# Examples for secondary school students - page 39

- Tubes

Iron tubes in the warehouse are stored in layers so that each tube top layer fit into the gaps of the lower layer. How many layers are needed to deposit 100 tubes if top layer has 9 tubes? How many tubes are in bottom layer of tubes? - Annual income

The annual incomes (in thousands of $) of fifteen families is: 60, 80, 90, 96, 120, 150, 200, 360, 480, 520, 1060, 1200, 1450, 2500, 7200 Calculate harmonic and geometric mean. - James

James paints a fence. If every day instead of 14 planks painted 16 would be done on one day earlier. How many of planks has a fence altogether? - Hexagon rotation

A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated? - Inscribed circle

Write the equation of a incircle of the triangle KLM if K [2,1], L [6,4], M [6,1]. - Square ABCD

Construct a square ABCD with cente S [3,2] and the side a = 4 cm. Point A lies on the x-axis. Construct square image in the displacement given by oriented segment SS'; S` [-1 - 4]. - Equation

How many real roots has equation ? ? - Two triangles SSA

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14 - Cleaners

Milan would clean up the room for 2.5 hours, Eric would take 10 hours. How long they swept the room together? - Diamond diagonals

Calculate the diamond's diagonal lengths if its content is 156 cm^{2}and the side length is 13 cm. - Prism

Base of perpendicular triangular prism is a right triangle with cathetuses 4.5 cm and 6 cm. What is the surface of the prism, if its volume of 54 cubic centimeters. - Four sides of trapezoid

In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles. - Null points

Calculate the roots of the equation: ? - Clock face

clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles. - Win in raffle

The raffle tickets were sold 200, 5 of which were winning. What is the probability that Peter, who bought one ticket will win? - Crates 2

In 6 crates is 45 kg of apples In 5 crates is equally In 1 in crate is 3 kg more How many kilograms in each crate? - Hockey game

In the hockey game was made 6 goals. Czech played against Finland. Czechs won 4:2. In what order to fall goals? How many game sequence was possible during the game? - Double-track

On double-track express met with a freight train. Express travel at speed 72 km/h, a freight train at speed 36 km/h. After what time period will be from 9 km apart? - 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? - Powers

Express the expression ? as the n-th power of the base 10.

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