# Examples for secondary school students - page 10

- Trains

From station 130 km away started passenger train and after 2.2 hours after the express train, which travels 37 km an hour more. Express train finish journey 7 minutes early. Calculate the average speed of this two trains. - Pumps

The tank is filled with two pumps in 16 minutes. The first pump is filled in 30 minutes earlier than two one. How many minutes is filled with the first pump? - Wire

One pull of wire is reduced its diameter by 14%. What will be diameter of wire with diameter 19 mm over 10 pulls? - Pyramid a+h

Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm. - n-gon II

What is the side length of the regular 5-gon circumscribed circle of radius 11 cm? - Compound interest

Calculate time when deposit in the bank with interest 2.5% p.a. doubles. - n-gon

Gabo draw n-gon, which angles are consecutive members of an arithmetic sequence. The smallest angle is 70° biggest 170°. How many sides have Gabo's n-gon? - Climb

Road has climbing 1:27. How big is a angle corresponds to this climbing? - Stairway

What angle rising stairway if step height in 17 cm and width 27 cm? - Square 2

Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate area of the square ABCD. - Angle between lines

Calculate the angle between these two lines: ? ? - Goat and circles

What is the radius of a circle centered on the other circle and the intersection of the two circles is equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which g - Sale

If the product twice price cut by 25%, what percentage was price cut in total? - Rotary cone

Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm^{3}. Calculate the radius of the base circle and height of the cone. - Tetrahedral pyramid

Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm^{2}and deviation angle of the side edges from the plane of the base is 60 degrees. - Circle section

Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector. - 4s pyramid

Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height? - Cut and cone

Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees. - Jewel

Rhombus-shaped jewel have area of 93 mm^{2}and the edge in long 13.2 mm. Calculate the size of rhombus acute angle. - Football league

In the 5th football league is 10 teams. How many ways can be filled first, second and third place?

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