# Examples for secondary school students

- 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? - 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 - 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? - 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 - 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? - 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: ? - Distance

Wha is the distance between the origin and the point (18; 22)? - 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. - Password

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. - 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? - 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? - 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 cm^{2}of cardboard we need to cover overlap and joints that are 5% of a - 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? - Comparing powers

How many times is number 5^{6}larger than number 4^{6}? - Leg

Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg. - Diagonals

Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°. - Inscribed rectangle

The circle area is 216. Determine the area of inscribed rectangle with one side 5 long. - V - slope

The slope of the line whose equation is -3x -9 = 0 is - 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. - 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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