# Examples for secondary school students - page 55

1. Trees A certain species of tree grows an average of 0.5 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 200 centimeters tall.
2. BTC bubble One of the world's experts in bubbles -- Prof. Robert Shiller, a Yale economist -- said Bitcoin "was an amazing example of a bubble" back in 2014. If you exchange fiat US dollar \$100 to BTC in 2010, now in 2017 have value of 72.9 millions dollars. Find.
3. AP - simple Determine the first nine elements of sequence if a10 = -1 and d = 4
4. Rectangle The length of the rectangle is 12 cm greater than 3 times its width. What dimensions and area this rectangle has if ts circumference is 104 cm.
5. Pyramid The pyramid has a base rectangle with a = 6cm, b = 8cm. The side edges are the same and their length = 12.5 cm. Calculate the surface of the pyramid.
6. The pool The pool has a volume of 40 m3 and the water temperature is 20 °C. How much water at 100 °C should we pour into the pool to increase the water temperature by 5 °C?
7. Body diagonal The cuboid has a volume of 32 cm3. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
8. Money Peter has 2x more money than Michael. But if Peter gave Michael € 16 Michael would have 3.5 times more money than Peter. Determine how much money was originally Peter and how much Michael. Grandfather gathered apples into baskets. He filled one large and three small baskets. Small baskets are identical and each can hold 3 kg of apples less than in a large basket. In small baskets together 3 kg of apples over a large basket. How many kilogram
10. Air pressure The meteorological station measured the air pressure of 1060 hPa (hectopascals). In addition to measuring instruments, there is a residential house that has a flat roof with dimensions of 10 m and 28 m. What pressure force in MN (meganewtons) force the ai
11. Inner angles The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.
12. Variance and average Of the 40 values were calculated average mx = 7.5 and variance sx = 2.25. After the control was found to lack the two items of the values of x41 = 3.8 and x42=7. Correct the above characteristics (mx and sx).
13. Two trains There are two trains running the same distance. 1st train will travel it in 7 hours 21minutes. 2nd the train will travel 5 hours 57minutes and 34 seconds and it is 14 km/h faster than the first train. What are speeds of trains and how long is this railway
14. Unknown amount of money Damian and Denis split an unknown amount in the ratio of 5:4 . Damian got six euros more than Denis. Calculate an unknown amount. Determine how much money got Damian and how Denis.
15. Desribed circle to rectangle Rectangle with sides 6 cm and 4 cm was circumscribed circle. What part of the content of the circle determined by the circumscribed circle occupies a rectangle? Express in perctentages(%).
16. Probably member Look at the series 2,6,25,96,285, ? What number should come next?
17. Combinations From how many elements we can create 990 combinations 2nd class without repeating?
18. First class The shipment contains 40 items. 36 are first grade, 4 are defective. How many ways can select 5 items, so that it is no more than one defective?
19. GP - 8 items Determine the first eight members of a geometric progression if a9=512, q=2
20. Exponential equation Solve for x: (4^x):0,5=2/64.

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