# Grade - examples - page 75

1. Cosine The point (8, 6) is on the terminal side of angle θ. cos θ = ?
2. 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.
3. Committees How many different committees of 6 people can be formed from a class of 30 students?
4. Acceleration The car accelerates at rate 0.5m/s2. How long travels 400 meters and what will be its speed?
5. 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.
6. 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?
7. 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.
8. Product Result of the product of the numbers 1, 2, 3, 1, 2, 0 is:
9. 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?
10. Map scale Garden has on plan on a scale of 1: 150 width 22 cm and length 35 cm. What is the real area of the garden?
11. Cars Johnny has 370 cars. Peter twice less. How many cars have Peter?
12. 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?
13. 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?
14. Snow balls Adam made 26 snowballs. Boris made less snowballs. How many snowballs Boris could do?
15. 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°.
16. 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?
17. Water level How high reaches the water in the cylindrical barell with a diameter of 12 cm if there is a liter of water? Express in cm with an accuracy of 1 decimal place.
18. 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?
19. Water pool Pool with volume 990hl completely filled, if water flows by one tap 8 hours and by second tap 6 hours. First tap give 10hl more than second per hour. How many hl flows in each of them in an hour?
20. Blackjack TU160 Bomber Tupolev TU160 started at 9:00 from the airport and flew at average speed of 1850 km/h toward the airfield B distant 3500 km. After evaluating the danger from the airport B started at 9:45 B towards A fighter MIG 29 at an average speed 2300 km/h. At

Do you have an interesting mathematical example that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.