James Chen TMUA Paper 2
20 questions · 75 min · Difficulty 51 · by James Chen
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Questions in this paper
- Question 1Rick Astley claims that he is never gonna give you up. Which of the following is/are necessary conditions to disprove his claim? - I. He…
- Question 2Vertical lines bisect each of the letters: H,O,T,T,O,G,O. The number of them which are lines of symmetry of the letters is P. Now, vertical…
- Question 3Taylor claims to the boy next door: “You belong with me”. A popular cheerleader hears the claim and responds: “There exists a moment in…
- Question 4How many pairs of integer solutions (x,y) are there to the equation 2^x+2^y=160?
- Question 5Only Akshith, James, Pranav, Rujul, and Siddhant are in a room. The probability that at least two of them share a birthday is P. The…
- Question 6Let the sequence u_n be defined such that u_(n+1)=u_nsin^(67)(x)cos^(69)(x) and u_1=67. For what range of values of x, in degrees, does u_n…
- Question 7How many solutions are there to the equation e^xsin x=1 with 0≤ x≤2π?
- Question 8Consider the claim that (x+y)/(2)>√(xy) for all positive x,y. Here is an attempted proof of this claim: (x-y)^2&>0 &&(1) x^2+y^2-2xy&>0…
- Question 9The Subway Sequence is defined as: u_0=She', u_1=Got', u_2=Away', and u_n=u_(n-3) for n≥3. What is u_((2025+2026+2027+…+2100))?
- Question 10A student mistakenly believes that (x+y)^2=x^2+y^2. The student attempts to evaluate P^2, where P=a+b. The difference between the correct…
- Question 11When setting a TMUA question, I write n statements, where none of them, some of them, or all of them are true. I then ask which of the…
- Question 12Which of these numbers is the smallest?
- Question 13Five students sit the TMUA and achieve integer scores. For their five scores, the following are true: - There are exactly two different…
- Question 14The function f(x) is continuous and defined for all real x. Which of the following conditions is/are sufficient for the function to have…
- Question 15A student attempts to prove, by contradiction, that √[n]2 is irrational for all integers n>2. Their proof begins as follows: Assume…
- Question 16What is the negation of the following statement? For all ε>0, there exists δ>0 such that if 0<|x-a|<δ then |f(x)-L|<ε.
- Question 17Alice and Bob are playing a game of Number Wordle. The answer they are trying to guess is a 5 digit number with no repeated digits. When…
- Question 18The cubic polynomial x^3-ax^2+bx-c is equivalent to (x-a)(x-b)(x-c), where a,b,c are real non-zero constants. What is the complete set of…
- Question 19An equilateral triangle with side-length 1 is drawn, and 5 points are plotted in or on the triangle. What is the minimum value of d such…
- Question 20The equation 5^2-5(2x^2+1)+x^4-x=0 has four solutions, two of which can be written as frac1Q(-1±√ P) and the other two of which can be…