Examples for secondary school students

1. Sum-log
The sum of two numbers is 32, the sum of their logarithms (base 10) is 2.2. Determine these numbers.
2. Fish tank
A fish tank at a pet store has 8 zebra fish. In how many different ways can George choose 2 zebra fish to buy?
3. ISO trapezium
Calculate area of isosceles trapezoid with base 95 long, leg 27 long and with the angle between the base and leg 70 degrees.
4. Two cars
Car A1 goes at average speed of 106 km/h and the second car A2 goes at 103 km/h. How many second will it take car A1 to circulate car A2? Assume that both cars are 5 meters long and the safety gap between cars is 1.5 meters.
5. Speedometer
The speedometer of a car reads 66 km/h. It's accurate to within 4.1% What is the maximum possible error?
6. Chord - TS v2
The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS?
7. Line segment
For the line segment whose endpoints are L[-1, 13] and M[18, 2], find the x and y value for the point located 4 over 7 the distance from L to M.
8. Combi-triangle
On each side of the square is marked 10 different points outside the vertices of the square. How many triangles can be constructed from this set of points, where each vertex of the triangle lie on the other side of the square?
9. Diameter
If the endpoints of a diameter of a circle are A(10, -1) and B (3, 10), what is the radius of the circle?
10. Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
11. Chord - TS
The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS?
12. Isosceles IV
In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
13. Gasholder
The gasholder has spherical shape with a diameter 20 m. How many m3 can hold in?
14. Green - Red
We have 5 bags. Each consist one green and 2 red balls. From each we pull just one ball. What is the probability that we doesn't pull any green ball?
15. Scouts
The boys from scout group traveled 5 days distance 115 km. Every day walked 1.5 km less than the previous day. How many kilometers scouts walked in the first day?
16. EQL triangle
Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
17. Task of the year
Determine the number of integers from 1 to 106 with ending four digits 2006.
18. Funnel
The funnel has the shape of an equilateral cone. Calculate the surface wetted with water if we poured into the funnel 7.1 liters of water.
19. Combinatorics
The city has 7 fountains. Works only 6. How many options are there that can squirt ?
20. Dog
Man goes with a dog on a long walk 17 km from the house. Man is walking at speed 4.9 km/h and a dog that constantly running between house and man at 12.6 km/h. How many kilometers will run the dog when they reach their destination?

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