# Examples for secondary school students

1. Loan 5 Abdul takes a loan of 200000 from Ali and agrees to repay in number of instalment, each instalment begin with the 2nd exceeding the previous one by 1000, if the first instalment is 500, find how many instalment will be necessary to be wipe out the loan?
2. Uphill and downhill The cyclist moves uphill at a constant speed of v1 = 10 km/h. When he reaches the top of the hill, he turns and passes the same track downhill at a speed of v2 = 40 km/h. What is the average speed of a cyclist?
3. Gravitation From the top of the 80m high tower, the body is thrown horizontally with an initial speed of 15 m/s. At what time and at what distance from the foot of the tower does the body hit the horizontal surface of the Earth? (use g = 10 ms-2)
4. Potatoes For three days the store sold 1400 kg of potatoes. The first day they sold 100 kilograms of potatoes less than the second day, the third-day three-fifths of what they sold the first day. How many kgs of potatoes sold every day?
5. Nine books Nine books are to be bought by a student. Art books cost \$6.00 each and biology books cost \$6.50 each . If the total amount spent was \$56.00, how many of each book was bought?
6. Rocket start The body launched vertically up returns to the start site in 6 seconds. What height did it have?
7. Centroid - two bodies A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1m attached so that its center lies on the longitudinal axis of the bar. Both bodies are of the same uniform material. The sphere is twice as heavy as the bar. Find the center of gravi
8. Percentage increase Increase number 400 by 3.5%
9. Find parameters Find parameters of the circle in the plane - coordinates of center and radius: ?
10. Carpenters Carpenters 1 and 2 spend 10 days and 5 days respectively to make one table. If 50 tables were made by the first carpenter and 30 tables were made by the second carpenter, What is the average time spent on the products?
11. Profit growth The profit of a company increased by 25% during the year 1992, increased by 40% during the year 1993, decreased by 20% in the year 1994 and increased by 10% during the year 1995. Find the average growth in the profit level over the four years periods?
12. Isosceles triangle 8 If the rate of the sides an isosceles triangle is 7:6:7, find the base angle correct to the nearest degree.
13. Lighthouse Marcel (point J) lies in the grass and sees the top of the tent (point T) and behind it the top of the lighthouse (P). | TT '| = 1.2m, | PP '| = 36m, | JT '| = 5m. Marcel lies 15 meters away from the sea (M). Calculate the lighthouse distance from the sea
14. Cable car Find the elevation difference of the cable car when it rises by 67 per mille and the rope length is 930 m.
15. Spherical cap 4 What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula.
16. A screen A screen is 1680 x 1050 pixels. What are the coordinates (and size in pixels) of an centered area which is exactly 33% of the screen size?
17. Three-digit integers How many three-digit natural numbers exist that do not contain zero and are divisible by five?
18. Sheep and cows There are only sheep and cows on the farm. Sheep is eight more than cows. The number of cows is half the number of sheep. How many animals live on the farm?
19. STRESSED word Each letter in STRESSED is printed on identical cards, one letter per card and assembled in random order. Calculate the probability that the cards spell DESSERTS when assembled.
20. Spherical cap Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm2. Determine the radius r of the sphere from which the spherical cap was cut.

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