Zach
20 questions · 75 min · Difficulty 47 · by Zach
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Questions in this paper
- Question 1Let a_n be the area bounded by the curves x=y, x^2+y^2=n and the positive x-axis. What is Σ_(n=1)^(100)a_n?
- Question 2The symbol \x\ denotes the fractional part of x. For example \10.4\=0.4, \2\=0. Given that f(x)=5x^3+2x^2+8x+1, find ∫_0^n f(\x\+1) dx…
- Question 3Let x and y be real numbers such that x^2+y^2=49. What is the greatest value of 12x-5y?
- Question 4For what values of x is x+3=1+1+x+1+2x+x^2+1+3x+3x^2+x^3+…?
- Question 5How many four-digit square numbers are multiples of 3, 4 and 5?
- Question 6Two identical ice sculptures are left to melt outside. Sculpture A melts in 6 hours. Sculpture B melts in 12 hours. Assuming each sculpture…
- Question 7Alvin and Simon can create a song in 5 days. Alvin and Theodore can create a song in 8 days. Simon and Theodore can create a song in 10…
- Question 8Find x such that ln(xln(xln(xln(xln(x…=e.
- Question 9Find the coefficient of x^(15) in the expansion of (2x^3+3x+4x^5)^5.
- Question 10Find the units digit of 34657^(267)+81.
- Question 11There are 129 coins on a table. 128 are fair, and one has heads on both sides. A coin is tossed 8 times and lands on heads every time. What…
- Question 12Find the sum of the solutions to 16^(log_2x)-10×27^(log_3x)+35×64^(log_8x)-50x+24=0.
- Question 13How many solutions does sin x+sin^2x+sin^3x+…=tan x have for 0≤ x≤2π?
- Question 14How many sets of positive integers (a,b,c) with a≤ b≤ c satisfy frac1a+frac1b+frac1c=1?
- Question 15For x≥0, x≠2, let f(x)=fracx√(x)-2√(x)√2-√(x). Define f(2) by continuous extension. Find fprime(2).
- Question 16A sheep called Shaun lives in a circular pen of radius 8. His position inside the pen is random. What is the probability that Shaun is…
- Question 17Solve: log_(x-2)9=log_x81.
- Question 18For which function is f(f(f(f(f(x)))))≠0?
- Question 19A proper divisor of a number is a positive factor that is smaller than the number. E.g. The proper divisors of 6 are 1, 2, 3. How many…
- Question 20Given that CB is an arc formed from the circle of radius a centred at A, and AB and AC are defined similarly, what is the area of the shape…