TMUA · Paper 2: Mathematical Reasoning

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It is given that if the sequence is geometric, then its ratio of consecutive terms is constant. It is also given that the ratio of consecutive terms of the sequence is not constant. Which of the f…
It is given that if $n$ is divisible by 12 then $n$ is divisible by 4, and that if $n$ is divisible by 4 then $n$ is even. Which of the following must be true?
It is given that $x$ is positive or $x$ is a root of $x^{2} + x = 0$ , and that $x$ is not positive. Which of the following must be true?
It is given that if a positive integer $N$ is a perfect square then $N$ is divisible by 4 or $N$ is odd. It is also given that $N$ is not divisible by 4. Which of the following must be true?
A function $g$ is such that: if $g$ is increasing, then $g (1) < g (2)$ ; and if $g$ is not increasing, then $g (1) < g (2)$ is not guaranteed. In fact, it is given that $g (1) \geq g (2)$ , and that $g$ i…
It is given that $a$ is positive if and only if $b$ is positive, and that $b$ is not positive. Which of the following must be true?
It is given that exactly one of the following two statements is true: 'the series converges' and 'the series diverges to infinity'. It is also given that the series converges. Which of the following m…
It is given that if $P$ then $Q$ , and if $R$ then not $Q$ . Which of the following must be true?
It is given that either $p$ is prime or $p$ is divisible by 3, that if $p$ is prime then $p$ is odd, and that $p$ is even. Which of the following must be true?
It is given that if the discriminant is zero, the quadratic has a repeated root; that the quadratic does not have a repeated root; and that the quadratic has real roots if the discriminant is positive…
It is given that if $a$ and $b$ are both positive then $a + b$ is positive, and that $a$ is positive and $a + b$ is not positive. Which of the following must be true?

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