# The most difficult examples - page 2

1. ICE train German runways test a new ICE train between Munich and Berlin. The train runs to Berlin at a slow speed of 100 km/h. Back from Berlin goes faster. How quickly did the train have to go on a return trip so that the total average train speed for both journeys
2. Volume of cube Solve the volume of a cube with width 26cm .
3. Algebrogram Solve algebrogram for sum of three numbers: BEK KEMR SOMR ________ HERCI
4. Triangle Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 158 b = 185 c = 201
5. ABCD AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
6. Billiard balls A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original. T
7. EQ2 Solve quadratic equation: ?
8. Fe vs. H2O The volume of what the body of the same weight is greater - iron or water?
9. Brackets 2 Add parenthesis to make true: 5-2×6-4+2=5
10. Triangle ABC v2 Area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x.
11. Prism bases Volume perpendicular quadrilateral prism is 360 cm3. The edges of the base and height of the prism are in the ratio 5:4:2 Determine the area of the base and walls of the prism.
12. Notebooks Liza a store owner buys 560 notebooks. He sold 3/8 of the notebook then she adds the stocks of notebook of 1/4 of the number of notebooks she bought. What is the total number of notebook she bought?
13. 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
14. Plane II A plane flew 50 km on a bearing 63degrees20 and the flew on a bearing 153degrees20 for 140km. Find the distance between the starting point and the ending point
15. Simple equation 3 24 = n • 27, solve for n
16. Diagonals in the diamond The length of one diagonal in diamond is 24 cm greater than the length of the second diagonal and diamond area is 50 m2. Determine the sizes of the diagonals.
17. Shade Shade the area on the grid that shows 5/8 x 2/4
18. Friends James and Jaroslav are friends. Together they had 48 toy cars. But if John took 8 cars from Jaroslav, Jaroslav will be have 1.5 times more toy cars than James. How many toy cars had Jaroslav and James?
19. Tiles How much you will pay CZK for laying tiles in a square room with a diagonal of 8 m if 1 m2 cost CZK 420?
20. 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

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