# Examples for 8th grade - page 36

1. Tournament
Determine how many ways can be chosen two representatives from 34 students to school tournament.
2. Disinfecting solution
How much distilled water is necessary to pour into 500 ml of 33% hydrogen peroxide solution to obtain 3% disinfecting solution?
3. Painters
The first team of painters would paint bridge in 15 days, the second in 10 days. After 3 days of working together second team goes out and continue only first team. How many days took second team to finish painting the bridge?
4. Reflector
Circular reflector throws light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has with the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane?
5. Class 8.A
Three quarters of class 8.A went skiing. Of those who remained at home one third was ill and the remaining six were on math olympic. How many students have class 8.A?
6. Angle
A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis.
7. Against each other
From two points A, B distant 23 km at the same time started two cars against each other at speeds 41 km/h and 65 km/h. How long does cars meet and what distance passes each of them?
8. Words
How many 3 letter "words" are possible using 14 letters of the alphabet? a) n - without repetition b) m - with repetition
9. Aluminum wire
Aluminum wire of 3 mm diameter has a total weight of 1909 kg and a density of 2700 kg/m3. How long is the wire bundle?
10. Railways - golden parachutes
As often happens in Slovakia habit, the state's financial institution which takes from poverty and gorilas give. A hardworking punishing taxes. Let's look at a short work of director Railway Company ZSSK - Mgr . P. K. : 18 months 'work' as director .
11. Sphere fall
How many percent fall volume of sphere if diameter fall 10×?
12. Permill
How many permill is 978 from 84370?
13. The camp
At the end of the camp a 8 friends exchanged addresses. Any friend gave remaining 7 friends his card. How many addresses they exchanged?
14. Triangular pyramid
Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm
15. Czech crown salary
The monthly salary of the employee is CZK 10,800. In the course of the year the bulk salary increased by CZK 500. Calculate which month (1 ... 12) was increased if its annual income was 133,600 CZK.
16. Two cars
Car A1 goes at average speed of 106 km/h and the second car A2 goes at 103 km/h. How many second will it take car A1 to circulate car A2? Assume that both cars are 5 meters long and the safety gap between cars is 1.5 meters.
17. Brothers and sisters
Lenka has as many brothers as sisters. Her brothers have twice as many sisters as brothers. How many brothers and sisters are in the family?
18. Clock hands
The hands on the clock shows the time 12 hours and 2 minutes. Calculate the size of a sharp angle between clock hands three hours later.
19. Unknown number
Samuel wrote unknown number. Then he had add 200000 to the number and the result multiply by three. When it calculated he was surprised, because the result would have received anyway, if write digit to the end of original number. Find unknown number.
20. Cylinder - h2
Cylinder volume is 2.6 liters. Base area is 1.3 dm2. Calculate the height of the cylinder.

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