Hi, I'm Ming Chun So, currently a Cambridge Maths student. I scored a 9.0 in the TMUA, as well as scoring the highest step scores in the world. I've tutored many people to sit the tmua, and from my experience, these are the most important steps to take when it comes to practice.
Algebraic manipulation and mental arithmetic are the backbone of the TMUA; they need to be fast, accurate, and instinctive. Every second you save on simple manipulation is time you can spend on the harder logic or reasoning parts.
On PrepTMUA, you’ll find targeted drills that make this kind of fluency second nature — especially in fraction simplification, expansion, and rearrangement. The goal is to make your algebra clean and automatic so you don’t lose time to basic slips.
When factorising polynomials, don’t waste time doing long division. Learn synthetic division, and once you’ve practised enough, you’ll be able to divide out linear factors in your head without writing any extra working out. The algebra skill sets on PrepTMUA are designed to help you internalise these shortcuts so you can manipulate expressions efficiently and confidently.
Similarly, polish your fraction manipulation, expansion, and simplification skills until you can simplify your working out to make them as efficient as possible. PrepTMUA question explanations often highlight these micro-optimisations — how top performers skip redundant steps while keeping full accuracy.
For calculus, use every shortcut available: when evaluating definite integrals, remember that even and odd function properties can reduce the amount of arithmetic you have to do. Also remember that you won’t need to use any A2 Level techniques, such as substitution or integration by parts. Spotting ways to simplify the integrand or use symmetry will be the way to go for most integrals in the TMUA. PrepTMUA’s custom-written calculus questions focus on symmetry and efficiency, training you to see these opportunities instantly.
Many students overlook the smaller topics in the TMUA specification, but these are where you can stand out from other candidates. For example, make sure you’re completely comfortable with things like the Fundamental Theorem of Calculus and the trapezium rule, as well as being familiar with using basic concepts from number theory such as factors/multiples, gcd and lcm. PrepTMUA’s topic-by-topic coverage ensures you don’t miss these small but high-yield areas — they often make the difference between a good and great score.
On Paper 2, the logic and reasoning questions require consistency and practice. Pick your favourite framework for understanding implication statements (e.g. using arrows, “if… then…” phrasing, or necessary/sufficient conditions) and stick with it. Once you’ve decided, learn how to translate everything into that form. Being systematic means you’ll never get tripped up by 50-50 situations. Then, practice negating statements and finding contrapositives accurately. PrepTMUA’s logic question sets give you consistent practice with these patterns, so you can build habits of clear reasoning under time pressure.
Algebraic manipulation and mental arithmetic are the backbone of the TMUA; they need to be fast, accurate, and instinctive. Every second you save on simple manipulation is time you can spend on the harder logic or reasoning parts.
On PrepTMUA, you’ll find targeted drills that make this kind of fluency second nature — especially in fraction simplification, expansion, and rearrangement. The goal is to make your algebra clean and automatic so you don’t lose time to basic slips.
When factorising polynomials, don’t waste time doing long division. Learn synthetic division, and once you’ve practised enough, you’ll be able to divide out linear factors in your head without writing any extra working out. The algebra skill sets on PrepTMUA are designed to help you internalise these shortcuts so you can manipulate expressions efficiently and confidently.
Similarly, polish your fraction manipulation, expansion, and simplification skills until you can simplify your working out to make them as efficient as possible. PrepTMUA question explanations often highlight these micro-optimisations — how top performers skip redundant steps while keeping full accuracy.
For calculus, use every shortcut available: when evaluating definite integrals, remember that even and odd function properties can reduce the amount of arithmetic you have to do. Also remember that you won’t need to use any A2 Level techniques, such as substitution or integration by parts. Spotting ways to simplify the integrand or use symmetry will be the way to go for most integrals in the TMUA. PrepTMUA’s custom-written calculus questions focus on symmetry and efficiency, training you to see these opportunities instantly.
Many students overlook the smaller topics in the TMUA specification, but these are where you can stand out from other candidates. For example, make sure you’re completely comfortable with things like the Fundamental Theorem of Calculus and the trapezium rule, as well as being familiar with using basic concepts from number theory such as factors/multiples, gcd and lcm. PrepTMUA’s topic-by-topic coverage ensures you don’t miss these small but high-yield areas — they often make the difference between a good and great score.
On Paper 2, the logic and reasoning questions require consistency and practice. Pick your favourite framework for understanding implication statements (e.g. using arrows, “if… then…” phrasing, or necessary/sufficient conditions) and stick with it. Once you’ve decided, learn how to translate everything into that form. Being systematic means you’ll never get tripped up by 50-50 situations. Then, practice negating statements and finding contrapositives accurately. PrepTMUA’s logic question sets give you consistent practice with these patterns, so you can build habits of clear reasoning under time pressure.