# Examples for secondary school students - page 20

1. Toys
3 children pulled 12 different toys from a box. Many ways can be divided toys so that each children had at least one toy?
2. Two valves
Water fill the pool by two valves for 11 days. After 7 days the first valve was stopped and the second valve fill pool for 7 days. How many days took to fill the pool each of the valves individually?
3. The cone
The lateral surface area of the cone is 4 cm2, the area of the base of the cone is 2 cm2. Determine the angle in degrees (deviation) of the cone sine and the cone base plane. (Cone side is the segment joining the vertex cone with any point of the base ci
4. Sun rays
If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current hei
5. 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 is
6. Vertical prism
The base of vertical prism is a right triangle with leg a = 5 cm and a hypotenuse c = 13 cm. The height of the prism is equal to the circumference of the base. Calculate the surface area and volume of the prism
7. Mushrooms
Fresh mushrooms contain 94% water, dried 14%. How many kg of fresh mushrooms is needed to collect to get 10 kg dried?
8. Segments
Which of the pairs of numbers on the number line encloses the longest segment: ?
9. Line
Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p?
10. Family
What is the probability that a family with 7 childrens have: exactly 5 girls? 7 girls and 0 boys? Consider the birth probability of a girl is 48.69% and boy 51.31%.
11. Funnel
The funnel has the shape of an equilateral cone. Calculate the surface wetted with water if we poured into the funnel 7.1 liters of water.
12. Loan
Apply for a \$ 59000 loan, the loan repayment period is 8 years, the interest rate 7%. How much should I pay for every month (or every year if paid yearly). Example is for practise geometric progression and/or periodic payment for an annuity.
13. Leg
Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg.
14. Diagonals in the diamond
The length of one diagonal in diamond is 24 cm greater than the length of the second diagonal and diamond area is 50 m2. Determine the sizes of the diagonals.
15. Triangle SAA
The triangle has one side long 71 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle.
16. Fire tank
Whole fire tank was discharged once in 5 days by first out by second in \$n days. Once firefighters pumped out 6/13 of water out from the tank and then let the water flow out both drain. How long take empty the tank?
17. Chord AB
What is the length of the chord AB if its distance from the center S of the circle k(S, 92 cm) is 10 cm?
18. Chemical parison
The blown parison (with shape of a sphere) have a volume 1.5 liters. What is its surface?
19. Isosceles trapezoid
The lengths of the bases of the isosceles trapezoid are in the ratio 5:3, the arms have a length of 5 cm and height = 4.8 cm. Calculate the circumference and area of a trapezoid.
20. Circle arc
Calculate the area of the circular arc in m2 where the diameter is 290 dm and a central angle is 135°. Result round to three decimal places.

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