TIMO - 2020 - Grade 9 - Preliminary Round - Paper 2

The lengths of 2 trains are 85m and 90m. If they are running in opposite directions, it takes them 7 seconds to completely cross each other. Find the speed of the faster train in km/h given that their speed ratio is 2 : 3.

Given $A=30\%B$, $A=50\%C$ and $A+B+C=285$, find $A$.

How many integers x are there given that both x + 2 and 3x + 4 must be 3-digit numbers?

If each letter represents a different digit, find the smallest value of U.

In a training lesson, an archer shot 30 arrows. He got 10 points for each arrow hitting the target and lost 5 points for each arrow missing the target. After completing the training lesson, he got 90 points. How many arrows hit the target?

Find $x+y$ if $\lvert2020-2x+y\rvert+(x-y-2021)^2=0$.

Find $x$ given $6=\sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}$.

Let $a$ be a positive integer. How many values of $a$ satisfy $a-2<\frac{2a+20}{a+2}$?

Find $P$ if $4P=2\times4+4\times6+6\times8+\cdots+48\times50$.

Let $f(x)$ be a cubic polynomial with $f(0)=1$, $f(1)=2$, $f(-1)=2$, and $f(2)=-1$. Find $f(-2)$.

Let $n$ and $\frac{123!}{5^n}$ be natural numbers. Find the maximum value of $n$.

A 3-digit number leaves remainders 6, 7, and 10 when divided by 8, 9, and 12 respectively. How many such numbers are there?

Find the remainder when $11^{111}$ is divided by 9.

Find the last digit of $8^{99}+9^{88}$.

How many positive factors does 2000 have?

Segment $AB$ has endpoints $A(2+x,y)$ and $B(-2,x)$ and midpoint $M(3,4)$. Find $y$.

Find the perimeter of the triangle with vertices $A(3,4)$, $B(0,0)$, $C(3,-3)$ in a rectangular coordinate system.

The figure shows three semicircles and rectangle $ABCD$. $C,D$ are the centres of the lower semicircles, each with radius 2 cm. Find the shaded area in cm².

Find the interior angle of a regular 12-sided polygon.

Figure 1 consists of three identical rectangles with the dimensions shown. Cutting along the dotted line gives three regions $A,B,C$ as in Figure 2. Find the area of region $A$ in cm².