BBB 2022 - Secondary 1 - Preliminary Round

Find the value of $x$ such that $2x-\frac32:\frac98=4x+\frac23$.

How many positive integers $x$ will satisfy $80-7x>15$?

A 4-digit natural number is divided by 12, 16 and 18 to get the same remainder of 2. What is the minimum value of this number?

It is known that the ratio of 3 interior angles in a triangle is 11:12:13. Find the value of the smallest exterior angle.

Find the value of unit digit of $1^{2023}+2^{2023}+3^{2023}$.

There are 300 people in a book club. 40% of the members are students. How many students should join in so that the number of students occupies 60% of the club?

Find the value of $x$ from the system of linear equations $\begin{cases}3x+8y=34\\2x+9y=41\end{cases}$.

Given $x>0$ and $x-\frac1x=3$, find the value of $x^2+\frac1{x^2}$.

How many 3-digit numbers divisible by 4 but not divisible by 6 are there?

Refer to the figure below, how many rectangle(s) is / are there?

Factorise $2x^2y-x^2-2xy+x-12y+6$.

How many integral values of $x$ satisfy $|x+7|-|x-5|=x-1$?

Find the value of $\frac1{1\times2\times3}+\frac1{2\times3\times4}+\frac1{3\times4\times5}+\cdots+\frac1{17\times18\times19}+\frac1{18\times19\times20}$.

Find the area of a triangle with vertices $A(2,0)$, $B(0,-4)$, $C(-2,1)$ in a rectangular coordinate system.

When do the hour hand and the minute hand overlap between 10am and 11am? (choose the closest answer)

How many simplified proper fractions with denominator 100 are there?

There are 54 diagonals in a regular $n$-sided polygon. Find the value of $n$.

Find the value of $1\times2+2\times3+3\times4+\cdots+25\times26+26\times27$.

Given a square. Wendy draws 2 quarters whose centers are vertices of the squares as follows. If the area of the white region is $32-8\pi$, find the area of the shaded region.

Numbers are drawn from 1234 integers 1 to 1234. At least how many numbers are drawn at random to ensure that there are two numbers whose difference is 5?