Sed (CoderLovesEggs) Paper 1 with Solutions
20 questions · 75 min · Difficulty 54 · by Sed (CoderLovesEggs)
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Questions in this paper
- Question 1The full range of values of x for which x^3-2x^2-x+2>0 is:
- Question 2The area bounded within x^2+y^2=1 and above y=-x+1 is:
- Question 3A regular hexagon H has centre O. Let L be a line through O which rotates clockwise continuously. Denote θ as the total clockwise angle…
- Question 4Let L_1,L_2 be the 2 tangent lines of (x-1)^2+(y-1)^2=4 which pass through (-2,4). The acute angle between L_1 and L_2 is 2θ. It follows…
- Question 5Consider the sequence: - a_1=2 - a_n=dfraca_(n-1)+1a_(n-1)-1 for n>1. The least value of n for which (Σ_(i=1)^n a_i)>5000 is:
- Question 6a,b are constants with a>b>0. When (a+bx)^3 is expanded, - the sum of the coefficients of x^i (0≤ i≤3) is 27; - the product of the…
- Question 7A bacteria has initial nonzero population B. After each hour, the bacteria population has a probability p of doubling, and a probability…
- Question 8The full range of values of k for which the graph of y=ksin x+(1-k) intersects the graph of y=sin x+(4+k) is:
- Question 9The area of the triangle formed by the stationary points of y=x^4-8x^2+17 is:
- Question 10You are given that ∫_0^πsin^5xd x=(16)/(15). Define the total area bounded between the curves y=x y=2sin^5x+x for 0≤ x≤ a as F(a). It…
- Question 11Let T=(4,6) be a point on the circle C:(x-3)^2+(y-4)^2=5. Let P=(p,q). The circle centred at P passing through T has area π(p^2+q^2) and is…
- Question 12When (ax-2)^2 is divided by (x-a), the remainder is a^2. The sum of the possible remainder values when (ax+2)^2 is divided by (x+a) is:
- Question 13The equations 2^x+2^(y+1)=p 2^y+2^(x+1)=q have a solution pair (x,y) precisely for:
- Question 14Which of the following integrals has the largest value? Assume trigonometric functions are in radians.
- Question 15The function f(x) satisfies: - f(x)=3x, 0≤ x≤1 - f(x-1)=f(1-x)=f(1+x) for all x The number of solutions to f(x)=dfrac x3-1 is:
- Question 16The tangent to y=x^3-3x at x=a (where a>0) intersects the curve again such that the area bounded between the curve and the tangent is…
- Question 17In triangle ABC, - ∠ BAC=30°; - AC=12; - dfrac67<sin(∠ ABC)≤1. Denote S as the area of ABC. It follows that the range of S is:
- Question 18The function f(n) satisfies: - f(1)=1; - f(2n)=f(n) for all n≥1; - f(2n+1)=dfracf(n)2 for all n≥1. It follows that (Σ_(i=1)^(2^n)f(i)) is…
- Question 19The minimum distance between the curves y=x^2+1 and x=y^2+1 is:
- Question 20For all integers n≥1, define the function f(x) as f(x)=(-1)^(n+1)√2^(2-2n)-(x-4+frac62^n)^2 for 4-2^(3-n)≤ x<4-2^(2-n) only. It follows…