Gresty Academy Paper 1
20 questions · 75 min · Difficulty 38 · by Gresty Academy
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Questions in this paper
- Question 1If y=min\2x,6x-x^2,9-x\ then max(y)=
- Question 2Evaluate 2^(20)+4^8+8^4+16^2+32^(0.8)+64^0
- Question 3The area of an equilateral triangle inscribed in a circle which is inscribed in a square of area 100 mathrm m^2 is
- Question 4The sum of all the coefficients in the expansion of (5x^2-3x-1)^(2025) is
- Question 5The equation of a circle centred at the origin with tangent y=mx+c is
- Question 6These three equations (with real coefficients) x-1+√2&=0 x^2+px-1&=0 x^3-5x^2+5x+q&=0 share a root. So p+q=
- Question 7For what positive values of a does ln(x)=ax^3 have no real solution for x? [Note: ln(x) is log_e x]
- Question 8Given two positive integers a and b, if the log to base 10 of their sum minus the log to base 10 of their difference equals 2, then the…
- Question 9If f(x)=sin^2(Ax) satisfies the functional equation f(x)=f(x+2) then the minimum positive value of A is
- Question 10The sum of the gradients of the normals to the curve y=frac2x^2 at the points where y=1 is
- Question 11The number of solutions to the equation e^(2x)+x-3=0 in the interval [1,100] is
- Question 12The second smallest value of |x| for which cos(3x+(8π)/(3))=-(√3)/(2) is
- Question 13If f(x)=1-frac1x then f^((999))(x)= [Note: f^((n))(x) means the composite of f with itself n times]
- Question 14If a_n=a_(n-1)+6n a_0=2 then a_(100)=
- Question 15If x>0 and 2√2x^2=1+√2 then x=
- Question 16Σ_(k=2)^(100)log_((frac1k))k=
- Question 17Which sequence of transformations turns y=((x-1)^2+2)/((x+2)^2-6) into y=((x-1)^2+2)/((x-4)^2-6)
- Question 18Which of the following has the most real solutions?
- Question 19The area of the region described by 4≤ y≤10 and x-2≤ y≤ x+2 is
- Question 20Given that: - θ is an angle of a triangle - cos(θ)=-frac12+frac ba - a<b - ab<0 then the range of possible values of θ is