What is the TMUA?

A taste of the style — pick an answer to reveal the worked solution.

1. Paper 1 · Applications

   Q1. How many distinct real values of $x$ satisfy $\log_2 x + \log_2(x-2) = 3$?

   A0B1C2D3EInfinitely many

2. Paper 2 · Reasoning

   Q2. Consider the statement: "For every real number $x$, if $x > 2$ then $x^2 > 4$." Which of the following is its negation?

   AThere exists a real $x$ with $x > 2$ and $x^2 \le 4$.BFor every real $x$, if $x \le 2$ then $x^2 \le 4$.CThere exists a real $x$ with $x \le 2$ and $x^2 > 4$.DFor every real $x$, if $x > 2$ then $x^2 \le 4$.EThere exists a real $x$ with $x > 2$ and $x^2 > 4$.

3. Paper 2 · Reasoning

   Q3. It is known that "if it rained, then the match was cancelled." You are told only that the match was cancelled. Which conclusion is logically valid?

   AIt rained.BIt did not rain.CNothing about the rain can be concluded.DIt rained if and only if the match was cancelled.EThe match is never cancelled when it is dry.