Reason - high school - math problems
Number of problems found: 334
- Sphere cut
A sphere segment is cut off from a sphere k with radius r = 1. The volume of the sphere inscribed in this segment is equal to 1/6 of the segment's volume. What is the distance of the cutting plane from the center of the sphere?
- Ten persons
Ten persons, each person makes a hand to each person. How many hands were given?
- Playing cards
From 32 playing cards containing 8 red cards, we choose 4 cards. What is the probability that just 2 will be red?
The price of one kohlrabi increased by € 0.40. The number of kohlrabies that a customer can buy for € 4 has thus decreased by 5. Find out the new price of one kohlrabi in euros.
- Big numbers
How many natural numbers less than 10 to the sixth can be written in numbers: a) 9.8.7 b) 9.8.0
- Integer sides
A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side?
Before Christmas, Eva bought two cylindrical candles - red and green. Red was 1 cm longer than green. She lit a red candle on Christmas Day at 5:30 p. M. , lit a green candle at 7:00 p. M. , and left them both on fire until they burned. At 9:30 p. M. , bo
- Final exam
At the final exam, the student answers from three areas, which are evaluated in a ratio of 1: 2: 2. What grade will John receive if he answered as follows: 3,1,2.
Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.
- Lookout tower
How high is the lookout tower? If each step was 3 cm lower, 60 more of them were on the lookout tower. If it were 3 cm higher again, it would be 40 less than it is now.
How many matches will be played in a football tournament in which there are two groups of 5 teams if one match is played in groups with each other and the group winners play a match for the overall winner of the tournament?
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 different. How many di
- Six questions test
There are six questions in the test. There are 3 answers to each - only one is correct. In order for a student to take the exam, at least four questions must be answered correctly. Alan didn't learn at all, so he circled the answers only by guessing. What
- 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 5 more double columns than three columns. How many students are in the class?
- Research in school
For particular research in high school, four pupils are to be selected from a class with 30 pupils. Calculate the number of all possible results of the select and further calculate the number of all possible results, if it depends on the order in which th
- Birthday paradox
How large must the group of people be so that the probability that two people have a birthday on the same day of the year is greater than 90%?
Adam has half the money in his right pocket than in his left pocket. If he transferred 40 crowns from the left pocket to the right, he would have the same in both pockets. Calculate how many crowns does Adam has in his left pocket more than in his right?
- Quiz or test
I have a quiz with 20 questions. Each question has 4 multiple choice answers, A, B, C, D. THERE IS NO WAY TO KNOW THE CORRECT ANSWER OF ANY GIVEN QUESTION, but the answers are static, in that if the "correct" answer to #1 = C, then it will always be equal
- The test
The test contains four questions, and there are five different answers to each of them, of which only one is correct, the others are incorrect. What is the probability that a student who does not know the answer to any question will guess the right answer
- Double probability
The probability of success of the planned action is 60%. What is the probability that we will achieve success at least once if this action is repeated twice?
Reason - math problems. Examples for secondary school students.