Cody
20 questions · 75 min · Difficulty 42 · by Cody
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Questions in this paper
- Question 1How many pairs of positive integers (n,p), where p is prime, satisfy n!+5=p?
- Question 2In the figure below, the outside equilateral triangle contains infinitely many equilateral triangles, each with the same centre. The ratio…
- Question 3The roots of x^3+kx+p=0 are a,b,c. Compute a^3b^4+a^4b^3+a^3c^4+a^4c^3+b^3c^4+b^4c^3.
- Question 4Which of the following is the graph of y=ln(sin x)?
- Question 5Find the area of the region satisfying 4≤ x^2+y^2≤9, y^2≥3x^2.
- Question 6A sequence is defined by x_(n+1)=frac1-2x_n√(x_n)3, 0<x_n<(frac12)^(2/3). If x_n→ a, find a.
- Question 7You roll four fair six-sided dice. What is the probability that the four numbers can form the sides of a rectangle?
- Question 8Find the sum of all nonnegative integers n such that 16+2binom n1+4binom n2+…+2^nbinom nn=8√(3^n).
- Question 9Find the remainder when x^(12)+7x^(10)+9x^8+6x^6+5x^4+2x^2+8 is divided by x^2+1.
- Question 10The following are three consecutive terms of an arithmetic progression: log_3 2, log_3(2^x+1), log_3(2^x+10). Find x.
- Question 11Let f(x)=|x^3|. What is f'(x)?
- Question 12A sequence (a_n) satisfies, for every integer n≥2, S_n=Σ_(k=0)^n a_k=(n^2+3)/(n-1). What is a_n as n→∞?
- Question 13Two football teams have 25 players combined. If Arithmetic FC sign Chris, their average age increases from 23 to 24. If Binomial United…
- Question 14Let I=∫_0^a(2^(-x^3)-frac12) d x. Find a such that (d I)/(d a)=0.
- Question 15Let f(x)=x^3-frac32x^2-6x+k. Find all k such that f has three real roots.
- Question 16Find the area between the curves sin(x^2+y^2)=1, sin(x^2+y^2)=-1, for 0≤ x^2+y^2≤2π.
- Question 17The three sides of a right triangle form the first three terms of an arithmetic sequence with positive common difference. The area is 18…
- Question 18How many positive integer pairs (x,y) satisfy x^3+9x^2y+27xy^2+27y^3=3^(18)?
- Question 19Find the greatest integer n such that 3^n divides 100!.
- Question 20Which of the following is largest?