# Grade - examples - page 72

1. Water reservoir The water reservoir is filled with one pump for 4 days by the second one for 9 days. Outlet can drain tank in 12 days. How long take fill the reservoir if both pumps are running and not closed outlet channel.
2. Shoes Peter decided to measure shoes size of his three friends. Measured accurately and wrote as follows: Venda and Jenda together 52 cm Jenda and Zdenda together 58 cm Zdenda and Venda together 54 cm a) How long measures Vendy, Jenda and Zdenda shoes together
3. Median In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb.
4. Pair They have together 39 years - he has 2 times as she was when he was equal as she has today ....
5. Snow balls Adam made 26 snowballs. Boris made less snowballs. How many snowballs Boris could do?
6. Homework Mother and Kate together weigh 24.5 kg more than the father. Father weighs 7.6 kg more than mother. Father weight 44.8 kg more than Kate. Determine weights of father mother and Kate.
7. Committees How many different committees of 6 people can be formed from a class of 30 students?
8. Division Divide by the number 0.2 is the same as multiply by what number?
9. Three shapes 1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle?
10. Inscribed triangle To a circle is inscribed triangle so that the it's vertexes divide circle into 3 arcs. The length of the arcs are in the ratio 2:3:7. Determine the interior angles of a triangle.
11. Pipe How long is the pipe with an outside diameter of 1.44 m if his coloring consumed 44 kg of color. 1 kg of color coverage is 9 m2.
12. Area and two angles Calculate the size of all sides and internal angles of a triangle ABC, if it is given by area S = 501.9; and two internal angles α = 15°28' and β = 45°.
13. Cosine The point (8, 6) is on the terminal side of angle θ. cos θ = ?
14. Lenka and money When Lenka bought pants from 1/3 of her savings shirt from 1/5 and 1/8 spent at the hairdresser, she is left 328 Kč. How much money was saved? How much hairdresser cost?
15. Shaving Mathematical problem from Sunday evening. If the beard is growing at 0.52 mm per day and that my length is 16.8 mm, how long I don't shave?
16. Garden pool Mr. Novak fill garden pool (cylinder; diameter of 200 cm) with 31.4 hl of water. What is the depth of the pool when the water level is 10 cm below the upper edge of the pool?
17. Cube basics How long is the edge length of a cube with volume 23 m3?
18. Tailor Tailor has an estimated 11 meters of 80 cm wide fabric. He will shape wholly 7 rectangles measuring 80 x 150 cm and nothing fabric does not remain. How many fabric he have?
19. Mine Wheel in traction tower has a diameter 5 m. How many meters will perform an elevator cabin if wheel rotates in the same direction 49 times?
20. The wall We have to build a cuboid wall with dimensions base 30 cm and 45 cm and height 3.25 meters. Calculate how many we need bricks if we spend 400 pieces of bricks to 1 m3 of wall?

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