tmua.me Medium Set A Paper 2
20 questions · 75 min · Difficulty 46 · by tmua.me
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Questions in this paper
- Question 1The real numbers a and b satisfy a+b=6, ab=7. What is the value of frac ab+frac ba ?
- Question 2Consider the following claim about nonzero real numbers a and b: If a frac1b. Which of the following is a counterexample to this claim?
- Question 3The graphs y=√(x+4) y=2-x intersect at P. What are the coordinates of P?
- Question 4Let f(x)=x^2+px+q, where p and q are real constants, and suppose that f(x)=0 has two distinct real roots. Consider the statements llP:&…
- Question 5For some positive real number x, the two roots of t^2-6t+k=0 are log_2 x and log_2(x+12). What is the value of k?
- Question 6A function f is defined for all real numbers. Consider the statement: For every real x, if x 3, then f(x)>1. Which of the following…
- Question 7Triangle ABC has base BC=12 and perpendicular height 8. The vertices D and E of rectangle DEFG lie on BC, with G on AB and F on AC, as…
- Question 8Let a and b be positive real numbers. Consider the statements - P: a+b≤4. - Q: (a+1)(b+1)≤9. Which of the following is correct?
- Question 9What is the area of the region consisting of all points (x,y) satisfying x≥0, y≥0, y≤ x^2, x+y≤2 ?
- Question 10Let a and b be distinct positive real numbers satisfying a+frac1a=b+frac1b. A student gives the following proof that a+b>2. 1. Multiplying…
- Question 11A sequence has eight terms, each equal to 0 or 1. Exactly three terms are equal to 1, and no two of these are consecutive. How many such…
- Question 12For a real constant k, the function f is defined for all real x by f(x)=x^3+3x^2+kx. Consider the statements - P: k≥3. - Q: For all real…
- Question 13A fair six-sided die, numbered 1 to 6, is rolled four times independently. Given that the largest result is exactly 2 greater than the…
- Question 14A function f assigns a real number to each positive integer. Consider the statement: For every positive real number a, there is a positive…
- Question 15What is the sum of cos^2θ over all the distinct solutions of cos^2θ=|sinθ-frac12| for which 0≤θ<2π?
- Question 16Let f(x)=ax^2+bx+c, where a, b and c are real constants and a≠0. Consider the condition the stationary point of y=f(x) lies above the…
- Question 17The function F is defined for all real x by F(x)=∫_0^x |t^3-4t| dt. What is the product of the x-coordinates of all the stationary points…
- Question 18The functions f and g are defined for all real numbers, take real values, and satisfy f(g(x))=x for every real x. Consider the following…
- Question 19The function f is defined for all real numbers. The graph y=-2f(3-x)+5 has a unique minimum at (1,-7). At which point does the graph…
- Question 20A student begins a proof that there are no positive integers a and b satisfying a^2+b^2=3ab. Assume that a solution exists, and choose one…