TMUA · Paper 2: Mathematical Reasoning

Truth of statements and their converses

11 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 11 questions

For real $x$ , consider: *'If $x^{2} = 9$ , then $x = 3$ .'* Which of these is correct?
For whole numbers $n$ , consider: *'If $n$ is divisible by 4, then $n$ is even.'* Which of these is correct?
For real numbers $a$ and $b$ , consider: *'If $a$ and $b$ are both positive, then $ab$ is positive.'* Which of these is correct?
For real $x$ , consider: *'If $x > 2$ , then $x^{2} > 4$ .'* Which of these is correct?
For whole numbers $x$ , consider: *'If $x^{2}$ is odd, then $x$ is odd.'* Which of these is correct?
For whole numbers $n \geq 2$ , consider: *'If $n$ is prime, then $n$ is odd.'* Which of these is correct?
For real $x$ , consider: *'If $∣ x ∣ < 2$ , then $x^{2} < 4$ .'* Which of these is correct?
For real $x$ , consider: *'If $x^{2} - 5 x + 6 = 0$ , then $x = 2$ .'* Which of these is correct?
For real $a$ and $b$ , consider: *'If $a > b$ , then $a^{2} > b^{2}$ .'* Which of these is correct?
For whole numbers $n$ , consider: *'If $n$ is divisible by both 4 and 6, then $n$ is divisible by 12.'* Which of these is correct?
For positive integers $n$ , consider: *'If $n^{2}$ is divisible by 12, then $n$ is divisible by 6.'* Which of these is correct?

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