# Examples for secondary school students

1. Virus We have a virus that lives one hour. Every half hour produce two child viruses. What will be the living population of the virus after 3.5 hours?
2. Alloy The first alloy is a mixture of two metals in the ratio 1:2, the second is a mixture of same metals in the ratio 2:3. At what ratio we have these two alloys put into the furnace to obtain a new metal alloy with ratio 17:27? (All three ratios correspond to
3. Segments Line segments 62 cm and 2.2 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide?
4. Hairs Suppose the length of the hair is affected by only the α-keratin synthesis, which is the major component. This synthesis takes place in the epithelial cells of the hair bulb. The structure of α-keratin is made up of α-helix, wherein in one revolution it i
5. Midpoint of segment Point A has coordinates [-16; 23] and the midpoint of the segment AB is the point [2; 12]. What are the coordinates of point B?
6. Stock market Simon one day decided to invest € 62000 to the stock market. After six months he invested July 25 stock markets fell by 47%. Fortunately for Simon from July 25 5 to October 25 his shares have risen by 39%. Simon is then: ?
7. Distance Wha is the distance between the origin and the point (18; 22)?
8. Package The package has no more than 66 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 1.3 m of cloth and on one dress 5 m. Determine the amount of the cloth in the package. The voltage station is every day changing the master password, which consists of three letters. Code generation process does not change and is based on the following procedure: The following letters (A) to (I) correspond to different numbers from 1 to 9.
10. Vector sum The magnitude of the vector u is 12 and the magnitude of the vector v is 8. Angle between vectors is 61°. What is the magnitude of the vector u + v?
11. Vectors Vector a has coordinates (8; 10) and vector b has coordinates (0; 17). If the vector c = b - a, what is the magnitude of the vector c?
12. Box Cardboard box shaped quadrangular prism with a rhombic base. Rhombus has a side 5 cm and one diagonal 8 cm long and height of the box is 12 cm. The box will open at the top. How many cm2 of cardboard we need to cover overlap and joints that are 5% of a
13. Pairs From the five girls and four boys teachers have to choose one pair of boy and girl. A) How many such pairs of (M + F)? B) How many pairs where only boys (M + M)? C) How many are all possible pairs?
14. Comparing powers How many times is number 56 larger than number 46?
15. Leg Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg.
16. Diagonals Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°.
17. Inscribed rectangle The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.
18. V - slope The slope of the line whose equation is -3x -9 = 0 is
19. 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.
20. Aircrafts Above the town hall tower flew the plane with constant speed 510 km/h and 15 minutes later the second plane at speed of 703 km/h. How long and how far from the town hall will be aircrafts caught up?

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