# Examples for secondary school students - page 52

1. Cuboid edges in ratio Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm3.
2. 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.
3. Tree Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree?
4. Roof 8 How many liters of air are under the roof of tower which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof.
5. Glass Trader ordered from the manufacturer 200 cut glass. The manufacturer confirmed the order that the glass in boxes sent a kit containing either four or six glasses. Total sent 41 boxes. a) How many boxes will contain only 4 glasses? b) How many boxes will co
6. VCP equation Solve the following equation with variations, combinations and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0
7. Three numbers What is three numbers which have the property: the sum of the reciprocals of the first and second numbers is 12/7, the first and third 11/24 and the second and the third 3/8.
8. Balls The urn is 8 white and 6 black balls. We pull 4 randomly balls. What is the probability that among them will be two white?
9. Cards Suppose that are three cards in the hats. One is red on both sides, one of which is black on both sides, and a third one side red and the second black. We are pulled out of a hat randomly one card and we see that one side of it is red. What is the probabi
10. Cube in sphere The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
11. Bags The first bag has a weight of 18 kg, the second bag is a one-third lighter than the first and the third bag has three times less the weight of all three bags together. Determine their weights.
12. Calculation How much is sum of square root of six and the square root of 225?
13. Water reservoir The reservoir shape of a cylinder having a diameter 8 m and a height 2.8 m. The device indicates that the reservoir contains 800 hectoliters of water. Calculate how much % of volume is used.
14. De Moivre's formula There are two distinct complex numbers z such that z3 is equal to 1 and z is not equal 1. Calculate the sum of these two numbers. A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter.
16. Axial cut The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
17. AP 6 Calculate the first five items of an arithmetic sequence if it is given: a2 – a3 + a5 = 20 a1 + a6 = 38
18. Angles in ratio The size of the angles of the triangle are in ratio x: y = 7: 5 and the angle z is 42° lower than the angle y. Find size of the angles x, y, z. Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm. The city has 22,000 residents. How long it is expected to have 25,000 residents if the average annual population growth is 1.4%?