TMUA (Test of Mathematics for University Admission)

Flashcards for the TMUA (Test of Mathematics for University Admission), split into mathematical knowledge and mathematical reasoning and then by the content specification's own sections, following the specification for assessment in October 2026 and January 2027. The reasoning cards cover logic, proof and identifying errors in arguments, each with a short example.

Adding it gives you your own copy, with every subdeck below. Each card then comes back just before you would forget it, and every one you get right or wrong counts towards your mastery of its topic. You can delete or suspend the parts you are not studying once it is yours.

Some of its cards

• What is a sequence given by a recurrence relation of the form $x_{n+1}=f(x_n)$?

  A sequence in which each term is found by applying a rule to the term before it
• What is speed, as a compound measure?

  Distance travelled divided by time taken
• What is a frequency tree used for?

  Showing how a set of outcomes splits at each stage of an experiment, with the frequency for each branch
• What shape is the graph of $y=mx+c$?

  A straight line with gradient $m$ and y-intercept $c$
• What is the equation of a straight line through $(x_1,y_1)$ with gradient $m$?

  $y-y_1=m(x-x_1)$
• What does the definite integral $\int_a^b f(x)\,dx$ represent when $f(x)\geq0$ on $[a,b]$?

  The area between the curve and the x-axis from $x=a$ to $x=b$
• $a^{m+n}$

  $a^m \times a^n$
• What is direct deductive proof?

  Starting from what is known or given and reasoning step by step to the result, each step following logically from the last
• What is the sine rule for a triangle with sides $a,b,c$ opposite angles $A,B,C$?

  $\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$
• What does the graph of $y=a^x$ look like for $a>1$?

  It stays close to 0 for negative $x$, passes through $(0,1)$, and increases without bound as $x$ increases

And 262 more once you add the deck.