# Grade - examples - page 45

1. Tetrahedron
Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
2. Parallelogram
The perimeter of the parallelogram is 417 cm. The length of one side is 1.7-times longer than the length of the shorter side. What is the length of sides of a parallelogram?
3. Pedestrian
Pedestrian came started at 8h in the morning with speed 4.4 km/h. At half-past eleven cyclist started at 26 km/h same way. How many minutes take cyclist to catch up pedestrian?
4. Trapezoid RT
The plot has a shape of a rectangular trapezium ABCD, where ABIICD with a right angle at the vertex B. side AB has a length 36 m. The lengths of the sides AB and BC are in the ratio 12:7. Lengths of the sides AB and CD are a ratio 3:2. Calculate consumptio
5. Rectangular trapezoid
The rectangular trapezoid ABCD is: /AB/ = /BC/ = /AC/. The length of the median is 6 cm. Calculate the circumference and area of a trapezoid.
6. Sequence
In the arithmetic sequence is given: Sn=2304, d=2, an=95 Calculate a1 and n.
7. Exp
If ?, then n is:
8. Rhombus problem
Perimeter of the rhombus is 204 dm and it area is 2244 dm2. Calculate the height of the rhombus.
9. Earth's diameter
The Earth's diameter on the equator is approximately 12750 km. How long does the Gripen flyover the Earth above the equator at 10 km if it is at an average speed of 1500 km / h?
10. Circumscription
Calculate radius of the Circumscribed circle in the rectangle with sides 20 and 19. It can be rectangle inscribed by circle?
11. Linear independence
Determine if vectors u=(-4; -5) and v=(20; 25) are linear Linear dependent.
12. Goniometric form
Determine goniometric form of a complex number ?.
13. Bus
At the A bus stop boarded 6 people into the bus and on each other bus stop one man more than the previous one. On E station never boarded. Stops are A, B, C, D, E. Calculate the number of people on the bus after leaving the station E.
14. Metal alloy
What is the ratio of metals in the alloy that is in the 50 tonnes of steel to 30 kg nickel?
15. Components
In the box are 8 white, 4 blue and 2 red components. What is the probability that we pull one white, one blue and one red component without returning?
16. Package
The package has no more than 67 m of cloth. If we just cut it all on the blouses or all on dresses, no cloth left remain. On the one blouse consumes 3.8 m of cloth and on one dress 1.7 m. Determine the amount of the cloth in the package.
17. Cuboid
The volume of the cuboid is 245 cm3. Each cuboid edge length can be expressed by a integer greater than 1 cm. What is the surface area of the cuboid?
18. Sequence
Calculate what member of the sequence specified by ? has value 86.
19. Three digits number
How many are three-digit integers such that in they no digit repeats?
20. Trapezoid ABCD v2
Trapezoid ABCD has length of bases in ratio 3:10. The area of riangle ACD is 825 dm2. What is the area of trapezoid ABCD?

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