BBB 2022 - Secondary 2 - Preliminary Round

How many integral solutions are there for $x$ if $-25\le9x-2\le64$?

It is known as the lengths of shorter sides for a right-angled triangle are 8cm and 15cm respectively. Find the perimeter of the triangle.

If $a$, $b$, $c$ and $d$ are all integers and $(x+1)(2x-3)(4x-5)=ax^3+bx^2+cx+d$ for all $x$, find the value of $a+b+c+d$.

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

Factorize $x^3-19x+30$.

If $x$ is an integer and satisfies $x^2-7x-30\le0$, how many values of $x$ are there?

An interior angle of a regular $n$-sided polygon is $(10n+6)^\circ$. Find $n$.

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

According to the pattern shown below, what is the 30th term in the sequence?

$3,\quad10,\quad21,\quad36,\quad55,\quad78,\quad\ldots$

Find the area of a triangle with vertices $A(-2,-3)$, $B(5,8)$, $C(-3,5)$ in a rectangular coordinate system.

If the highest common factor of a 4-digit number and 3920 is 280, find the largest possible value of this number.

Find the minimum value of $2x^2-16x-36$.

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

There are 350 diagonals in a regular $n$-sided polygon. Find the value of $n$.

How many 4-digit number has exactly 3 factors are there?

If a straight line $L$ passes through $A(-5,3)$ and $B(40,-6)$. Find the $x$-intercept of $L$.

Find the value of $\sqrt{56-\sqrt{56-\sqrt{56-\cdots}}}$.

How many rectangles are there in the figure below?

Numbers are drawn from 1000 integers 1 to 1000. At least how many numbers are drawn at random to ensure that there are two numbers whose product is 1200?

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.