1. The perimeter The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX?
2. Two heights and a side Construct triangle ABC when the given side is c = 7 cm, height to side a va = 5 cm and height to side b: vb = 4 cm.
3. Performance Two masons with the same performance would have made of plaster for 6 days. One of them, however, has increased its daily performance by 50%. How long would take they now to make plaster together?
4. Bulbs and electricity In the sports hall, 875 identical light bulbs light for 2 hours. How long does it take for 100 such light bulbs to consume the same amount of electricity?
5. 40% volume 40% volume with 104 uph (units per labor hour) 8 people working. What is the volume?
6. Angle of diagonal Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.
7. An oil An oil drum is cut in half. One half is used as a water trough. Use the dimensions; length 82cm, width 56cm to estimate the capacity of the water trough in liters.
8. Equilateral cylinder A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere.
9. Scientific notation Approximately 7.5x105 gallons of water flow over a waterfall each second. There are 8.6x104 seconds in 1 day. Select the approximate number of gallons of water that flow over the waterfall in 1 day.
10. Resistance A resistor having an electrical resistance of 1.5 k ohms passes an electrical current of 0.1 A. Calculate what voltage is between the terminals of the resistor.
11. Triangles Five sticks with a length of 2,3,4,5,6 cm. How many ways can you choose three sticks to form three sides of a triangle? The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm2 of material will we need when we 10% is waste?
13. Ditch Ditch profile is an isosceles trapezoid with bases of length 80m and 60m. The slope of the side wall of the ditch is 80°. Calculate the ditch depth.
14. 15 teachers 15 teachers teach for a combined amount of 128 days over a period of 64 days. What is this expressed as a percentage?
15. Blocks There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there?
16. Area of iso-trap Find the area of an isosceles trapezoid if the lengths of its bases are 16 cm and 30 cm, and the diagonals are perpendicular to each other.
17. Bricklayers When a bricklayer works himself to redeem the house in 8 days, the other bricklayer will be finished in 10 days. How long will it take to make 3 such houses together?
18. A square A square with length of diagonals 12cm give: a) Calculate the area of a square b) rhombus with the same area as the square, has one diagonal with length of 16 cm. Calculate the length of the other diagonal.
19. Ratio of edges The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
20. Big cube Calculate the surface of the cube, which is composed of 64 small cubes with an edge 1 cm long.

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