tmua.me Medium Set E Paper 2
20 questions · 75 min · Difficulty 50 · by tmua.me
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Questions in this paper
- Question 1What is the value of frac3^(21)-3^(20)3^(20)+3^(19) ?
- Question 2Consider the following claim about positive numbers a, b and c: If a, b and c are the side lengths of a triangle, then a^2, b^2 and c^2 are…
- Question 3Consider the statement: If a quadrilateral is a square, then its diagonals are perpendicular and equal in length. Which of the following is…
- Question 4How many integer values of x satisfy x=2sin((π x)/(6))?
- Question 5Let b and c be integers. Consider the statements ll P:& b^2-8c is the square of a positive integer, [3pt] Q:& 2x^2+bx+c=0 has two distinct…
- Question 6How many integer values of x satisfy log_(1/2)(x^2)≥log_(1/2)(2x+3)?
- Question 7The curve C has equation y=(x^4-9)/(x^2+3). The tangent to C at the point where x=1 meets the coordinate axes at A and B. What is the area…
- Question 8Let a and b be positive real numbers. Consider the statements - P: 4ab>1. - Q: The line y=ax+b and the curve y=√(x) have no common point…
- Question 9The points A, B and P lie on a circle with centre O. The chord AB has length 12, and P lies on the major arc AB with PA=PB. The area of…
- Question 10A collection contains at least two distinct points in a plane. Consider the statement: > Every point in the collection has another point in…
- Question 11A sequence is defined by u_1=2, u_2=1, u_(n+2)=3u_n every integer n≥1. What is the value of u_1+u_2+…+u_(20)?
- Question 12Three distinct positive real numbers form one data set. A second data set is obtained by taking the reciprocal of each number in the first…
- Question 13A student gives the following argument about f(x)=x-frac1x, x≠0. 1. Differentiating gives f'(x)=1+dfrac1x^2. 2. Hence f'(x)>0 for every…
- Question 14A bag contains two red balls and three blue balls. Two balls are drawn at random, one after the other without replacement, and their…
- Question 15Let a and b be real constants. Consider the statements - P: a≥ b^2. - Q: x^4+ax^2+bx+1>0 for every real number x. Which of the following is…
- Question 16For which real values of k does the equation sinθ+cosθ+|sinθ-cosθ|=k have exactly two distinct solutions satisfying 0≤θ<2π?
- Question 17The polynomial f(x)=x^3+ax^2+bx+c has integer coefficients, and both f(0) and f(1) are odd integers. You may use the fact that any rational…
- Question 18A train is 120 m long. At a constant speed it takes 30 seconds to pass completely past a straight platform. At three-quarters of that…
- Question 19A sector of angle θ radians is removed from a circular sheet of radius 6 cm, where 0<θ<2π. The straight edges of the remaining sector are…
- Question 20Ten distinct real numbers are written in a row. A *subsequence* is a choice of some of these numbers that keeps their original order. The…