TIMO - 2020 - Grade 8 - Preliminary Round - Paper 2

Two trains are running in opposite directions with speed 74km/h and 70km/h respectively. It takes them 6 seconds to completely cross each other. If the length of two trains doubles each other, find the length of the longer train.

Given $X:Y=8:3$, $Z:X=3:16$ and $X+Y+Z=150$, find $X$.

How many integers $x$ are there such that $29x+13$ is a 3-digit number?

If each letter represents a different digit, how many different values for 4-digit number MATH are there?

A jigsaw puzzle costs 8 dollars, a teddy bear costs 4 dollars and a doll costs 5 dollars. Teacher bought 14 toys including jigsaw puzzles, teddy bears and dolls. She had to pay 92 dollars altogether. How many teddy bears did she buy?

Find $x$ if $(2020-2x)-(x-2021)=0$.

Find $A$ given $A=\frac{2022}{2021+\frac{2022}{2021+\frac{2022}{2021+\cdots}}}$.

Given integers $x,y$ satisfying $2x+3y=2xy+5$, find the maximum value of $x+y$.

Find $P=\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\cdots+\frac{1}{\sqrt{98}+\sqrt{99}}+\frac{1}{\sqrt{99}+\sqrt{100}}$.

How many integers $x$ satisfy $x^2+x\leq12$?

How many factors does the number 728 have?

A 4-digit number divided by 8 or 12 leaves a remainder 4. Find its largest possible value.

If the 10-digit number $\overline{20212022AB}$ is divisible by 22, find the sum of all possible values of $A$.

Find the last digit of $4+4^2+4^3+\cdots+4^{2020}+4^{2021}$.

Lucas writes consecutive odd natural numbers on the board: $1,3,5,7,\ldots$. At least how many numbers must he write so that their sum is divisible by 84?

Given a right triangle with perimeter 40cm and a hypotenuse of length 17cm. Find the area of that triangle in cm².

A rectangle has area 240 and integral side lengths. How many different values of perimeter the rectangle can have?

How many diagonals are there in a regular 20-sided polygon?

Lucy arranges 13 cubes to form the figure 1 below. Then she removes the cube in the middle to get figure 2 and sees that the total surface area increases 20cm². What is the total surface area of figure 2 in cm²?

Given two identical right triangles with the dimension below. Find the area of the shaded region.