TIMO - 2018 - Grade 8 - Preliminary Round - Paper 4

Find the 3-digit number $\overline{CBC}$. The non-zero digits $B,C$ satisfy: (i) $\overline{BCB}$ is divisible by 11; (ii) $\overline{BBC}$ is divisible by 6.

Andy goes northwest for 13km, then goes northeast for 12km and goes southeast for 4km. How far is he now from the original position?

If $\overline{abcd}+\overline{badc}=15532$, calculate $a+b-c-d$.

It is now 12 o'clock. How many minutes will pass before the minute hand and hour hand overlap again?

There are 13 pieces of white chopsticks, 11 pieces of yellow chopsticks and 14 pieces of brown chopsticks mixed together. Close your eyes. If you want to get 2 pairs of chopsticks that are not yellow, at least how many pieces of chopsticks are needed to be taken?

Find $y$ if $\lvert2x+6y+8\rvert+\lvert x-3y+4\rvert=0$.

Factorize $x^4+y^4-3x^2y^2$.

How many negative integer solutions $x$ satisfy $-97\leq7x+3\leq32$?

Given that $(x-3)$ is a factor of $x^3-2x^2+3x+m$, find $m$.

Given $f(x)=ax^2+bx+c$, $f(-1)=3$, $f(2)=18$ and $f(-2)=6$, find $f(1)$.

Find the remainder when $902^{209}$ is divided by 5.

A positive integer $x$ satisfies $x^2\equiv4\pmod{11}$ and $x>25$. Find its minimum value.

Find the last digit of $A=1+7+7^2+7^3+\cdots+7^{887}+7^{888}$.

How many positive integers that smaller than 65 and it is co-prime with 65 is/ are there?

Find the number of positive factors of 37500.

Given right-angled triangles $\triangle ABC\sim\triangle FED$ with legs $AB=5$ and $BC=12$, find $\frac{DF}{EF}$.

Given points $A(9,4)$, $B(1,3)$ and $C(9,8)$ on a coordinate plane, find the area of triangle $ABC$.

A cylinder is formed by two circles and a folded square. Its volume is 6776 cm³. Find the area of one circle. Take $\pi=\frac{22}{7}$.

An exterior angle of a regular $n$-sided polygon is $(2n+16)^\circ$. Find $n$.

How many diagonals does a convex 90-sided polygon have?