tmua.me Medium Set A Paper 1
20 questions · 75 min · Difficulty 43 · by tmua.me
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Questions in this paper
- Question 1The equations x^2+ax+12=0 x^2+(a+3)x+3=0 have a common real solution. What is the value of a?
- Question 2Six real numbers a≤ b≤ c≤ d≤ e≤ f have mean 10. The mean of a,b,c,d is 7, and the mean of c,d,e,f is 12. What is the median of the six…
- Question 3A circle passes through O=(0,0) and A=(8,0). The tangent to the circle at O is the line y=-2x. The line y=x meets the circle again at P…
- Question 4The tangent to the curve y=x^3+ax^2 at the point where x=2 has gradient 4. What is the y-intercept of this tangent?
- Question 5For every positive integer n, the sum of the first n terms of a sequence u_1,u_2,u_3,… is 2n^2+3n. What is the least value of n for which…
- Question 6The equation 2cos^2θ=3sinθcosθ has four distinct solutions θ_1,θ_2,θ_3,θ_4 with 0≤θ<2π. What is the value of sin^2θ_1+si…
- Question 7A function f, defined for all real numbers, satisfies f(x)+2f(1-x)=x^2 for every real x. For which values of the real constant k does the…
- Question 8A fair six-sided die, numbered 1 to 6, is rolled. If the result is 1, 2 or 3, the die is rolled once more and the score is the sum of the…
- Question 9A circle of radius 5 has parallel chords AB and CD of lengths 6 and 8, respectively. The chords lie on opposite sides of the centre O. What…
- Question 10The curve y=f(x) satisfies f'(x)=6x-4. The normal to the curve at the point with x-coordinate 1 passes through (0,5). What is the value of…
- Question 11Nonzero real numbers x, y and z satisfy x+y+z=0, x^2+y^2+z^2=14, x^3+y^3+z^3=-18. What is the value of frac1x+frac1y+frac1z ?
- Question 12What is the coefficient of x^5 in the expansion of (1-x)^4(1+x)^7 ?
- Question 13A point P moves at constant speed around a fixed vertical circle, completing one revolution in 36 seconds. The greatest and least heights…
- Question 14What is the least positive integer N for which N/12 is the square of an integer and N/18 is the cube of an integer?
- Question 15The graph of y=f(x) is shown for -1≤ x≤8, which is the domain of f. Its only zeros are -1, 0, 3 and 8. What is the total length of the set…
- Question 16The circle C has equation (x-3)^2+(y-3)^2=1. Consider all circles whose centres lie in the first quadrant and which are tangent to both…
- Question 17A bag contains three red counters and two blue counters. A counter is chosen at random. If it is red, it is returned to the bag. If it is…
- Question 18A particle moves on a straight line. At time t seconds its coordinate, in metres, is x(t)=t(t-2)(t-5). For how many seconds in total during…
- Question 19A sequence of positive numbers is defined by u_1=frac12, u_(k+1)=(u_k)/(1+u_k) (k≥1). For a positive integer n, u_nu_(n+1)=frac1156. What…
- Question 20For some real constants a and b, the polynomial x^4+ax^3+(a+3)x^2+bx+4 is the square of a quadratic polynomial with real coefficients. What…