TIMO - 2017 - Grade 9 - Preliminary Round - Paper 5

Billy has some 1 dollars, 2 dollars and 5 dollars coins. The number of 1 dollars coins is 12 times of that of 2 dollars coins. Billy has 100 dollars in total. Find the number of 5 dollars coins.

If the sum of ten consecutive odd numbers is 300, find the value of smallest number.

The calendar below shows four dates $a,b,c,d$ in March, with $a+b+c+d=40$. On which day of the week does March 1 fall?

What is the sum of ten consecutive 2-digit numbers where the first and last numbers are perfect squares?

How many integers $x$ make both $x+7$ and $2x+9$ 2-digit numbers?

Find $\frac1{2-\frac1{2-\frac1{2-\frac12}}}$.

Solve $2^0x+2^1x+2^2x+\cdots+2^{2021}x=2^{2024}-4$ for $x$.

Solve $\begin{cases}3x+9y=7\\9x-3y=-4\end{cases}$ and find $x-y$.

Let $b$ be a constant. The coefficient of $x^2$ in $(2x-3)(x^2-bx)$ is 9. Find the coefficient of $x$.

Find the greatest integer smaller than $A=\sqrt{20+\sqrt{20+\sqrt{20+\sqrt{20+\sqrt{20}}}}}$.

How many 3-digits number leaves remainder 4 when divided by 5 and leaves a remainder 5 when divided by 6?

The 10-digit number $\overline{A20213101B}$ is divisible by 44. Find $A+B$.

Find the units digit of $2022^{2021}$.

How many positive factors does 1400 have?

Find the largest value of $n$ such that $\frac{321!}{10^n}$ is a natural number.

The figure contains a regular hexagon, a regular pentagon, a square and an equilateral triangle. If $\angle1+\angle3-\angle2=x^\circ$, find $x$.

Given that the area of a rectangle is 528. Find the smallest value of the perimeter of the rectangle if both the length and the width are integers.

27 small cubes with side length 1 are stacked to get the figure below. Find its total surface area.

Point $P(2,7)$ lies on $AB$ with $AP:BP=1:1$. Given $A(-5+x,4-y)$ and $B(7-y,6-x)$, find $x^2-y^2$.

A square with side length 35 is inscribed in a circle. Find the area of the circle. Take $\pi=\frac{22}7$.