tmua.me Medium Set B Paper 2
20 questions · 75 min · Difficulty 53 · by tmua.me
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Questions in this paper
- Question 1For a real number x≠2, what is the value of (x^3-8)/(x-2)-x(x+2) ?
- Question 2A real sequence u_1,u_2,u_3,… has the following property: For every positive integer n, if u_n>0, then u_(n+1)>0. Which of the following is…
- Question 3An angle θ satisfies (cosθ)/(1-sinθ)=2. What is the value of sinθ?
- Question 4A triangle has side lengths a, b and c, where a≤ b≤ c. Consider the statements - P: a+b>√2 c. - Q: The angle opposite the side of length c…
- Question 5Consider the following claim about positive integers m and n: If m+n is prime, then mn+1 is prime. Which of the following is a…
- Question 6A bag contains four balls: two red, one blue and one green. Three balls are drawn one after another without replacement, with each…
- Question 7A sequence is defined by u_1=1, u_(n+1)=3u_n+2 (n≥1). What is the value of frac1u_1+1+frac1u_2+1+frac1u_3+1+frac1u_4+1+frac1u_5+1 ?
- Question 8A rectangular array of real numbers has at least three rows and at least three columns. Consider the statement: > Each row contains at…
- Question 9Let a and b be positive real numbers. Consider the conditions P: a+b is rational, Q: a^2+b^2 is rational. Which of the following is correct?
- Question 10In triangle ABC, the vertex A has coordinates (0,4) and M is the midpoint of AC. The line BM has equation y=x+1. The line through B…
- Question 11What is the sum of the squares of all the distinct real solutions of log_2(x^2-3x+2)+log_2(x^2-5x+6)=1?
- Question 12Let a be a real number and let b be a positive real number. Consider the conditions P: a^2+b^2≤ 1, Q: ax+b≤√(x^2+1) every real number x…
- Question 13The graph y=f(x), where f is a quadratic polynomial, lies above the x-axis for 0≤ x≤2. The area between the graph, the x-axis and the lines…
- Question 14A student attempts to prove that the equation x^3-x=6 has no positive real solution. 1. Suppose that x>0 is a solution. 2. Dividing the…
- Question 15The vertices of a square ABCD are labelled in order. A point P lies strictly inside the square and satisfies PA=√5, PB=√(13), PD=√(17)…
- Question 16Two coins are tossed independently. Their probabilities of landing heads are p and q, where 0<p<1 and 0<q<1. Consider the statements - P…
- Question 17What is the value of Σ_(n=1)^(20)(2n)/(n^4+n^2+1) ?
- Question 18A real-valued function f, defined for every real number, satisfies f(x)+f(x+1)=2x+1 for every real x. Consider the statements - I…
- Question 19Thirty temperatures have a mean of 18°mathrm C. When the temperatures are entered into a computer, ten are entered using their numerical…
- Question 20Let a_1,…,a_n be real numbers, where n≥2 and a_1+…+a_n>0. A student wants to prove that some cyclic rearrangement of the list has every…