# Examples for secondary school students - page 14

1. Geometric progression Fill 4 numbers between 4 and -12500 to form geometric progression.
2. Divisibility Determine the smallest integer which divided 11 gives remainder 4 when divided 15 gives remainder 10 and when divided by 19 gives remainder 16.
3. 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?
4. Wiring Conduit has a cross section 482 mm. Maybe put it into 6 conductors with a cross section S2 \$mm2?
5. Nine-gon Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
6. Mystery of stereometrie Two regular tetrahedrons have surfaces 88 cm2 and 198 cm2. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places.
7. Lock Combination lock will open when the right choice of 5 numbers (from 1 to 12 inclusive) is selected. A. How many different lock combinations are possible? B. Is he combination lock named appropriately?
8. Sphere and cone Within the sphere of radius G = 33 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
9. 3y inflation Price of the roll rise in the first year by 9%, the second year fell by 5% and in the third year increased by 3%. Calculate the average annual increase in price of the roll.
10. Side c In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
11. Pit Pit has shape of a truncated pyramid with rectangular bases and is 0.8 m deep. The length and width of the pit is the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of pit we use 0.6 l of green colour. How many liters of paint is needed when w
12. Cuboid Find the cuboid that has the same surface area as the volume.
13. Height difference What height difference overcome if we pass road 1 km long with a pitch21 per mille?
14. AVG of INT What is the average of the integers from 9 throuht 52 inclusive?
15. Circle From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x0, y0] and radius of the circle r.
16. Black building Keith built building with a rectangular shape 6.5 m × 3.9 m. Calculate how much percent exceeded the limit 25 m2 for small building. Building not built in accordance with the law is called "black building". Calculate the angle that the walls were clenchin Average climb of the road is given by ratio 1:15. By what angle road average climb?
18. Elevation What must be the elevation of an observer in order that he may be able to see an object on the earth 536 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
19. Dices We will throw two dice. What is the probability that the ratio between numbers on first and second dice will be 1:2?
20. Triangle and its heights Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.

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