# Examples for secondary school students

1. Pharmacy The pharmacy add to 3 liters of 95-percent alcohol 5 liters of 38.04 percent alcohol. How many percent pharmacy got?
2. Right triangle eq2 Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
3. Rhombus and diagonals The a rhombus area is 150 cm2 and the ratio of the diagonals is 3:4. Calculate the length of its height.
4. Points in plane The plane is given 12 points, 5 of which is located on a straight line. How many different lines could by draw from this points?
5. Cuboids Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)
6. Medians and sides Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides.
7. Tower model Tower height is 300 meters, weight 8000 tons. How high is the model of the tower weight 1 kg? (State the result in the centimeters). The model is made from exactly the same material as the original no numbers need to be rounded. The result is a three-dig
8. Square vs rectangle Square and rectangle have the same area contents. The length of the rectangle is 9 greater and width 6 less than side of the square. Calculate the side of a square.
9. Two trucks Two trucks left cities A and B against each other and met after an hour. The first car came to B 27 minutes later than the second car to A. Calculate the car speed if the distance between cities A, B is 90 km.
10. Combinations If the number of elements increase by 3, it increases the number of combinations of the second class of these elements 5 times. How many are the elements?
11. Modulo Find x in modulo equation: 47x = 4 (mod 9) Hint - read as: what number 47x divided by 9 (modulo 9) give remainder 4 .
12. Doubling The message is spreading that each day has doubled the number of people who know about it. All know message for 20 days. How long known it eighth people?
13. Minimum of sum Find a positive number that the sum of the number and its inverted value was minimal.
14. Inverse matrix Find how many times is the larger determinant is the matrix A, which equals 9 as the determinant of its inverse matrix.
15. Probably member Look at the series 2,6,25,96,285, ? What number should come next?
16. Variation equation Solve combinatorics equation: V(2, x+8)=72
17. One percent One percent of all the lights in the city are LED, the remaining 99% are conventional. Other types are not there. John counted them honestly but he had counted only conventional. After a good dinner he registered numbers and he have notice that from all
18. The inverse The inverse matrix for matrix A has a determinant value of 0.333. What value has a determinant of the matrix A?
19. Rectangle pool Determine dimensions of open pool with a square bottom with a capacity 32 m3 to have painted/bricked walls with least amount of material.
20. Gasoline canisters 35 liters of gasoline is to be divided into 4 canisters so that in the third canister will have 5 liters less than in the first canister, the fourth canister 10 liters more than the third canister and the second canister half of that in the first canis

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