# Examples for secondary school students - page 26

1. Skier
At this point, the first skier lead 20 km before the second skier and travels at a constant speed 19 km/h. The second skier rides at 24 km/h. How long take him to catch up the first?
2. Square side
Calculate length of side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0.
3. ISO Triangle V2
Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle.
4. Math logic
There are 20 children in the group, each two children have a different name. Alena and John are among them. How many ways can we choose 8 children to be among the selected A) was John B) was John and Alena C) at least one was Alena, John D) maximum one w
5. Sequence
Write the first 7 members of an arithmetic sequence: a1=-3, d=6.
6. Pyramid 8
Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.
7. Retail
At what price bought retail 1 kg goods from wholesale, if lost in the distribution is 4% of weight of the goods and retail still have a profit of 6.3%? Goods are sold at retail for 25 euro per kg.
8. Compare II
Which of the numbers 710, 107 is greater?
9. Friends in cinema
5 friends went to the cinema. How many possible ways can sit in a row, if one of them wants to sit in the middle and the remaining's place does not matter?
10. Snowman
In a circle with a diameter 50 cm are drawn 3 circles /as a snowman/ where: its diameters are integers, each larger circle diameter is 3 cm larger than the diameter of the previous circle. Determine snowman height if we wish highest snowman.
11. Isosceles trapezoid
Isosceles trapezoid ABCD, AB||CD is given by |CD| = c = 12 cm, height v = 16 cm and |CAB| = 20°. Calculate area of the trapezoid.
12. Rectangular triangles
The lengths of corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles? At what ratio are the contents of these triangles? Smaller rectangular triangle has legs 6 and 8 c
13. Digits
How many natural numbers greater than 4000 which are formed from the numbers 0,1,3,7,9 with the figures not repeated, B) How many will the number of natural numbers less than 4000 and the numbers can be repeated?
14. Surface area
The volume of a cone is 1000 cm3 and the content area of the axis cut is 100 cm2. Calculate the surface area of the cone.
15. ICE train
German runways test a new ICE train between Munich and Berlin. The train runs to Berlin at a slow speed of 100 km/h. Back from Berlin goes faster. How quickly did the train have to go on a return trip so that the total average train speed for both journeys
16. Cinema
How many ways can be divided 11 free tickets to the premiere of "Jáchyme throw it in the machine" between 6 pensioners?
17. Brass tube
The outer perimeter of brass tube (ρ = 8.5 g/cm3) is 38 cm. Its mass is 5 kg, length 54 cm. What is the pipe wall thickness?
18. Automaker
The automaker now produces daily 4 new cars more than last year so the production of 360 cars will save just one full working day. How many working days to produce 360 vehicles needed last year?
19. Angles of the triangle
ABC is a triangle. The size of the angles alpha, beta are in a ratio 4: 7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC.
20. Tournament
Determine how many ways can be chosen two representatives from 34 students to school tournament.

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