# Examples for secondary school students - page 19

1. Property The length of the rectangle-shaped property is 8 meters less than three times of the width. If we increase the width 5% of a length and lendth reduce by 14% of the width it will increase the property perimeter by 13 meters. How much will the property cost
2. Average What is the average speed of the car, where half of the distance covered passed at speed 66 km/h and the other half at 86 km/h.
3. Triangular pyramid It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm3. What is it content (surface area)?
4. Volume from surface area What is the volume of the cube whose surface area is 96 cm2?
5. Geometric sequence 3 In geometric sequence is a8 = 312500; a11= 39062500; sn=1953124. Calculate the first item a1, quotient q and n - number of members by their sum s_n.
6. Cubes Surfaces of cubes, one of which has an edge of 48 cm shorter than the other, differ by 36288 dm2. Determine the length of the edges of this cubes.
7. Hexagonal pyramid Base of the pyramid is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high.
8. Carpet The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make rectangular cut of roll that piece of carpet will be longest possible and it fit into the room. How long is a piece of carpet? Note .: carpet will not be parallel with the diag
9. Area codes How many 6 digit area codes are possible if the first number can't be zero?
10. Numbers How many different 7 digit natural numbers in which no digit is repeated, can be composed from digits 0,1,2,3,4,5,6?
11. Center In the triangle ABC is point D[1,-2,6], which is the center of the |BC| and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z].
12. Cotangent If the angle α is acute, and cotg α = 1/3. Determine the value of sin α, cos α, tg α.
13. Angles in a triangle The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=83°. What sizes have other angles in a triangle?
14. Park In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.
15. School trip Class has 17 students. What different ways students can be accommodated in the hostel, where available 3× 2-bed, 1× 3-bed and 2× 4-bed rooms. (Each room has its own unique number)
16. Center Calculate the coordinates of the circle center: ?
17. Statue On the pedestal high 4 m is statue 2.7 m high. At what distance from the statue must observer stand to see it in maximum viewing angle? Distance from the eye of the observer from the ground is 1.7 m.
18. Cone If the segment of the line y = -3x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone?
19. Above Earth To what height must a boy be raised above the earth in order to see one-fifth of its surface.
20. Biquadratic By introducing a new variable solve biquadratic equation: ?

Do you have an interesting mathematical example that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.