# Examples for secondary school students

- Pharmacy

The pharmacy add to 3 liters of 95-percent alcohol 5 liters of 38.04 percent alcohol. How many percent pharmacy got? - 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. - Rhombus and diagonals

The a rhombus area is 150 cm^{2}and the ratio of the diagonals is 3:4. Calculate the length of its height. - 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? - 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) - 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. - 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 - 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. - 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. - 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? - Modulo

Find x in modulo equation: 47x = 4 (mod 9) Hint - read as: what number 47x divided by 9 (modulo 9) give remainder 4 . - 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? - Minimum of sum

Find a positive number that the sum of the number and its inverted value was minimal. - Inverse matrix

Find how many times is the larger determinant is the matrix A, which equals 9 as the determinant of its inverse matrix. - Probably member

Look at the series 2,6,25,96,285, ? What number should come next? - Variation equation

Solve combinatorics equation: V(2, x+8)=72 - 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 - The inverse

The inverse matrix for matrix A has a determinant value of 0.333. What value has a determinant of the matrix A? - Rectangle pool

Determine dimensions of open pool with a square bottom with a capacity 32 m^{3}to have painted/bricked walls with least amount of material. - 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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