tmua.fyi Mock Paper 2 (2)
20 questions · 75 min · Difficulty 25 · by tmua.fyi
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Questions in this paper
- Question 1Exactly one of the following statements is true. Which one?
- Question 2Consider the statement: if a quadrilateral is a square then it has four equal sides.' Which of the following is its converse?
- Question 3The statement ∀ x∈mathbb R, ∃ y∈mathbb R such that xy=1' is false. Which of the following is its negation?
- Question 4The line y=mx+c (with c≠0) and the circle x^2+y^2=a^2 (with a>0) are given. Consider statement P: the line is tangent to the circle', and…
- Question 5To prove that √2 is irrational, a student writes √2=frac pq in lowest terms and correctly deduces that p and q are both even. What makes…
- Question 6For a real number x, consider statement P: x^2<9', and statement Q: x<3'. Then P is:
- Question 7Consider the following argument. Line 1: frac14>frac18. Line 2: (frac12)^2>(frac12)^3. Line 3: Taking log_(10) of both sides…
- Question 8Consider the claim: for every positive integer n, the value n^2+n+1 is odd.' Which of the following is a counterexample?
- Question 9Which of the following statements are true? I: for every real x>0, there is a real y with y^2=x. II: there is a real y such that for every…
- Question 10How many ordered pairs (x,y) of positive real numbers satisfy both log_2 x+log_2 y=5 and x+y=12?
- Question 11For a positive integer n, the statement n^2≡1pmod8' is true if and only if:
- Question 12A sequence is defined by u_1=2, u_2=3 and u_(n+2)=fracu_(n+1)u_n. Find u_(2025).
- Question 13Three boxes each carry a label. Exactly one box contains a prize, and exactly one of the three labels is true. Box 1 reads the prize is in…
- Question 14Integers a,b and c are such that a+b,b+c and c+a are all even. Which of the following must be true? I: a,b and c all have the same parity…
- Question 15What is the minimum value of frac12+cos x over all real x?
- Question 16In the expansion of (x^p+x^(-q))^n, where p,q and n are positive integers, consider statement P: the expansion has a term independent of…
- Question 17Which of the following is the smallest?
- Question 18Given that ∫_0^2 f(x) d x=7, find ∫_0^2 f(2-x) d x.
- Question 19How many integers from 1 to 100 inclusive are divisible by neither 2 nor 3?
- Question 20For which real values of k does the equation x^4+kx^2+1=0 have at least one real solution?