# Examples for secondary school students - page 9

1. Speed of Slovakian trains Rudolf decided to take the train from the station 'Trnava' to 'Zemianske Kostoľany'. In the train timetables found train R 725 Remata : km0Bratislava hl.st.12:574Bratislava-Vinohrady13:0113:0219Pezinok13:1213:1346Trnava13:3013:3263Leopoldov13:4514:0168H
2. Without Euclid laws Right triangle ABC with right angle at the C has a=5 and hypotenuse c=19. Calculate the height h of this triangle without the use of Euclidean laws.
3. Hole In the center of the cube with edge 14 cm we will drill cylinder shape hole. Volume of the hole must be 27% of the cube. What drill diameter should be chosen?
4. Seedcake Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?
5. Euclid1 Right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?
6. Phone numbers How many 7-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated?
7. Diofant equation In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)
8. Octahedron - sum On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also.
9. Two doctors Doctor A will determine the correct diagnosis with a probability 93% and doctor B with a probability 79%. Calculate probability of correct diagnosis if patient is diagnosed by both doctors.
10. Cuboid Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58°
11. Area of RT In the right triangle has orthogonal projections of legs to the hypotenuse lengths 7 cm and 12 cm. Determine the area of ​​this triangle.
12. 4side pyramid Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.
13. Freedom In the city are 3/9 of women married for 3/6 men. What proportion of the townspeople is free (not married)? Express as a decimal number.
14. Map On the tourist map at a scale of 1 : 50000 is distance between two points along a straight road 3.7 cm. How long travels this distance on a bike at 30 km/h? Time express in minutes.
15. Triangle ABC Right triangle ABC with right angle at the C, |BC|=18, |AB|=33. Calculate the height of the triangle hAB to the side AB.
16. Pumps The tank is filled with two pumps in 16 minutes. The first pump is filled in 30 minutes earlier than two one. How many minutes is filled with the first pump?
17. Building How high is the building that throws horizontal shadow 95.4 m long at angle 50°?
18. 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.
19. Pyramid a+h Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm.
20. Wire One pull of wire is reduced its diameter by 14%. What will be diameter of wire with diameter 19 mm over 10 pulls?

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