Clavis TMUA Set B Paper 2
20 questions · 75 min · Difficulty 27 · by Clavis
Read the questions freely. Sign in to answer them, start a timed paper and save your progress.
Questions in this paper
- Question 1The function f is defined for x>0 by f(x)=frac(2x-3)^2√(x). Find the value of f'(1).
- Question 2Find the value of ∫_0^2(3x-1)^2 dx.
- Question 3Consider the following claim: For all real numbers x, if x^2>x then x>1. Which of the following is/are a counterexample to the claim? - I…
- Question 4Let n be a positive integer, and consider the two statements: P: n^2 is a multiple of 9 Q: n is a multiple of 3 Which one of the following…
- Question 5Let n be a positive integer, and let P be the statement if n is a multiple of 10, then n is a multiple of 5 and n is even. Which of the…
- Question 6Consider the following statement (*) about a real number k: (*) For all real numbers x, x^2+kx+k>0. What is the complete set of values of k…
- Question 7Here is an attempted proof of the following claim. If sinθ=cosθ then θ=fracπ4. - (I) Suppose sinθ=cosθ. - (II) Squaring both sides gives…
- Question 8The function f is defined for all real x by f(x)=x|x|. Which of the following statements must be true? - I f is an even function. - II f is…
- Question 9A positive integer is called *tidy* if and only if all of its digits, written in base 10, are different from one another. For example 1023…
- Question 10The line L has equation y=mx+c, and d is the distance from the origin to L. Which one of the following is sufficient on its own to…
- Question 11Which of the following statements is/are true? - I For every positive integer n there is a positive integer m such that m<n. - II There is…
- Question 12Consider the following statement: There is a positive integer n such that for every positive integer m, m+n is composite. Which one of the…
- Question 13Consider the following attempt to solve the equation (x-3)(x+1)=2(x-3). - (I) Dividing both sides by (x-3) gives x+1=2. - (II) Therefore…
- Question 14In this question f is a function defined for all real x. Consider the following three conditions: - I f(-x)=-f(x) for all real x - II…
- Question 15The real numbers a and b satisfy a frac1b
- Question 16Consider the following statement (*) about a real number x: (*) For every real number y, x+y^2≥2y. What is the complete set of values of x…
- Question 17The function f is a polynomial with f(x)>0 for all real x, and the function g is defined for all real x by g(x)=∫_0^x f(t) dt. Which of the…
- Question 18The function f is a non-zero polynomial defined for all real x. Which one of the following is a necessary condition for the equation f(x)=0…
- Question 19A positive integer is called *stepped* if and only if its digits, read from left to right, are strictly increasing. For example 137 and 5…
- Question 20The function f is defined for all real x and satisfies f(x+2)=f(x) all real x. Which of the following statements is/are necessarily true? -…