Enrollment for paid education is subject to a separate competition. For applicants entering paid education, the same set of tests is set as for budget education
The cost of educational services provided for citizens of the Russian Federation who have passed entrance tests at NRNU MEPhI and its separate subdivisions in fall semester 2019-2020 school year
NRNU MEPhI (Moscow)
| Form of study | Training period | Tuition fee per semester (rubles) | |||
| 01.06.01. | Mathematics and Mechanics | full-time | 4 years | 150 600 | |
| 02.06.01 | Computer and Information Sciences | researcher, teacher researcher | full-time | 4 years | 150 600 |
| 03.06.01. | Physics and Astronomy | researcher, teacher researcher | full-time | 4 years | 155 000 |
| 04.06.01. | Chemical sciences | researcher, teacher researcher | full-time | 4 years | 155 000 |
| 06.06.01 | Biological sciences | researcher, teacher researcher | full-time | 4 years | 155 000 |
| 09.06.01. | researcher, teacher researcher | full-time | 4 years | 155 000 | |
| 10.06.01. | Information Security | researcher, teacher researcher | full-time | 4 years | 155 000 |
| 11.06.01. | Electronics, radio engineering and communication systems | researcher, teacher researcher | full-time | 4 years | 155 000 |
| 12.06.01. | Photonics, instrumentation, optical and biotechnical systems and technologies | researcher, teacher researcher | full-time | 4 years | 155 000 |
| 13.06.01. | Electrical and heat engineering | researcher, teacher researcher | full-time | 4 years | 155 000 |
| 14.06.01. | Nuclear, thermal and renewable energy and related technologies | researcher, teacher researcher | full-time | 4 years | 165 800 |
| 15.06.01 | Mechanical engineering | researcher, teacher researcher | full-time | 4 years | 155 000 |
| 16.06.01. | Physical and technical sciences and technologies | researcher, teacher researcher | full-time | 4 years | 165 800 |
| 18.06.01 | Chemical Technology | researcher, teacher researcher | full-time | 4 years | 155 000 |
| 22.06.01. | Material technology | researcher, teacher researcher | full-time | 4 years | 155 000 |
| 24.06.01. | Aviation and rocket-space technology | researcher, teacher researcher | full-time | 4 years | 165 800 |
| 27.06.01. | Management in technical systems | researcher, teacher researcher | full-time | 4 years | 155 000 |
| 37.06.01 | Psychological Sciences | researcher, teacher researcher | full-time | 4 years | 150 600 |
| 38.06.01 | Economy | researcher, teacher researcher | full-time | 3 years | 150 600 |
| 40.06.01 | Jurisprudence | researcher, teacher researcher | full-time | 3 years | 150 600 |
CHILD NRNU MEPhI
| Name of specialty and (or) direction of training | Qualifications (bachelor, master, specialist, technician, etc.) | Form of study | Training period | ||
| 04.06.01 | Chemical sciences | full-time | 4 years | 63 500,00 | |
| correspondence | 5 years | 15 100,00 | |||
| 14.06.01 | Researcher. Research instructor | full-time | 4 years | 79 300,00 | |
| correspondence | 5 years | 15 100,00 | |||
| 03.06.01 | Physics and Astronomy | Researcher. Research instructor | full-time | 4 years | 63 500,00 |
| correspondence | 5 years | 15 100,00 | |||
| 09.06.01 | Informatics and computer engineering | Researcher. Research instructor | full-time | 4 years | 63 500,00 |
| correspondence | 5 years | 15 100,00 |
IATE NRNU MEPhI
| Specialty (direction) code | Name of specialty and (or) direction of training | Qualifications (bachelor, master, specialist, technician, etc.) | Form of study | Training period | Tuition fee per semester (rubles) |
| 01.06.01 | Mathematics and Mechanics | Researcher. |
full-time | 4 years | 74 660,00 |
| 03.06.01 | Physics and Astronomy | Researcher. Research instructor |
full-time | 4 years | 80 311,00 |
| 04.06.01 | Chemical sciences | Researcher. Research instructor |
full-time | 4 years | 80 311,00 |
| 06.06.01 | Biological sciences | Researcher. Research instructor |
full-time | 4 years | 80 311,00 |
| 09.06.01 | Informatics and computer engineering | Researcher. Research instructor |
full-time | 4 years | 80 311,00 |
| 12.06.01 | Photonics, instrumentation, optical and biotechnical systems and technologies | Researcher. Research instructor |
full-time | 4 years | 80 311,00 |
| 14.06.01 | Nuclear, thermal and renewable energy and related technologies | Researcher. Research instructor |
