# Examples for secondary school students

1. Circle Circle is given by centre on S[-7; 10] and maximum chord 13 long. How many intersect points have circle with the coordinate axes?
2. Flowerbed Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 5.5 meters and an angle opposite to the base size is 94°. What is the distance from the base to opposite vertex?
3. Sales vs profit Apple sells 22 percent less computes than the Acer but the profit from their sales is 2.2 times higher than Acer. How many times are Apple computer more expensive than Acer?
4. Numbers How many different 3 digit natural numbers in which no digit is repeated, can be composed from digits 0,1,2?
5. Painter Pavel Painter Pavel painted the fence for 16 hours and painter Petr the same fence painted for 13 h. How long should take painted the fence together?
6. Cable car 2 Cable car rises at an angle 41° and connects the upper and lower station with an altitude difference of 1175 m. How long is the track of cable car?
7. Prism X The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?
8. Circle section Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector
9. Sector The perimeter of a circular sector with an angle 1.8 rad is 64 cm. Determine the radius of the circle from which the sector comes.
10. Fire tank Whole fire tank was discharged once in 5 days by first out by second in \$n days. Once firefighters pumped out 6/13 of water out from the tank and then let the water flow out both drain. How long take empty the tank?
11. Equation Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
12. Trains From station 130 km away started passenger train and after 2.2 hours after the express train, which travels 37 km an hour more. Express train finish journey 7 minutes early. Calculate the average speed of this two trains.
13. Hexagon A Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
14. Axial section Axial section of the cylinder has a diagonal 31 cm long and we know that the area of the side and the area of base is in ratio 3:2. Calculate the height and radius of the cylinder base.
15. G forces Calculate deceleration of car (as multiple of gravitational acceleration g = 9.81 m/s2) which occurs when a car in a frontal collision slows down uniformly from a speed 111 km/h to 0 km/h in 1.2 meters trajectory.
16. House roof The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m2 is needed to cover roof if roof pitch is 57° and we calculate 11% of waste, connections and overlapping of area roof?
17. Tower The top of the tower is a regular hexagonal pyramid with base edge 8 meters long and a height 5 meters. How many m2 of the sheet is required to cover the top of the tower if we count 8% of the sheet waste?
18. Simple interest 3 Find the simple interest if 11928 USD at 2% for 10 weeks.
19. Abyss Stone was pushed into the abyss: 2 seconds after we heard hitting the bottom. How deep is the abyss (neglecting air resistance)? (gravitational acceleration g = 9.81 m/s2 and the speed of sound in air v = 343 m/s)
20. Cuboid diagonal Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees.

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