# Examples for secondary school students - page 41

1. Office Office building was built in the shape of a regular hexagon inscribed in a circle with a radius of 12 m. The height of the walls is 7m. How much CZK cost plastering the walls of the building, if per 1 m square cost CZK 400?
2. Chords How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones?
3. Statistics The sum of all deviations from the arithmetic mean of the numerical sequence 4, 6, 51, 77, 90, 93, 95, 109, 113, 117 is:
4. 3 days Worker checked 2,950 products in 3 days. Second day checked 25% more than the first day. The third day 15% more products than the second day. How many products he checked in each day.
5. Volume of three cuboids Calculate the total volume of all cuboids for which the the size of the edges are in a ratio of 1:2:3, and one of the edges has a size 6 cm. It is given a quadratic function y = -4x2+5x+c with unknown coefficient c. Determine the smallest integer c for which the graph of f intersects the x-axis at two different points.
7. Speedometer The speedometer of a car reads 66 km/h. It's accurate to within 4.1% What is the maximum possible error?
8. Four sides of trapezoid Trapezoid is given by length of four sides: 40.5 42.5 52.8 35.0. Calculate its area.
9. SD - mean Mean is 10 and standard deviation is 3.5. If the data set contains 40 data values, approximately how many of the data values will fall within the range 6.5 to 13.5?
10. Cone Into rotating cone with dimensions r = 8 cm and h = 8 cm incribe cylinder with maximum volume so that the cylinder axis is perpendicular to the axis of the cone. Determine the dimensions of the cylinder.
11. Triangle IRT In isosceles right triangle ABC with right angle at vertex C is coordinates: A (-1, 2); C (-5, -2) Calculate the length of segment AB.
12. Medicine We test medicine on 6 patients. For all drug doesn't work. If the drug success rate of 20%, what is the probability that medicine does not work?
13. Support colum Calculate the volume and surface of the support column that is shaped as perpendicular quadrangular prism whose base is a rhombus with a diagonals u1 = 102 cm u2 = 64 cm. Column height is 1. 5m.
14. Cube 9 What was the original edge length of the cube if after cutting 39 small cubes with an edge length 2 dm left 200 dm3?
15. ABS What is the value of ? ?
16. Sequence Between numbers 1 and 53 insert n members of the arithmetic sequence that its sum is 702. Quadratic equation ? has roots x1 = -26 and x2 = -86. Calculate the coefficients b and c.
18. Triangle The triangle has known all three sides: a=5.5 m, b=5.3 m, c= 7.8 m. Calculate area of ​this triangle.
19. Rhombus and diagonals The a rhombus area is 150 cm2 and the ratio of the diagonals is 3:4. Calculate the length of its height.
20. Compound interest Compound interest: Clara deposited CZK 100,000 in the bank with an annual interest rate of 1.5%. Both money and interest remain deposited in the bank. How many CZK will be in the bank after 3 years?

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