TIMO - 2021 - Grade 8 - Preliminary Round - Paper 1

Given a 2-digit number AB which is divisible by 3. If we switch the position of 2 digits, the number increases 63 units. What is the sum of A and B?

The admission ticket at a fair is 2 dollars for children and 4 dollars for adults. On a certain day, 2000 people entered the fair and 5200 dollars was collected. How many children attended the fair that day?

Freddy goes north for 9km, then goes west for 40km. How many km is he now from the original position?

Given $A:B=8:3$, $A:C=6:5$ and $A+B+C=106$, find $B$.

A train was running at the speed of 50 km/h. A car was running at the speed of 80km/h in the same direction. It took the car 15 seconds to cross the train completely. What is the length of the train in meters?

Find $x$ given $15x+83=(4x-5)-(2x+3)$.

Given $a+b=31$ and $a^2+b^2=521$, find $a^3+b^3$.

How many positive integer solutions $z$ satisfy $27<140-3z$?

Given $x^2+y^2+2x+1=0$, find $(x-y)^{2020}+(x+y)^{2021}$.

Given that the sum of the first n natural numbers starting from 1 is 210, find the value of n.

How many 3-digit numbers divisible by 2 but not divisible by 4 are there?

Find the units digit of $3^{100}$.

How many positive factors of 252 are there?

Find $2\times4+4\times6+6\times8+\cdots+16\times18+18\times20$.

Given $n!=1\times2\times3\times\cdots\times(n-1)\times n$, how many trailing zeros does $30!$ have?

Given a right-angled triangle with area of 96cm². The length of the shortest side is 12cm. Find the length of the longest side.

They need 3 jars of paint to cover all faces of a cube as in Figure 1. How many jars of paint do they need to cover all faces of the solid in Figure 2?

Given a trapezium ABCD with area of 48cm². Point M and N are the midpoints of AD and BC respectively. P is a random point lying between C and D. Find the area of the shaded region.

Find the sum of interior angles in a regular 8-sided polygon.

Given a square with side length 14 cm as shown below, find the area of the shaded region. Take $\pi=\frac{22}{7}$.