Examples for secondary school students - page 75 of 213
Number of problems found: 4256
- Summands
We want to split the number 110 into three summands so that the first and the second summand are in ratio 4:5, and the third with the first are in ratio 7:3. Calculate the smallest summands. - Triangle in a square
In a square ABCD with side a = 6 cm, point E is the center of side AB, and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides. - Accommodated 25881
Fifty-one students are accommodated in the tourist hostel in 15 four-bed and three-bedrooms. How many rooms are there if there are 2 spaces left after housing? a) There are four-bed rooms. b) There are three-bed rooms. - Right triangle - ratio
The lengths of the legs of the right triangle ABC are in ratio b = 2:3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle.
- Six questions test
There are six questions in the test. There are three answers to each - only one is correct. To take the exam, students must answer at least four questions correctly. Alan didn't learn, so he circled the answers only by guessing. What is the probability th - Traffic sign
There is a traffic sign for climbing on the road with an angle of 7%. Calculate at what angle the road rises (falls). - Fighter
A military fighter flies at an altitude of 10 km. The ground position was aimed at an altitude angle of 23° and 12 seconds later at an altitude angle of 27°. Calculate the speed of the fighter in km/h. - The right triangle
In the right triangle ABC with a right angle at C, we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles. - Isosceles triangle
Calculate the size of the interior angles and the length of the base of the isosceles triangle if the arm's length is 17 cm and the height of the base is 12 cm.
- Probability 25631
A private company will hire two IT specialists. Tomáš is among the five registered candidates. What is the probability that he will not be accepted? - Cyclist 25591
The cyclist rode 44 km and 400 m in three days. In the first hour, he covered the course 5% longer than in the second hour, and in the third hour, he covered 1 km more than in the first hour. How many km did he travel in the third hour? - Water mixing
We have 520 ml of hot water and 640 ml of water at 48°C. What is the temperature of approximately hot water when the resulting mixture has a temperature of 65°C? - Columns of two and three
When students in one class stand in columns of two, there is none left. When he stands in columns of three, there is one student left. There are five more double columns than three columns. How many students are in the class? - Insulating 25471
The septic tank is 6 m high, and its diameter is 2.4 m. How many packages of insulating paint must the painter order if he consumes 1 kg per 5 m² and the paint is delivered in two kg cans?
- Different 25431
Tickets have 9 numbered windows. How many different codes can be set for each other if 3 or 4 windows are punched? - Magnitude 25411
There is a circle with a radius of 10 cm and its chord, which is 12 cm long. Calculate the magnitude of the central angle that belongs to this chord. - Respective 25361
Three resistors are connected according to the scheme (R1 in parallel with R2 and series with R3: R1||R2 + R3) so that R1=0.6 Ω, R2=2 Ω, R3=3 Ω, current I1 = 10 A. Calculate all the currents passing through the respective resistors R1, R2, R3 and all the - Determine 25341
In a two-digit number, the number of tens is three more than the number of ones. If we multiply the original number by a number written with the same digits but in the reverse order, we get the product 3 478. Determine the actual number. - In the dairy
There were three times more milk packages in the dairy than half a liter. Four times more liters remained when sold in 10 liters and ten half-liter containers than in half-liter packages. How many packages were there originally?
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