Beyond Horizon Set 4 Paper 1
20 questions · 75 min · Difficulty 35 · by Beyond Horizon
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Questions in this paper
- Question 1Find the area bounded by the straight lines x=-1 and x=1 and the graphs of f(x) and g(x), where f(x)=x^3 and g(x)= x^5&if -1≤ x≤0, x&if 0≤…
- Question 2The largest volume of a cube that can be enclosed in a sphere of diameter 2 cm, is, in cm^3,
- Question 3If α, β are the roots of ax^2+bx+c=0, then the equation whose roots are α^2, β^2 is
- Question 4Evaluate the following sum (1·1!)+(2·2!)+(3·3!)+…+(50·50!).
- Question 5The number of distinct points common to the curves x^2+4y^2=1 and 4x^2+y^2=4 is
- Question 6In a parallelogram PQRS, P is the point (-1,-1), Q is (8,0) and R is (7,5). Then S is the point
- Question 7How many real solutions are there to the equation 2tan^4x-5tan^2x+3=0 in the interval 0≤ x<2π?
- Question 8Given that (dy)/(dx)=4x^2-(3-2x)/(x^3), x≠0 and y=6 when x=1, find y in terms of x.
- Question 9Evaluate Σ_(n=1)^(50)log_(10)2^(1-n).
- Question 10In the expansion of (a+bx)^4 the coefficient of x^3 is 4 times the coefficient of x^2. Given that a and b are non-zero positive integers…
- Question 11The functions f and g are given by f(x)=4x^2+10x+5 and g(x)=x^3+5x^2+8x-10. What is the complete set of values of x for which one of the…
- Question 12Find the value of ∫_1^5frac4-3xx√(x) dx.
- Question 13Find the number of solutions of the equation xsin3x=cos x in the interval 0≤ x≤3π.
- Question 14The number of ways in which three non-negative integers n_1, n_2, n_3 can be chosen such that n_1+n_2+n_3=10 is
- Question 15Find the complete set of values of the constant c for which the cubic equation x^3-3x+c=0 has three distinct real solutions.
- Question 16In the interval 0≤ x≤2π, the equation sin(3cos(3x)+1)=0 has exactly
- Question 17An equilateral triangle has centre O and side length 2. A straight line through O intersects the triangle at two distinct points P and Q…
- Question 18What is the area of the polygon formed by all the points (x,y) in the plane satisfying the inequality |x-2|+|y-2|≤8?
- Question 19Let A be a point on the circle with the equation x^2+y^2=4, and let B be a point on the circle with the equation x^2+y^2=9. If the angle…
- Question 20What is the degree of the following polynomial (d^2)/(dx^2)[(3x-2)^4(2-x)^5]+(d)/(dx)[(3x+2)^4(4x^2-3)^2]?