# Examples for secondary school students - page 21

1. Snowman 2 On the medal, which has the shape of a circle with a diameter 18 cm is sketched snowman so that the following requirements are met: 1. snowman is composed of three circles, 2. space over snowman is the same as under it, 3. diameters of all circles express
2. Circular motion Mass point moves moves uniformly in a circle with radius r = 3.4 m angular velocity ω = 3.6 rad/s. Calculate the period, frequency, and the centripetal acceleration of this movement.
3. Forth and back Car goes from point A to point B at speed 78 km/h and back at 82 km/h. If went there and back at speed 81 km/h journey would take five minutes less. What is the distance between points A and B?
4. Tetrahedron Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
5. Exp If ?, then n is:
6. Sequence In the arithmetic sequence is given: Sn=2304, d=2, an=95 Calculate a1 and n.
7. Linear independence Determine if vectors u=(-4; -5) and v=(20; 25) are linear Linear dependent.
8. 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.
9. Goniometric form Determine goniometric form of a complex number ?.
10. Metal alloy What is the ratio of metals in the alloy that is in the 50 tonnes of steel to 30 kg nickel?
11. 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.
12. Sequence Calculate what member of the sequence specified by ? has value 86.
13. Subway Subway train went between two stations that gradually accelerated for 26 seconds and reached a speed of 72 km/h. At this rate, went 56 seconds. Then 16 seconds slowed to a stop. What was the distance between the stations?
14. Three digits number How many are three-digit integers such that in they no digit repeats?
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. Pure quadratic equation Solve pure quadratic equation ?.
17. Temperature calculus Calculate percentage of temperature increase if changed from -9°C to 22°C?
18. Circles 2 Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 12 cm, 14 cm, 18 cm.
19. Price of state Estimate the cost of the state based on following reason. State price is expressed as a percentage respectively share in the redistribution of national GDP. Employee creates monthly value € 868 (super-gross wage).Then tax him 35.2% employer contributions
20. Diamond Determine the side of diamond if its content is S = 353 cm2 and one diagonal u2 = 45 cm.

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