tmua.me Medium Set F Paper 2
20 questions · 75 min · Difficulty 54 · by tmua.me
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Questions in this paper
- Question 1Consider the following claim about positive real numbers x and y: > If x and y each round to 2 to the nearest integer, then x+y rounds to 4…
- Question 2The real numbers a and b satisfy 3a+2b=7, 2a+3b=8. What is the value of a^2-b^2?
- Question 3The graph y=(2x+1)/(x-3) (x≠3) has no point in common with the horizontal line y=k. What is the value of k?
- Question 4For a particular real number x, consider the statement S: If x^2 1. Which of the following statements about x is logically equivalent to S?
- Question 5For how many positive integer values of k does the equation 9^x-8·3^x+k=0 have two distinct real solutions for x, one positive and the…
- Question 6Let a and b be real numbers. Consider the statements - P: a≥|b|. - Q: a(x^2+1)+2bx≥0 for every real number x. Which of the following…
- Question 7Triangle ABC is right-angled at A, with AB=8 and AC=6. A semicircle with centre O lies inside the triangle. Its diameter lies on BC, and…
- Question 8A list consists of five distinct positive real numbers. One number is removed, leaving a list of four numbers. Consider the statements - P…
- Question 9A sequence is defined by u_1=3, u_(n+1)=u_n+(-1)^(n+1)n n≥1. What is the sum of all the positive terms among u_1,u_2,…,u_(20)?
- Question 10Let a and b be positive real numbers satisfying a+b+ab=3, and write s=a+b. A student gives the following proof that ab≤1. 1. Since…
- Question 11Three fair six-sided dice, each numbered 1 to 6, are rolled independently. Given that the largest of the three scores occurs at least…
- Question 12A function f is defined for every real number. Consider the statement: > For every real number k>0, there exist distinct real numbers x and…
- Question 13A particle moves along a straight line. At time t seconds its coordinate, in metres, is s(t)=(t^2-5t+4)/(t), 1≤ t≤4. What is its average…
- Question 14Let a and b be positive integers. Consider the statements - P: a and b are consecutive integers. - Q: The highest common factor of a+b and…
- Question 15A triangle has vertices (0,0), (6,0) and (0,6). A straight line ℓ passes through the interior of the triangle. Consider the statements - P…
- Question 16For which real values of k does the equation sin^2θ-(k+1)sinθ+(k^2)/(4)=0 have exactly four distinct solutions satisfying 0≤θ≤2π?
- Question 17A finite set of points in the plane is not contained in a straight line. The following proof shows that some straight line contains exactly…
- Question 18Two lists of real numbers have numbers of entries in the ratio 3:2. Their means are 20 and 12.5, respectively. One entry is moved from the…
- Question 19Four distinct real numbers a,b,c,d satisfy a+b+c+d=0, a^3+b^3+c^3+d^3=0. Which of the following statements must be true? - I. The median of…
- Question 20A square ABCD has side length √2. Four circles, each of radius 1, are drawn with centres at A, B, C and D. What is the area of the part of…