tmua.me Medium Set D Paper 2
20 questions · 75 min · Difficulty 47 · by tmua.me
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Questions in this paper
- Question 1The positive real numbers a and b satisfy a:b=3:2. What is the value of (dfrac1a-dfrac1b)/(dfrac1a+dfrac1b) ?
- Question 2A sequence has at least three terms, all of which are positive real numbers. Consider the statement: If the sequence is both an arithmetic…
- Question 3The angle θ satisfies cosθ=-√3sinθ, 0°<θ<180°. What is the value of θ?
- Question 4Consider the following claim about a positive integer n: If n has an even number of positive divisors, then n is even. Which of the…
- Question 5The lines PA and PB are tangents to a circle with centre O, touching it at A and B. The point M is the midpoint of the chord AB. PA=PB=10…
- Question 6Two coins are tossed independently. Their probabilities of landing heads are p and q, where 0<p<1 and 0<q<1. Consider the conditions: - P…
- Question 7The real number x satisfies log_2((x)/(8))=√(log_2(8x)). What is the value of x?
- Question 8Let a and b be nonzero real numbers such that a+b and a^3+b^3 are rational. A student gives the following proof that ab is rational. 1…
- Question 9A sequence is defined by u_1=1, u_(n+1)=2u_n+n (n≥1). It is given that u_(11)=3060. What is the value of u_1+u_2+…+u_(10)?
- Question 10Let x and y be positive real numbers. Consider the statements - P: x≥2 and y≥2. - Q: xy≥ x+y. Which of the following correctly describes P…
- Question 11Let a be a real number with 0<a<1. The total area between the curve y=(x^2-1)/(x^2), the x-axis and the lines x=a and x=1/a is 4. What is a?
- Question 12A circle has centre (h,k) and positive radius. Consider the statements - P: Both h and k are rational. - Q: The circle passes through at…
- Question 13What is the total length of the parts of the range 0≤θ 1+sinθ hold?
- Question 14A nonempty collection C consists of functions from the real numbers to the real numbers. Consider the statement: > For every function f in…
- Question 15Two lamps, X and Y, are initially off. Each switches on once, at a time between 0 and 6 minutes. Their switching-on times x and y are…
- Question 16For a non-degenerate triangle, consider the statements - P: Its side lengths, written from shortest to longest, form an arithmetic…
- Question 17Two circular wheels have radii 4 cm and 1 cm, and their centres O and P are 6 cm apart. A thin belt is pulled taut around the outside of…
- Question 18A list contains 20 numbers, each of which is 0, 2, 6 or 9. Exactly five of the numbers are 2, and exactly three are 9. The median of the…
- Question 19Let n≥3, and let a_1 a_n-a_2>…>a_n-a_(n-1). *[Missing argument]* This establishes a_(n-1)-a_i=a_n-a_(i+1) (1≤ i≤ n-2). Rearranging shows…
- Question 20For a real constant a, define f(x)=x^3+ax for all real x. It is known that f(x+1)>f(x) for every real x. Consider the statements - I…