# Examples for secondary school students - page 29 A ship travels 84 km on a bearing of 17°, and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.
2. The hall The hall had a rectangular ground plan one dimension 20 m longer than the other. After rebuilding the length of the hall declined by 5 m and the width has increased by 10 m. Floor area increased by 300 m2. What were the original dimensions of the hall?
3. Fraction Fraction ? write as fraction a/b, a, b is integers numerator/denominator.
4. Copiers The new copier copying a folder of papers 5 min. faster than the old. The operator used new, but out of toner and exchange took 5 min. In that time copied on the old. The whole work has been done for 9 min. How long would the work done only by old copier?
5. Rectangle - sides What is the perimeter of a rectangle with area 266 cm2 if length of the shorter side is 5 cm shorter than the length of the longer side?
6. Alloy The first alloy is a mixture of two metals in the ratio 1:2, the second is a mixture of same metals in the ratio 2:3. At what ratio we have these two alloys put into the furnace to obtain a new metal alloy with ratio 17:27? (All three ratios correspond to.
7. Eight blocks Dana had the task to save the eight blocks of these rules: 1. Between two red cubes must be a different color. 2. Between two blue must be two different colors. 3. Between two green must be three different colors. 4. Between two yellow blocks must be four
8. See harmonics It is true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. Central segment crosses the intersection of the diagonals and is parallel to the bases.
9. Logarithmic equation Solve equation: log33(3x + 21) = 0
10. Sphere area A cube with edge 1 m long is circumscribed sphere (vertices of the cube lies on the surface of a sphere). Determine the surface area of the sphere.
11. To the cinema Jane at 8 am got message that all 1093 school pupils will go to the cinema. Within 20 min she said it to the three friends. Each of them again for 20 minutes said to the other three. In this way the message spread further. At what time all the children in.
12. Arc Convert to arc measures (radians): 924 ° Result write as a multiple of π
13. Cylinder surface, volume The area of the cylinder surface and the cylinder jacket are in the ratio 3: 5. The height of the cylinder is 5 cm shorter than the radius of the base. Calculate surface area and volume of the cylinder.
14. Rope How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and length 350 mm (central mandrel have a diameter 50 mm)?
15. Hiker and cyclist At 7 PM hiker started at 6 km/h to hike. After 3 hrs. later started on the same trip cyclist at speed of 15 km/h. After an hour of driving a flat tire and take him half hours to correct defect. At what time catch up cyclist with hiker?
16. Exponential equation In the set R solve the equation: ?
17. Distance Wha is the distance between the origin and the point (18; 22)?
18. Pot Calculate the height of 3 liter pot with shape cylinder with a diameter of 10 cm.
19. Scouts Three scouts went on a three day trip. The second day went 4 km more than the first day. The third day went two times less than the first day. They went along 54 km. How many kilometers went every day together?
20. Three-digit numbers How many three-digit numbers are from the numbers 0 2 4 6 8 (with/without repetition)?

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