# Examples for secondary school students - page 43

1. Work at plant Handyman has vowed to do repair work at the plant for 25 days. However, work had to be shortened and therefore gained helper. Together they made all the corrections for 13 1/3 days. How long the work would take helper himself?
2. Float boya A 0.5 meter spherical float is used as a location mark for a fishing boat anchor. It floats in salt water. Find the depth to which the float sinks if the material of which the float is made weighs 8 kilograms per cubic meter and salt water weighs 1027 kg/m
3. Bonbons Create a mixture of 50 kg of candy on price 700Kč. Candies has prices: 820Kč, 660Kč and 580Kč. Use cross rule.
4. Isosceles trapezoid In an isosceles trapezoid KLMN intersection of the diagonals is marked by the letter S. Calculate the area of trapezoid if /KS/: /SM/ = 2:1 and a triangle KSN is 14 cm2.
5. Triangle midpoints Determine coordinates of triangle ABC vertices if we know tirangle sides midpoints SAB [0;3] SBC [1;6] SAC [4;5], its sides AB, BC, AC.
6. Combinations How many different combinations of two-digit number divisible by 4 arises from the digits 3, 5 and 7?
7. Angles by cosine law Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).
8. Combined interest Combined interest: Carol has deposited CZK 100,000 in the bank with an annual interest rate of 1.5%. The money was put into the account 5.5.2016 and withdraw them all before Christmas 20.12.2016. How much money did she withdraw?
9. Cuboid and eq2 Calculate the volume of cuboid with square base and height 6 cm if the surface area is 48 cm2.
10. Inscribed circle XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm.
11. Lift The largest angle at which the lift rises is 16°31'. Give climb angle in permille.
12. Trinity How many different triads can be selected from the group 43 students?
13. Candies There are two types of candies in the store at 20 CZK/kg and 80 CZK/kg. How much will be cost a mix if we mix 22kg cheaper and 4kg more expensive candies?
14. Repairman Repairman has vowed to do repair work at the plant for 25 days. However work had to be shortened, and therefore he took helper worker. Together they made all the corrections for the whole days. How long it would take work to helper worker?
15. Roof 7 The roof has the shape of a regular quadrangular pyramid with a base edge of 12 m and a height of 4 m. How many percent is folds and waste if in construction was consumed 181.4m2 of plate?
16. Sum on dice We have two dice. What is the greater likelihood of fall a total sum 7 or 8 ? (write 7, 8 or 0 if the probabilities are the same)?
17. Tent Pyramid-shaped tent has a base square with a side length of 2 m and a height 1.7 m. How many meters of canvas is nneded to make it if for a waste should be added 10%?
18. Acceleration 2 if a car traveling at a velocity of 80 m/s/south accelerated to a velocity of 100 m/s east in 5 seconds, what is the cars acceleration? using Pythagorean theorem
19. Pyramid 4sides Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.
20. Neighborhood I have 7 cups: 1 2 3 4 5 6 7. How many opportunities of standings cups are there if 1 and 2 are always neighborhood?

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