Examples for secondary school students - page 166 of 237
Number of problems found: 4730
- Perimeter - ASA theorem
Calculate the perimeter of the triangle ABC if a = 12 cm, the angle beta is 38 degrees, and the gamma is 92 degrees. - Concentration - salt solution
We added 300 g of water to 400 g of salt solution, reducing the solution's concentration by 5%. How much water did the original solution contain, and what was its concentration? - Square Matrix Rows
Determine how many rows the 7th-order square matrix contains. - Matrix elements Determine how many elements a third-order square matrix contains.
- The little pub
In an unnamed Prague pub, the Czech Trade Inspection (ČOI) measured draft large beers. From thirty measured half-liters, the sample mean was 0.457085 l and the sample standard deviation was 0.00303. Test at the 1% and 5% significance level the hypothesis - Cuboids
Two separate cuboids with different orientations are 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) - Rhombus and diagonals
The rhombus area is 150 cm2, and the ratio of the diagonals is 3:4. Calculate the length of its height. - Material transport
Two trucks were supposed to load the building materials in 10 days. After 6 days of work, the first car broke down, and the second one carried building materials for another 9 days. How many days would the first and second cars take the building materials - Points in plane
The plane is given 12 points, 5 of which are located on a straight line. How many different lines could be drawn from these points? - Tower model
The tower's height is 300 meters, and its weight is 8000 tons. How high is the model of the tower's weight of 1 kg? (State the result in centimeters). The model is made from exactly the same material as the original no numbers need to be rounded. A result - Power equation
Solve the power equation: 2.1463 = 0.4179x0.419 - Dataset
Data: 11,15,11,16,12,17,13,21,14,21,15,22 Find the dispersion of a given dataset. - Hostel people
The hostel has 90 people; There are three times more boys than girls, and there are 70 fewer teachers than boys and girls together. How many teachers are there? - Medians and sides
Triangle ABC in the plane Oxy has the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try to calculate the lengths of all medians and all sides. - Two similar triangles
Find unknown sides of a similar triangles: a = 6 cm, b = 8 cm, c =?, a '=?, b '= 12 cm, c' = 15 cm - Coffee blend
From two types of coffee priced at 450 CZK/kg and 730 CZK/kg, 20 kg of a blend priced at 520 CZK/kg is to be prepared. How many kilograms of each type of coffee are needed? - Square vs rectangle
A square and a rectangle have the same areas. The rectangle's length is nine greater, and the width is six less than the side of the square. Calculate the side of a square. - Plane and helicopter
From two airports, a plane and a helicopter took off at the same time. The helicopter was flying to the airport from which the plane took off, the plane to the airport from which the helicopter took off. When they passed each other, the helicopter had flo - 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 and B is 90 km. - Fraction equation
Calculate x: (x-1) over (x-2) + (x-2) over (x-4) = 4
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