# Examples for secondary school students - page 28

1. 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.
2. Electrics - conductor The wire is 106 meters long at 0 °C and at every temperature increase of 1 °C the length increases by 0.15 mm per 1 m length of wire. Determine a function which represents the overall length of the wire as a function of temperature. What is the length of t
3. Ray Light ray loses 1/19 of brightness passing through glass plate. What is the brightness of the ray after passing through 7 identical plates?
4. Circles How many different circles is determined by 9 points at the plane, if 6 of them lie in a straight line?
5. Cosine Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.
6. Euclid 5 Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
7. Function For linear function f(x) = ax + ​​b ‬ is f(14)=179; f(15)=154. Calculate m, if f(m) = 2019 .
8. Peleton Cycling race was run at an average speed of 45 km/h. One cyclist lost with defect 8 minutes. How long and how far he must go at speed 51 km/h to catch peleton again?
9. Tin with oil Tin with oil has the shape of a rotating cylinder whose height is equal to the diameter of its base. Canned surface is 1884 cm2. Calculate how many liters of oil is in the tin.
10. Car rent Rental cars are paid a fixed daily fee plus 16 cents for each kilometer traveled. Samuel want to rent a car for a day and worked out that will pay 175 euros. When paying he got a 20% discount on the daily fee, the cost per kilometer is unchanged. Samuel th
11. Factors Can the expression ? be factored into rational factors?
12. Variations 3rd class From how many elements we can create 13,800 variations 3rd class without repeating?
13. Derivation Exists a function whose derivation is the same function?
14. Bus stop Determine at what time the bus leaves from the bus stop outside the village, if you know that when you leave home at 8:00 and go at speed 3 km/h, you come to a stop 9 minutes after the departure of the bus, and when you go speed at 4 km/h, you come to the
15. Rotary cylinder The rotating cylinder has a surface area 69.08 cm2. The area of the shell is 62.8 cm 2. What is the diameter of the cylinder?
16. Chord - TS The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS?
17. The hall The hall had a rectangular ground plan one dimension 20 m longer than the other. After rebuilding the length of the hall declined by 5 m and the width has increased by 10 m. Floor area increased by 300 m2. What were the original dimensions of the hall?
18. Copiers The new copier copying a folder of papers 5 min. faster than the old. The operator used new, but out of toner and exchange took 5 min. In that time copied on the old. The whole work has been done for 9 min. How long would the work done only by old copier?
19. Rectangle - sides What is the perimeter of a rectangle with area 266 cm2 if length of the shorter side is 5 cm shorter than the length of the longer side?
20. Fraction Fraction ? write as fraction a/b, a, b is integers numerator/denominator.

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