# Grade - examples - page 46

1. Chase
Paul travel at 60 km/h. After 18 km ride found that he forgot an important book. His brother Thomas behind him carrying it. How fast must Thomas go to catch up with Paul in 31 minutes?
2. Pumps
6 pump fills the tank for 3 and a half days. How long will fill the tank 7 equally powerful pumps?
3. Complete construction
Construct triangle ABC if hypotenuse c = 7 cm and angle ABC = 30 degrees. / Use Thales' theorem - circle /. Measure and write down the length of legs.
4. Unit vector 2D
Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
5. Sphere
Intersect between plane and a sphere is a circle with a radius of 60 mm. Cone whose base is this circle and whose apex is at the center of the sphere has a height of 34 mm. Calculate the surface area and volume of a sphere.
6. Triangle
Calculate the sides of the triangle if its area S = 630 and the second cathethus is shorter by 17.
7. Diameter
If the endpoints of a diameter of a circle are A(10, -1) and B (3, 10), what is the radius of the circle?
8. Sisters
Sisters Hanka and Vera goes mostly tograndmother by bicycle. Journey took Hanka 30 minutes and Vera 20 minutes. How long will Vera catch up with Hanka when started from home five minutes later than Hanka?
9. Rounding 2
Round the following negative number: -143.021
10. Cubic
Convert 660 m3 of natural gas volume to energy units kWh. Combustion of 1 cubic meter of natural gas is released energy 10.55 kWh.
11. Clock
How many hours are 15 days?
12. Angles ratio
In a triangle ABC true relationship c is less than b and b is less than a. Internal angles of the triangle are in the ratio 5:4:9. The size of the internal angle beta is:
13. Money
Everyone complains about the lack of money. In fact, there is no shortage of money, but the relative scarcity of goods and things that people buy for money. Calculate what percentage of the price of all goods and services rose immediately, if everyone has
14. Cross-country competition
Cross-country competition was attended by 76% of pupils of class 9.B. Class consis of 16 boys, two of whom did not run and 4 girls did not run. How many girls go to class 9.B?
15. Vacation
Parents piggybacking children on vacation to its grandmother and grandfather at a city distant 150 kilometers. They agreed to meet halfway. Parents will be travel at 90 km/h, grandmother and grandfather at 60 km/h. Parents depart at 12:00 hours. When grand
16. Abyss
Stone was pushed into the abyss: 2 seconds after we heard hitting the bottom. How deep is the abyss (neglecting air resistance)? (gravitational acceleration g = 9.81 m/s2 and the speed of sound in air v = 343 m/s)
17. Cube - wall
V kocke ABCDEFGH je ?. Aký je povrch kocky?
18. Paper box
Calculate the consumption of paper on the box-shaped quadrangular prism with rhombic footstall, base edge a=6 cm and the adjacent base edges forms an angle alpha = 60 °. Box height is 10 cm. How many m2 of the paper consumed 100 such boxes?
19. Car amortization
Assume that the car has a life 13 years and new cost 24000 euros. Calculate how much a month is amortized cost of the car over its lifetime. Amortization is the gradual reduction of assets (cars, buildings), mainly due using or aging.
20. Roller
Roller has a diameter of 0.96 m and a width 169 cm. How many m2 of road level when he turns 42-times?

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