratios - Standard
• Teaser #78 - tests ability to work out probabilities in a fairground game - Standard
• Teaser #89 - tests distance, speed and time with a common trap - Standard
• Teaser #147 - tests how to find tan 2x given tan(x/2) - Standard
• Teaser #102 - tests ability to simplify a sum of large powers of 2 - Standard
• Teaser #62 - tests calculating probability of false positive at a Taylor Swift concert - Standard
• Teaser #11 - tests ability to evaluate 0.25^0.25 - Standard
• Teaser #85 - tests understanding of finding % of % of % of a number - Standard
• Weekend Workout #18 - tests ability to convert recurring decimals to fractions - Standard
• Teaser #97 - tests understanding of probability two balls picked are different colours given ratios of balls in bag - Standard
• Teaser #396 - tests basic manipulation of fractions within a question on geometric series - Standard
• Teaser #287 - tests knowledge of sin and cos double angles and calculating them with fraction and decimal manipulation - Standard
• Teaser #425 - tests ability to spot two sets of similar triangles to find a length within a trapezium - Medium
• Teaser #51 - tests ability to manipulate percentages to solve a followers puzzle - Medium
• Teaser #427 - tests ability to arrange various expressions in increasing order by clever approximations - Medium
• Teaser #435 - tests ability to use formula for tan(2x) to find tan(pi/12) - Medium
• Teaser #81 - tests ability to extract information and put on Venn Diagram and solve - Medium
• Teaser #424 - tests ability to find fraction of an interval where sin(3x)>=1/2 - Medium
• Teaser #160 - tests knowledge of calculating P('A|'B) using Venn Diagram - Medium
• Teaser #414 - tests manipulation of logs and then recognising coprime numbers are the lowest form of a fraction - Medium
• Teaser #68 - tests ability to extract equation from word problem and solve - Medium
• Teaser #426 - tests understanding of how to solve an exponential equation with x being a power of a power of a power - Medium
• Teaser #161 - tests ability to evaluate a fraction involving power towers - Medium
• Teaser #399 - tests ability to manipulate percentages as part of a question on probability - Medium
• Teaser #225 - tests ability to evaluate a power tower including fractions - Medium
• Teaser #370 - tests ability to manipulate percentages as part of a question on probability - Medium
• Teaser #106 - tests understanding of how to calculate compound interest (the final calculation is beyond TMUA) - Medium
• Teaser #331 - tests ability to enter percentage data into a Venn Diagram and work out a probability using basic combinatorics - Medium
• Teaser #325 - tests knowledge of a) recognising and b) summing an arithmetic/geometric series, involving fraction manipulation - Medium
• Teaser #299 - tests knowledge of a) recognising and b) summing an arithmetic/geometric series, involving fraction manipulation - Medium
• Teaser #444 - tests ability to solve two trig inequalities and find the fraction of a range satisfying both - Quite Tough
• Teaser #503 - tests understanding of how to find when an integral approximation of y=sin^2(x) underestimates the area - Quite Tough

[Note: We also have a 'Fractions, Decimals and Percentages' 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).]

Practice makes perfect - good luck in your studies!