full-time | 4 years | 108 900,00 |
| 38.06.01 | Economy | Researcher. Research instructor |
full-time | 3 years | 74 660,00 |
| For foreign students (training in English) | |||||
| 14.06.01 | Nuclear, thermal and renewable energy and related technologies | Researcher. Research instructor |
full-time | 4 years | 141 415,00 |
SarFTI NRNU MEPhI
| specialty code (direction) | Name of specialty and (or) direction of training | Qualifications (bachelor, master, specialist, technician, etc.) | Form of study | Training period | Tuition fee per semester (rubles) |
| 01.06.01 | Mathematics and Mechanics | full-time | 4 years | 69 978 | |
| 03.06.01 | Physics and Astronomy | Researcher, Teacher-researcher | full-time | 4 years | 73 422 |
| 09.06.01 | Informatics and computer engineering | Researcher, Teacher-researcher | full-time | 4 years | 73 422 |
STI NRNU MEPhI
| specialty code (direction) | Name of specialty and (or) direction of training | Qualifications (bachelor, master, specialist, technician, etc.) | Form of study | Training period | Tuition fee per semester (rubles) |
| 09.06.01 | Informatics and computer engineering | Researcher. Research instructor | full-time | 4 years | 92 700 |
| correspondence | 5 years | 24 000 | |||
| 18.06.01 | Chemical Technology | Researcher. Research instructor | full-time | 4 years | 92 700 |
| correspondence | 5 years | 24 000 |
SPTI NRNU MEPhI
| specialty code (direction) | Name of specialty and (or) direction of training | Qualifications (bachelor, master, specialist, technician, etc.) | Form of study | Training period | Tuition fee per semester (rubles) |
| 01.06.01 | Mathematics and Mechanics | Researcher. Research instructor | full-time | 4 years | 72800 |
| 09.06.01 | Informatics and computer engineering | Researcher. Research instructor | full-time | 4 years | 76200 |
| 15.06.01 | Mechanical engineering | Researcher. Research instructor | full-time | 4 years | 76200 |
| 4 years |
MOSCOW, June 30 - RIA Novosti, Alexander Lesnykh. Admissions committees of Russian universities have been working for a week. This means that very soon it will become clear which of the applicants will go to study for budget money, and who will have to fork out for paid education. RIA Novosti studied the prices in the top 10 universities of the country according to the Round University Ranking 2019 and identified the most expensive and most affordable specialties.
Lomonosov Moscow State University
The main university in the country has the highest salary. Of those faculties that have already published prices for contract education, the most expensive specialty is "general medicine" at the Faculty of Fundamental Medicine - 493 thousand rubles a year. The second direction, pharmacy, also hit the top - 436 thousand a year.
Comparable prices at the Graduate School of Cultural Policy and Humanitarian Management. Studying for a producer will cost 492 thousand rubles a year.
Several specialties in the exact and humanitarian sciences are almost a quarter cheaper. Faculties of space research, computational mathematics and cybernetics, mechmat - 390 thousand. The same number - the faculties of political science, public administration, world politics, translation, television and arts or journalism.
National Research Nuclear University "MEPhI"
Training in the most expensive specialties offered at NRNU MEPhI will cost 300 and more thousand rubles a year. For this money, you can get a diploma in nuclear physics and technology, nuclear reactors and materials, electronics and automation of physical installations, as well as high-tech plasma and power plants. You will have to pay 20 thousand more for the study of medical practice at the Engineering Physics Institute of Biomedicine, National Research Nuclear University MEPhI.
It costs a little less to study professions related to the IT industry: software engineering, information security, including in the law enforcement sphere - 260 thousand per year. The same is the cost of training in specialties associated with laser technologies, applied mathematics and physics, nanoelectronics, photonics and robotics.
The most accessible majors at the university are economics, business informatics, economic security, international relations, and applied mathematics and computer science. The cost of training is 230 thousand rubles per year.
