tmua.fyi Mock Paper 2
20 questions · 75 min · Difficulty 30 · by tmua.fyi
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Questions in this paper
- Question 1Exactly one of the following statements is true. Which one?
- Question 2Let n be a positive integer. Consider statement P: n is prime', and statement Q: n is of the form 6k±1 for some integer k'. Then Q is:
- Question 3Consider the claim: For every integer n≥2, the value n^2-n+11 is prime.' Which of the following is a counterexample?
- Question 4Let x and y be real numbers. Consider statement P: x+y>0', and statement Q: x^3+y^3>0'. Then Q is:
- Question 5f is a function defined for all real numbers, with f(1)=3 and f(4)=-2. Consider the statements: I: f(x)=0 has a solution with 1<x<4; II…
- Question 6f is a differentiable function. Consider statement P: x=2 is a turning point of f', and statement Q: f'(2)=0'. Then Q is:
- Question 7The following argument claims to show that every real number equals 0. Line 1: Let a=b. Line 2: Then a^2=ab. Line 3: So a^2-b^2=ab-b^2…
- Question 8Consider the statement: If a function g is defined on [0,1], then ∫_0^1 g(x) d x equals the area enclosed between the graph of g and the…
- Question 9Which of the following statements are true? I: There exists a real y such that for all real x, x^2≥ y. II: For all real x, there exists a…
- Question 10How many real solutions with x>0 does the equation (ln x)^2-3ln x+1=0 have?
- Question 11For a positive integer n, let R_n be the repunit consisting of n ones (so R_1=1, R_2=11, R_3=111, and so on). The statement 3 divides R_n'…
- Question 12What is the maximum value of f(x)=2x^3-9x^2+12x+1 on the closed interval 0≤ x≤3?
- Question 13S(x) is a property of a real number x, and exactly one of the following four claims about S is true. Which one? A: S(x) holds whenever…
- Question 14b is a real number, and x=b is a root of the equation bx^2-(b^2+1)x+b=0. Which of the following describes the complete set of possible…
- Question 15What is the maximum value of x+2y subject to x^2+y^2≤5?
- Question 16Consider the statement about an integer n: if n^2 is even then n is even'. Which of the following is its contrapositive?
- Question 17Which of the following statements are true? I: no integer of the form 4k+3 is the sum of two perfect squares. II: the product of two…
- Question 18f is a continuous function and a<b. Consider statement P: f(a) and f(b) have opposite signs', and statement Q: f has a root in the open…
- Question 19For which of these functions is it true that f'(x)>0 for all real x? I: f(x)=x^3. II: f(x)=e^x. III: f(x)=x+sin x.
- Question 20A sequence of integers satisfies u_(n+1)=3u_n-4, with u_1 an integer. Which of the following statements are true? I: u_n-2 is a multiple of…