# Examples for secondary school students

1. Field with vegetables Field planted with vegetables has shape of a rectangular isosceles triangle with leg length of 24 m. At the vertices of the triangle are positioned rotating sprinklers with a range of 12 m. How much of the field sprinkler doesn't irrigated?
2. Cuboid Find the cuboid that has the same surface area as the volume.
3. Balls We have n identical balls (numbered 1-n) is selected without replacement. Determine 1) The probability that at least one tensile strength number coincides with the number of balls? 2) Determine the mean and variance of the number of balls, which coincides
4. Orchard Route passes trapezoidal orchard perpendicular to the parallel sides. It is 80 cm wide. The lengths of the bases are in the ratio 5:3 and the length of the longer base to the length of the path is in the ratio 5:6. How many square meters occupies the ro
5. Geometric sequence In the geometric sequence is a4 = 20 a9 = -160. Calculate the first member a1 and quotient q.
6. Swing A child weighing 12 kg is sitting on a swing at a distance of 130 cm from the axis of rotation. How far away from the axis of rotation (center) must sit down his mother weighs 57 kg if she wants to be swing in balance?
7. Perimeter and legs Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.
8. Chemical parison The blown parison (with shape of a sphere) have a volume 1.5 liters. What is its surface?
9. High wall I have a wall 2m high. I need a 15 degree angle (upward) to second wall 4 meters away. How high must the second wall?
10. Flowerbed Flowerbed has the shape of a truncated pyramid, the bottom edge of the base a = 10 m, the upper base b = 9 m. Deviation angle between edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be planted if 1 m2 =
11. Cylinder surface, volume The area of the cylinder surface and the cylinder jacket are in the ratio 3: 5. The height of the cylinder is 5 cm shorter than the radius of the base. Calculate surface area and volume of the cylinder.
12. Pyramid - angle Calculate the surface of regular quadrangular pyramid whose base edge measured 6 cm and the deviation from the plane of the side wall plane of the base is 50 degrees.
13. Neighborhood I have 7 cups: 1 2 3 4 5 6 7. How many opportunities of standings cups are there if 1 and 2 are always neighborhood?
14. Cylinder - area The diameter of the cylinder is one-third the length of the height of the cylinder. Calculate the surface of cylinder if its volume is 2 m3.
15. Surface of the cylinder Calculate the surface area of the cylinder when its volume is 45 l and the perimeter of base is three times of the height.
16. Volume and surface Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm2.
17. Axial section Axial section of the cylinder has a diagonal 40 cm. The size of the shell and the base surface are in the ratio 3:2. Calculate the volume and surface area of this cylinder.
18. Antennas If you give me two antennas will be same. If you give me again your two antenna I have a 5× so many than you. How many antennas have both mans?
19. Father and son Father is three times older than his son. 12 years ago father was nine times older than the son. How old are father and son?
20. Numbers Write smallest three-digit number, which in division 5 and 7 gives the rest 2.

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