Tomsk State University (TSU)
The fee for studying technical sciences is almost one hundred thousand rubles less. Applied informatics, software engineering, biology, soil science, innovation, computer security, electronic systems and complexes, as well as fundamental and applied chemistry and some others will cost the student's parents 156 thousand rubles a year.
MIPT
At the Moscow Institute of Physics and Technology, the most expensive specialty is technical physics, the cost of training is 315 thousand rubles a year.
For all the rest - applied mathematics and computer science, applied mathematics and physics, computer science and computer technology, biotechnology, systems analysis and management and computer security - a single price has been set, 270 thousand.
Novosibirsk State University (NSU)
At NSU, training in all specialties is practically the same. The most expensive - medical treatment - will cost 190 thousand rubles a year. Ten thousand cheaper - linguistics, oriental studies and African studies, biology, chemistry and fundamental and applied chemistry. All the remaining specialties cost 160 thousand a year. Among them are mathematics, physics, physical informatics, geology, philology, history and jurisprudence.
Saint Petersburg State University
The top 3 most expensive specialties of St. Petersburg State University include international management (506 thousand per year), management (446 thousand) and part-time jurisprudence (452 thousand).
In the middle of the list are disciplines related to oriental studies and African studies. These are ten programs providing for the study of the history and philology of Eastern countries, as well as the study of several local languages. For example, comprehending the history of Arab countries, you can learn Arabic and, in addition, one of three languages - Hebrew, Turkish or Persian. The course costs 344 thousand rubles annually.
The list of the most accessible specialties of St. Petersburg State University includes philosophy, history, religious studies, liberal arts and Jewish culture. Tuition fees will have to pay 208 thousand per year. The same money costs a specialty in physical education and sports.
And those who dream of learning to play the organ, harpsichord or carillon professionally will have to pay “only” 203 thousand rubles a year for the training.
Tomsk Polytechnic University
In Tomsk Polytechnic, the most expensive specialty is design (295 thousand rubles a year). It is followed by nuclear physics and technology, electronics and automation of physical installations, as well as design, operation and engineering of nuclear power plants for 273 thousand a year each.
The most affordable specialties cost 172 thousand a year. These are mechanical engineering, metallurgy, agricultural engineering and applied informatics.
RUDN
The most accessible directions will cost 236 thousand annually at the Faculty of Physics, Mathematics and Natural Sciences. Here you can learn modeling and analysis of business processes, information technology in enterprise management, specialties related to computer science.
To the children I work withI highly recommend taking part in math olympiads. For some, this is preparation for entering the 5th grade of a good school (Kurchatov school №2077, 1543, 1514, 1567, etc.), for others - an opportunity to measure their strength, for the third - an interesting event and a warm-up for the mind. Regardless of the results, at each Olympiad, the child gains invaluable experience, which will be useful at future Olympiads and at the entrance exams.
In this post, I share information about several math olympiads for junior grades 2016-2017 (in chronological order):
The post is regularly updated. Stay tuned!
https://www.facebook.com/matolimp
Options for assignments from different years: http://matolimp.ru/olympiads/olympiads- for 1-4- grades/
Primary school Olympiad in MIREA 2019
Time: February 10, 2018
Venue: MIREA
Detailed information about the 2018 Olympics:
http://mathbaby.ru/
Options for assignments from previous years can be found at the link
Registration required!
Olympiad in Russian language and mathematics in gymnasium 1514 (grade 4)
Held in February at gymnasium 1514. Papers in mathematics and Russian are assessed independently. A successful performance is counted as the maximum score in the corresponding entrance exam for the 5th grade of the upper secondary school.
Time: February 2, 2019.
Venue: gymnasium No. 1514 ( Moscow, Krupskaya st., 12)
The official website of the school: http://gym1514uz.mskobr.ru/
Kurchatov Mathematics Olympiad - 2019 (4th grade) First round
Tasks, answers, solutions, results
Time: February 10, 2018.
Venue: Kurchatov school (No. 1189 named after Kurchatov)
School website: official.
Options for assignments from previous years: 2013
Assignments for other years on the website matolimp.ru
Open Mathematical Olympiad of the school "Moomin-Troll" (grades 1-11)
It is held annually in March at the Moomin-Troll school.
Information about the Olympiad is on the school website.
Pre-registration is required to participate in the Olympiad.
Options for assignments for grade 4 for, and years.
Time: March 2019.
