TIMO - 2019 - Grade 7 - Heat Round - Paper 3 Next → There are 5 pieces of white chopsticks, 7 pieces of yellow chopsticks and 9 pieces of blue chopsticks mixed together. If you want to get 3 pairs of chopsticks with same colours in the dark, at least how many pieces of chopsticks are needed to be taken?
Robert goes east for 21km, then goes south for 28km. How many km is he now from the original position?
Given $A:B=3:7$, $B:C=5:11$, $C:D=2:3$ and $A+B+C+D=970$, find $B$.
Find the average of these ten numbers: 2015, 2026, 2006, 2005, 2018, 1989, 2046, 2039, 2007, 2029.
There are some chickens and rabbits in a cage. The number of chickens is five times as the number of rabbits. The total number of chicken legs is 78 more than that of rabbit. How many rabbit(s) is / are there?
Find $x$ if $(3x+4)+(4x-18)=0$.
Given $\lvert x+2\rvert+(y-3)^2=0$, calculate $(x+y)+(x+y)^2+\cdots+(x+y)^{2018}$.
How many negative integer solutions $x$ satisfy $7x+24>-27$?
Given positive real numbers $a,b$ with $a^2-b^2=96$ and $a+b=12$, find $a-b$.
Factorize $x^2-8x+12$.
Find the sum of all positive factors of 1014.
Given $x>0$ and $x+\frac1x=5$, find $x^2+\frac1{x^2}$.
Find the last digit of $A=1+4+9+16+25+\cdots+529+576+625$.
When a 4-digit number is divided by 4, 6 or 8, the remainder is 3. What is the smallest possible value of that 4-digit number?
Given rational $x>0$ with $x=2+\frac3{2+\frac3{2+\cdots}}$, find $x$.
$E,F$ are the midpoints of $AB,BC$ respectively. The area of parallelogram $ABCD$ is 240. Find the area of triangle $DEF$.
$M(-5,-5)$ is the midpoint of $A(-3,1)$ and $B(x,y)$. Find $x+y$.
Some cubes with side length 1cm are combined according to the pattern shown below. If there are 19 layers, find the surface area in cm².
The hypotenuse of a right-angled triangle is 20, find the maximum area of the triangle.
A circle has radius 77, and its circumference equals the area of a square. Find the side length of the square. Take $\pi=\frac{22}{7}$.
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