tmua.fyi Paper 2 Challenge 2
20 questions · 75 min · Difficulty 35 · by tmua.fyi
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Questions in this paper
- Question 1Which of the following is a counterexample to the claim that n^2+n+41 is prime for every positive integer n?
- Question 2Consider the statement: if a and b are both rational then a+b is rational. Which of the following is its contrapositive?
- Question 3For the quadratic ax^2+bx+c with a≠0 and a,b,c real, the condition ac<0 is
- Question 4Consider these three statements about real numbers. P: for every x there exists y such that y^2=x. Q: there exists x such that xy=0 for…
- Question 5The numbers 1,2,3,…,2026 are written on a board. Repeatedly, two of the numbers, a and b, are rubbed out and |a-b| is written in their…
- Question 6The following argument is offered, where a and b are non-zero real numbers. (1) &a=b (2) &a^2=ab (3) &a^2-b^2=ab-b^2 (4) &(a-b)(a+b)=b(a-b)…
- Question 7Which statement best justifies the claim that n^3-n is divisible by 6 for every integer n?
- Question 8Consider the claim: if 3 divides a^2+b^2 then 3 divides a and 3 divides b, where a and b are integers. Which of the following is correct?
- Question 9A sequence (a_n) and a number L are given. Consider the statement for every ε>0 there exists N such that |a_n-L| N. Which of the following…
- Question 10Which of the following establishes that a 10×10 board cannot be tiled by 1×4 pieces, each of which covers four squares in a row or in a…
- Question 11The diagram shows a sketch of y=f'(x), the derivative of a function f defined for all real x. The curve meets the x-axis at x=-2 and x=1…
- Question 12Five points are placed inside a square of side 2. Which argument shows that some two of them are a distance at most √2 apart?
- Question 13On an island there are 13 red, 15 green and 17 blue chameleons. Whenever two chameleons of different colours meet, both change to the third…
- Question 14The inequality x^2+bx+c>0 holds for every real x if and only if
- Question 15Two squares at opposite ends of a diagonal are removed from an 8×8 board, as shown. Can the remaining 62 squares be covered exactly by 31…
- Question 16Let S be a set of ten distinct positive integers, each less than 100. Which of the following must be true?
- Question 17Consider the statement for all real x, if x>1 then x^2>x. Which of the following is correct?
- Question 18How many of the ten digits can occur as the final digit of a perfect square?
- Question 19For positive real a and b, which single fact is enough to prove that frac ab+frac ba≥2?
- Question 20Consider the statement: for every integer n such that n^2+n is odd, n is a multiple of 7. Which of the following is correct?