BBB 2022 - Senior Secondary - Preliminary Round

It is known that $x$ is rational, $x>0$ and $x=5+\frac{14}{5+\frac{14}{5+\cdots}}$. Find the value of $x$.

An interior angle of a regular $n$-sided polygon is $(12n-24)^\circ$. Find the value of $n$.

$x$ is an acute angle and satisfies $\cot x=\frac34$. Find the value of $\frac{\sin^2x+\cos^2x}{\cos^2x-\sin^2x}$.

In a rectangular coordinate system, a triangle is formed by vertices $A(5,3)$, $B(-1,4)$, $C(x,y)$. If the centroid of this triangle is $(4,2)$, find the value of $x-y$.

How many integral solution(s) is / are there for $x$ if $2\le\frac{(x-3)^2}{2}-5\le12$?

There are 20 students in a class. In how many different ways can the teacher choose 1 monitor and 2 vice-monitors?

A straight line L passes through points $A(x,7)$ and $B(2,1)$ with the slope 3. Find $x$.

Three identical cubes are combined to form one large cuboid with surface area of 224cm². Find the volume of that cuboid.

If $y=\frac{-12}{x^2+6x+6}$ and $x,y$ are integers, find the maximum value of $y$.

The radius of a sector is 8 and its perimeter is 50. Find the area of this sector.

Find the area of the region bounded by the $y$-axis and two lines with the equation $x+2y-1=0$ and $2x-y-7=0$.

How many factors of 12000 are square numbers?

Given that $f(x)=\sum_{n=1}^{x}(-1)^{n-1}\frac n3$ for every positive integer $x$. Find the value of $f(2022)$.

Find the value of $x$ in the system of equations.

$\begin{cases}2x+y+z=-6\\x-y+2z=-6\\x+3y+z=5\end{cases}$

Given that $a>b>c$ and $\overline{12a3b456c}$ is divisible by 44. Find the greatest value of $\overline{abc}$.

Given $x$ and $y$ are positive integers and $2022^x+2023^y$ can be divisible by 11, find the minimum value of $x+y$.

Given a square. Wendy draws 4 semi-circles quarters whose diameters are the sides of the square as follows. If the area of the shaded region is $8\pi-16$, find the area of the white region.

In $\triangle ABC$, $AB=12$, $BC=6$ and $B=60^\circ$, find the value of $\frac{\sin B}{\sin A}$.

Numbers are drawn from 2000 integers 1 to 2000. At least how many numbers are drawn at random to ensure that there are two numbers whose product is 3600?

There are 3 black balls and 2 white balls. If 5 balls are drawn randomly one by one without replacement, find the probability that the 2nd one is a white ball.