tmua.me Medium Set D Paper 1
20 questions · 75 min · Difficulty 46 · by tmua.me
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Questions in this paper
- Question 1A sequence is defined by u_n=n(frac34)^(n-1) (n=1,2,3,…). You may use the relation fracu_(n+1)u_n=(3(n+1))/(4n). For which values of n does…
- Question 2The functions f and g are given by f(x)=√(x-1), g(x)=frac1x-3, where each function is defined wherever its formula has a real value. Which…
- Question 3Let n be an integer satisfying 1≤ n<240. The fraction n/240 can sometimes be written as a terminating decimal with exactly three digits…
- Question 4Three faces of a cuboid meet at a vertex. The diagonals of these three faces have lengths √(13), √(20) and 5. What is the volume of the…
- Question 5What are all the real values of x satisfying ∫_1^x (t^2-4t+3) dt=0 ?
- Question 6In triangle ABC, the point D is the midpoint of BC. It is given that ∠ BAD=30°, ∠ DAC=45°. What is the value of AB/AC?
- Question 7For each nonzero real number x, let u=x+frac1x, v=x^2+frac1x^2. You may use the identity v=u^2-2. How many distinct real values of x…
- Question 8The positive integer n is such that the sum of the coefficient of x and the coefficient of x^2 in the expansion of (1+x)^n is 45. What is…
- Question 9Two solid blocks A and B have densities 8 g/cm^3 and 6 g/cm^3, respectively. Their masses are in the ratio 2:3, and the sum of their…
- Question 10For a real constant a, a curve has equation y=fracx^2+ax-a-3√(x), x>0. For which values of a does the curve have both a local maximum and a…
- Question 11The function f is defined for all real x by f(x)=4^x-6·2^x. What is the real solution of f(x+1)-f(x)=9?
- Question 12In triangle ABC, the points A and B have coordinates (0,0) and (6,0). The three lines drawn through the vertices perpendicular to their…
- Question 13The side lengths of a triangle are x, x+1 and 2x-1. Its largest angle is 120°. What is the sum of all possible values of x?
- Question 14A continuous function f satisfies f(0)=f(1)=f(4)=0. Its graph lies above the x-axis for 0<x<1 and below the x-axis for 1<x<4. The area…
- Question 15Coins A and B have probabilities p and q of landing heads, respectively, where 0<q<p<1. All tosses are independent. It is given that…
- Question 16For 1≤ x<4, the function f is defined by f(x)=(x^2-4x)(x^2-4x+6). Which inequality describes the complete set of values of y=f(x)?
- Question 17A circle has centre (2,-3). The line y=2x+1 is tangent to the circle. The other tangent parallel to this line meets the x-axis at P. What…
- Question 18Five real numbers, in increasing order, form an arithmetic progression. Their sum is 15, and the sum of their absolute values is 19. What…
- Question 19Five real numbers x_1,x_2,x_3,x_4,x_5 have mean 3. The ten products formed by choosing two different positions in this list have mean 8…
- Question 20For a real number k, the equations x^2+kx-2=0 x^2+x+k^2-3=0 have exactly one common real solution. What is the sum of all possible values…