1. Big number
hat is the remainder when dividing number 10 to 47 - 111 by number 9?
2. Inscribed circle
The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c.
3. Remainder
A is an arbitrary integer that gives remainder 1 in the division with 6. B is an arbitrary integer that gives remainder 2 the division by. What makes remainder in division by 3 product of numbers A x B ?
4. Chord
It is given to a circle k(r=6 cm) and the points A, B such that / AB / = 8 cm lies on k. Calculate the distance of the center of circle S to the midpoint C of the segment AB.
5. Z9–I–4 MO 2017
Numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 were prepared for a train journey with three wagons. They wanted to sit out so that three numbers were seated in each carriage and the largest of each of the three was equal to the sum of the remaining two. The conduct
6. Functions f,g
Find g(1) if g(x) = 3x - x2 Find f(5) if f(x) = x + 1/2
7. Iron collecting
Class 7A collected 3.2 tonnes of iron more than class 7B. Together they collected 6.4 tonnes of iron to the secondary raw material collection. How much did each class collect?
8. MO Z9–I–2 - 2017
In the VODY trapezoid, VO is a longer base and the diagonal intersection K divides the VD line in a 3:2 ratio. The area of the KOV triangle is 13.5 cm2. Find the area of the entire trapezoid.
The ladder is 10 m long The ladder is 8 m high How many meters is the distant heel from the wall?
10. Average age
The average age of all people at the celebration was equal to the number of people present. After the departure of one person who was 29 years old, average age was again equal to the number present. How many people were originally to celebrate?
11. Container
The container has a cylindrical shape the base diameter 0.8 m and the area of the base is equal to the area of the wall. How many liters of water can we pour into the container?
12. One million
Write the million number (1000000) by using only 9 numbers and algebraic operations plus, minus, times, divided, powers, and squares. Find at least three different solutions.
13. Alcohol mixture
Three liters of 96 percent alcohol we set up a certain amount of distilled water to form a 54-percent alcohol. How many liters of distilled water were used?
14. Points on line segment
Points P & Q belong to segment AB. If AB=a, AP = 2PQ = 2QB, find the distance: between point A and the midpoint of the segment QB.
What is the slope of a ladder 6.2 m long and 5.12 m in height.
16. Is right triangle
Decide if the triangle XYZ is rectangular: x = 4 m, y = 6 m, z = 4 m
17. Rhombus construction
Construct ABCD rhombus if its diagonal AC=9 cm and side AB = 6 cm. Inscribe a circle in it touching all sides...