# Grade - examples - page 90

1. Rings - intersect
There are 15 pupils on the sporting ring. 10 pupils go to football, 8 pupils go to floorball. How many pupils go to both rings at the same time?
2. Arithmetic average
The arithmetic mean of the five numbers is exactly 8. The sum of these four numbers is 30. What is the fifth number?
3. MATES
In MATES (Small Television tipping) from 35 randomly numbers drawn 5 winning numbers. How many possible combinations there is?
4. Ratio of two unknown numbers
Two numbers are given. Their sum is 30. We calculate one-sixth of a larger number and add to both numbers. So we get new numbers whose ratio is 5:7. Which two numbers were given?
5. Extreme temperatures
USA hit extreme heat wave. Calculate percentage of the air temperature change from normal summer temperature 23 °C to 40 °C.
6. Power
Number ?. Find the value of x.
7. Unknown number
Unknown number is divisible by exactly three different primes. When we compare these primes in ascending order, the following applies: • Difference first and second prime number is half the difference between the third and second prime numbers. • The produ
8. Have solution
The sum of four consecutive even numbers is 96. Determine these numbers.
9. Arc-sector
arc length = 17 cm area of sector = 55 cm2 arc angle = ? the radius of the sector = ?
10. Triangle
Determine if it is possible to construct a triangle with sides 28 31 34 by calculation.
11. The field
The player crossed the field diagonally and walked the length of 250 m. Calculate the length of the field, circumference if one side of field 25 meters.
12. Pipe
Steel pipe has a length 2.5 meters. About how many decimetres is 1/3 less than 4/8 of this steel pipe?
13. Travel by bus
Five girls traveling by bus. Each holds in each hand two baskets. Each basket contains 5 cats. Each cat has 5 kittens. 3 girls getting off the bus and another girl without baskets go on board. The bus control driver. How many legs are in the bus?
14. Hexagon rotation
A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?
15. Cakes
On the table was 56 cakes. When Peter went home, leaving them eight times less. How many cakes left?
16. Rectangular field
One dimension of the rectangular field is 56 m greater than second dimension. If each side of the rectangle increases by 10 m, increases the surface field is 1480 m2 . Determine dimencions of the field.
17. Four sides of trapezoid
In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles.
18. Square circles
Calculate the length of the described and inscribed circle to the square ABCD with a side of 5cm.
19. Rhombus
One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus.
20. Obtuse angle
The line OH is the height of the triangle DOM, line MN is the bisector of angle DMO. obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image)

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