# Examples for secondary school students

1. Simple interest 2 Find the simple interest if 13905 USD at 4.5% for 6 months.
2. Simple interest 4 Find the simple interest if 5243 USD at 4.3% for 261 days. Assume a 361-day year.
3. Two valves Water fill the pool by two valves for 11 days. After 7 days the first valve was stopped and the second valve fill pool for 7 days. How many days took to fill the pool each of the valves individually?
4. Slope of the pool Calculate slope (rise:run) of the bottom of swimming pool long 30 m. Water depth at beginning of pool is 1.13 m (for children) and depth at end is 1.84 m (for swimmers). Slope express as percentage and as angle in degrees.
5. Mushrooms Fresh mushrooms contain 94% water, dried 14%. How many kg of fresh mushrooms is needed to collect to get 10 kg dried?
6. Two runners Two runners ran simultaneously towards each other from locations distant 34.6 km. The average speed of the first runner was 1/5 higher than the average speed of the second runner. How long should each ran a 34.6 km, if you know that they meet after 67 m
7. Shot Shot with a mass 43 g flying at 256 m/s penetrates into the wood to a depth 25 cm. What is the average force of resistance of wood?
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. Ball Ball was fired at an angle of 35° at initial velocity 437 m/s. Determine the length of the litter. (g = 9.81 m/s2).
10. Circular motion Mass point moves moves uniformly in a circle with radius r = 3.4 m angular velocity ω = 3.6 rad/s. Calculate the period, frequency, and the centripetal acceleration of this movement.
11. Average What is the average speed of the car, where half of the distance covered passed at speed 66 km/h and the other half at 86 km/h.
12. Bomber The aircraft flies at an altitude of 4100 m above the ground at speed 777 km/h. At what horizontal distance from the point B should be release any body from the aircraft body to fall into point B? (g = 9.81 m/s2)
13. 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?
14. Car At what horizontal distance reaches the car weight m = 753 kg speed v = 74 km/h when the car engine develops a tensile force F = 3061 N. (Neglect resistance of the environment.)
15. Center of gravity The mass points are distributed in space as follows - specify by coordinates and weight. Find the center of gravity of the mass points system: A1 [1; -20; 3] m1 = 46 kg A2 [-20; 2; 9] m2 = 81 kg A3
16. Against each other From two points A, B distant 23 km at the same time started two cars against each other at speeds 41 km/h and 65 km/h. How long does cars meet and what distance passes each of them?
17. Shooter The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot?
18. Square side Calculate length of side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0.
19. Train The train is running at speeds of 96 km/h. From the beginning of braking to full stop train run for 3.3 minutes. If the train slows the braking equally, calculate the distance of the place from the station where you need to start to brake.
20. 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:

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