Examples for secondary school students - page 75 of 214
Number of problems found: 4267
- Wagons
We have six wagons: two white, two blue, and two red. We assemble trains from them; wagons of the same color are exactly the same, so if we change only two white wagons on a train, it's still the same train because I don't know any difference. How many di - The tower
The observer sees the tower's base 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands? - Selected 26381
Seven people need to be selected from the sports club, where 11 men and nine women. How many ways can we do this if seven women are on the team? - Finite arithmetic sequence
How many numbers should be inserted between the numbers 1 and 25 so that all numbers create a finite arithmetic sequence and that the sum of all members of this group is 117?
- Percentage 26321
Maroš, the captain of the football team Coyotes from Kojetín, converted 15 penalties out of 20, so he has a success rate of 75%. How many percentage points will his success rate increase if he converts the following 5 penalties without hesitation? - Inclined plane
1. How much work W do we have to do to pull a body weighing 200 kg along an inclined plane with a length of 4 m to a total height of 1.5 m? 2. Find the force we need to exert to do this if we neglect frictional resistance. 3. Find the force we would need - Motorcyclist 26141
The passenger car left at 7:00 and was heading east at a speed of 60km/h. A motorcyclist left the same place and headed north at 40 km/h. What will be their air distance at ten o'clock? - Two chords
From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords. - Regular hexagonal prism
Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.
- Three-quarters 25931
Jarek went strawberry picking for a day. In the morning, he collected two-fifths of the required amount; in the afternoon, he collected 5 kg less than in the morning. In total, he collected three-quarters of the required amount. How many kilograms of stra - 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.
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