Clavis TMUA Set C Paper 1
20 questions · 75 min · Difficulty 23 · by Clavis
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Questions in this paper
- Question 1Find the value of Σ_(k=0)^(25)sin(30+90k)°.
- Question 2Find the coefficient of x^2 in (1+x)^2+(1+x)^3+(1+x)^4+…+(1+x)^(10).
- Question 3The positive real numbers x and y satisfy log_2(xy)=5 (log_2x)(log_2y)=6. Find the sum of the possible values of x.
- Question 4Find the minimum value of 9^(cos x)-6(3^(cos x))+11 for real x.
- Question 5The following sequence of transformations is applied, in order, to the curve y=x^2: - 1. a translation of 3 units in the positive…
- Question 6The 1st, 2nd and 3rd terms of a geometric progression are also the 1st, 5th and 7th terms respectively of an arithmetic progression. The…
- Question 7Find the coefficient of x^3 in the expansion of (1+x+x^2)^4.
- Question 8Find the shortest distance between the curve y=x^2+3 and the line y=2x-1.
- Question 9Find the sum of all the solutions of 2cos^2x=1+cos x in the range 0°<x<360°.
- Question 10The sequence x_1,x_2,x_3,… is defined by x_1=256 x_(n+1)=√(x_n) for n≥1. Find the least value of n for which x_n<2.
- Question 11A quantity V satisfies (dV)/(dt)=6√(t) t≥0 and V=5 when t=0. Find the value of V when t=9.
- Question 12Find the length of the tangent from the point (7,4) to the circle with equation x^2+y^2-4x+2y-4=0.
- Question 13For how many real values of a does the equation (x-a)(x^2+x+a)=0 have exactly two distinct real solutions for x?
- Question 14The area enclosed between the line y=mx and the curve y=x^3 is 8, where m>0. Find the value of m.
- Question 15The quadratic expression x^2-10x+16 factorises as (x-α)(x-β), where α and β are positive real numbers. Which one of the following has roots…
- Question 16Find the complete set of values of x for which (x+3)(x-1)(2-x)>0 (x+1)(x-4)<0.
- Question 17A set of five distinct positive integers has mean 10 and median 10. Find the largest possible value of the greatest integer in the set.
- Question 18Find the sum of all the solutions of |2cos x|=1 in the range 0≤ x≤2π.
- Question 19Find the positive difference between the two real values of x satisfying (log_3x)^2-log_3(x^4)+3=0.
- Question 20A square has side length 8. A second square is drawn with its vertices at the midpoints of the sides of the first square, a third square is…