Beyond Horizon Set 2 Paper 1
20 questions · 75 min · Difficulty 49 · by Beyond Horizon
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Questions in this paper
- Question 1How many solutions does the equation xtan x=2 have in the interval -3π≤ x≤ 3π?
- Question 2The least possible value of the gradient of the curve y=(3x+b)(x-b)^2 at the point where x=2, as b varies, is:
- Question 3It is given that y=(1+cos x)sin 3x 0<x<π The complete set of values of x for which y is negative is:
- Question 4The function dfrac2-x2√[3]x^2 is defined for all x≠ 0. The complete set of values of x for which the function is decreasing is
- Question 5Find the complete set of values of p for which the equation x^2-3px+y^2-4y-p^2+6p+7=0 describes a circle in the xy-plane.
- Question 6Find the finite area enclosed between the line y=0 and the curve y=x^2-5|x|-24.
- Question 7For any real number x, let lfloor xrfloor denote the greatest integer m such that m≤ x. Evaluate the following integral ∫_(-2)^2lfloor…
- Question 8This question is about pairs of functions f and g that satisfy f(x)-g(x)=3sin x f(x)g(x)=cos^2x for all real numbers x. Across all…
- Question 9This sequence of transformations is applied to the curve y=3x^2: - 1. Translation by 2 -4 - 2. Reflection in the y-axis - 3. Stretch…
- Question 10Given that (a^3+(3)/(b^3))((3)/(a^3)-b^3)=8 where a and b are real numbers, what is the least value of ab?
- Question 11A hollow right circular cone rests on a sphere. The height of the cone is 4 metres and the radius of the base is 1 metre. The volume of the…
- Question 12In the range 0≤ x<2π, the equation 4sin^2x+4cos x=frac92
- Question 13Consider a rectangular cardboard box of height 3, breadth 4, and length 10 units. There is a lizard in one corner A of the box and an…
- Question 14The equation in x 8x^4-16x^3+8x^2+k=0 has four real solutions:
- Question 15The number of pairs of positive integers x,y which solve the equation x^3+6x^2y+12xy^2+8y^3=2^(27) is
- Question 16Evaluate the following integral ∫_0^(100)e^(x-lfloor xrfloor) dx
- Question 17Consider six players P_1,P_2,P_3,P_4,P_5, and P_6. A team consists of two players (Thus, there are 15 distinct teams). Two teams play a…
- Question 18If (log_3x)(log_4x)(log_5x)=(log_3x)(log_4x)+(log_4x)(log_5x)+(log_5x)(log_3x) and x≠ 1, then x is
- Question 19The smallest value of I(a)=∫_0^1(x^2-2a)^2 dx, as a varies, is
- Question 20Let f(x)=(tan x)^(3/2)-3tan x+√(tan x) Consider the three integrals I_1=∫_0^1f(x) dx, I_2=∫_(0.3)^(1.3)f(x) dx, I_3=∫_(0.5)^(1.5)f(x) dx…