# Grade - examples - page 7

1. Area of RT
Calculate the area of a right triangle which hypotenuse has length 10 and one hypotenuse segment has lenght 5.
2. Eiffel Tower
Eiffel Tower in Paris is 300 meters high, is made of steel. Its weight is 8000 tons. How tall is the tower model made ​​of the same material, if it weigh is 2.4 kg?
3. Ace
From complete sets of playing cards (32 cards) we pulled out one card. What is the probability of pulling the ace?
4. Two cars
Two cars started against each other at the same time to journey long 293 km. First car went 41 km/h and second 41 km/h. What distance will be between this cars 20 minutes before meet?
5. School trip
School trip cost 247.2 Eur for one class (24 students). How much would cost a trip for two classes? (both classes together have 53 students)
6. Flags
How many different flags can be made from colors white, red, green, purple, orange, yellow, blue so that each flag consisted of three different colors?
7. Forces
In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
8. Circles
The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle.
9. Family
10. Cylinders
Area of the side of two cylinders is same rectangle of 50 cm × 11 cm. Which cylinder has a larger volume and by how much?
11. MO SK/CZ Z9–I–3
John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
12. Youth track
Youth track from Hronská Dúbrava to Banská Štiavnica which announced cancellation attracted considerable media attention and public opposition, has cost 6.3 euro per capita and revenue 13 cents per capita. Calculate size of subsidies to trip group of 28.
13. Reverse Pythagorean theorem
Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ?
14. Compare
Compare fractions ?. Which fraction of the lower?
15. Widescreen monitor
Computer business hit by a wave of widescreen monitors and televisions. Calculate the area of ​​the LCD monitor with a diagonal size 20 inches at ratio 4:3 and then 16:9 aspect ratio. Is buying widescreen monitors with same diagonal more advantageous tha
16. Holidays
Calculate how many hours take holidays, if take 5 weeks.
17. It is rectangular?
Size of two of the angles in a triangle are: α=110°, β=40°. Is it a right triangle?
18. Tanks
Fire tank has cuboid shape with a rectangular floor measuring 13.7 m × 9.8 m. Water depth is 2.4 m. Water was pumped from the tank into barrels with a capacity of 2.7 hl. How many barrels were used, if the water level in the tank fallen 5 cm? Wr
19. Circle arc
Circle segment has a circumference of 135.26 dm and 2096.58 dm2 area. Calculate the radius of the circle and size of central angle.
20. Vans
In how many ways can 9 shuttle vans line up at the airport?

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