Yotta Paper 1
20 questions · 75 min · Difficulty 59 · by Yotta
Read the questions freely. Sign in to answer them, start a timed paper and save your progress.
Questions in this paper
- Question 1Find the sum of the x-coordinates of the six points of intersection of y=π x(x-1)(x-2)(x-3)(x-4)(x-5) and y=frac517x+fracπ3.
- Question 2A cubic function f(x) is such that f(2)=4, f(3)=9, f(-1)=1, and the coefficient of x^3 is 2. Find f(4).
- Question 3Let f_0(x)=x, and f_(n+1)(x)=|f_n(x)-k| for non-negative integers n, and positive real number k. Let α and β respectively equal the least…
- Question 4Positive integers a,b and c satisfy abc+bc+ab+ac+a+b+c=104. What is a^2+b^2+c^2+2(a+b+c)+1?
- Question 5Let u_n=2u_(n-1)+7u_(n-2), where u_1=4 and u_2=12. What does the value of fracu_ku_(k-1) tend towards as k tends towards infinity?
- Question 6f(x) is a polynomial function defined for all real x. Given that f(x^2-12x+45) has two roots at x=-3 and x=15, and has a minimum value of…
- Question 7How many real solutions are there to 2(27^x)-3^(2x+1)-4(3^(x+1))+5=0?
- Question 8The graph of y=tan(cos(sin(x))) has a period of P and a maximum value of M. Which row is correct?
- Question 9How many real solutions are there to ln(sin(x))=ln(1-(4x)/(7π))?
- Question 10A fair coin is flipped repeatedly until 4 consecutive heads are obtained. Find the expected number of coin flips.
- Question 11Worker n, where n is an integer, can do a task by themself in 2^n days. Let f(k) represent the time taken when workers 0 to k inclusive are…
- Question 12Which of these values is the smallest?
- Question 13Find the sum of the reciprocals of all of the factors of 1600.
- Question 14The digital root of a number is where you find the sum of the digits of a number, then find the sum of the answer, and repeat until you get…
- Question 15The function f(x) has the property that f(x)=f(6-x) for all real x. Given that: &(∫_2^3 f(x) d x)^2+(∫_4^6 f(x) d x)^2 & +(∫_2^4 f(x) d…
- Question 16A point A is chosen on the curve with equation: (x-2)^2+(y-3)^2=4 and another point B is chosen on the curve with equation…
- Question 17f(x)=1!x^2!x^3!x^4!x^5!x^(6!x). Which of these is the closest value of f(frac12)?
- Question 1845 people are standing in a line. How many ways are there to choose 17 of them such that no two chosen people are next to each other, and…
- Question 19Consider f(x)=ln(√(x^2-2x+1)). Which of the following statements is true about f(x)?
- Question 20The function F(x), where x is a non-negative real number, is the result of subtracting the integer part of x from x. For example, F(3)=0…