Venue: School "Mumi-Troll" (Volokolamskoe sh., 1) passage
School website: http://www.mumi-troll.ru
Mathematical competition "Spring Olympus" (grades 1-7)
Tasks, answers, solutions, results of the Spring Olympus 2019
Estimated time: April
Of 2019
Website: http://www.matznanie.ru/
Kurchatov Olympiad in Mathematics (grade 4) Second round
Tasks, answers, solutions, results
The Olympiad is held at the Kurchatov school №2077 (former school №1189 named after Kurchatov).
Time: April 2018.
Venue: Kurchatov School No. 2077 (No. 1189 named after Kurchatov) travel
School website: official.
Math competition "Autumn Olympus" (grades 1-9) 2019
Time: end of September
The first stage - October 2019
Second stage - November 201
Detailed information on the website of the Olympiad. Registration by link.
The results of the "Autumn Olympiad 2019" and the lists of winners can be viewed here .
Website: http://matznanie.ru/
All-Russian Olympiad for schoolchildren for 4 grades 2019 (school stage)
The date of the:
Variant assignments 2016:
http://vos.olimpiada.ru/upload/files/Arhive_tasks/2016-17/school/math/tasks-math-4-msk-sch-16-7.pdf
NEW YEAR
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Municipal state educational institution
secondary school number 10
for students of grade 7
2014 - 2015 academic year
Compiled by: mathematic teacher
Konovalova Tatiana Vladimirovna
Sverdlovsk region, Kushva
2014 year
Explanatory note.
The Olympiad is held with the aim of increasing students' interest in mathematics, broadening their horizons, identifying the most talented students, and improving the general level of teaching mathematics in primary grades.
Students who wish are allowed to participate in this Olympiad. Students are offered 15 tasks, arranged as the difficulty increases. For each task, you need to write a solution-reasoning. 1 hour 30 minutes are given for work
Then the sheets with the decisions and the participant's data are handed over and sent for verification and processing.
For students in grades 7, 15 tasks of the competition are divided into 5 parts:
3 of the easiest tasks considered in the lessons (№1,2,3,), estimated at 2 points each;
3 more difficult tasks (No. 4,5,6), estimated at 3 points;
4 problems (№ 7,8,9, 10), for the solution of each of which 4 points are given;
2 more difficult tasks (No. 11, 12), estimated at 4 points.
3 most difficult tasks (No. 13,14,15), estimated at 5 points.
Thus, the participant of the competition can collect a maximum of 59 points.
The tasks are selected so that among the participants of the Olympiad there will not be a single one who will score 0 points!
MKOU SOSH number 10
school round olympiad in mathematics
7th grade
(2 points) Vasya can get the number 100 using ten sevens, brackets and signs of arithmetic operations:
100 = (77: 7 - 7: 7) (77: 7 - 7: 7). Improve its result: using fewer sevens and get 100 ( just give one example).
(2 score ) There are 9 people sitting in one room, and their average age is 25 years. There are 11 people sitting in another room, and their average age is 45 years. What is the average age of all 20 people?( justify the answer ).
(3 score) The snail climbs a branch 10 dm long. During the day it rises by 4 inches, and during the night it slides down by 3 inches. How many days will it take for the snail to reach the end of the branch? ( justify the answer).
(3 score) How many 20x45 cm rectangular plates can be cut from a 120x240 cm plywood sheet? ( justify the answer).
(4 score) When it's noon in Moscow, it's 3 o'clock in the morning in Chicago. When it is 3 o'clock in Moscow in the morning, it is noon in Petropavlovsk-Kamchatsky. What time is it in Chicago when it is 3 o'clock in the morning in Petropavlovsk-Kamchatsky? ( justify the answer).
(4 score) The edge of the cube is equal to 1 dm. The fly crawls along the edges of a cube without going over one edge twice (but possibly going over one vertex several times). What is the longest way she can crawl? ( justify the answer).
(4 score) 12 boys and 8 girls are members of the math club. Two new girls and one boy are admitted to the club every week. How many members will there be in the club on the day when boys and girls are equally divided? ( justify the answer).
(4 score) Three friends came out in white, blue, green dresses and shoes of the same colors. It is known that only Anya has the same color of dress and shoes. Vali's dress and shoes were not white. Natasha was wearing green shoes. Decide on the color of each friend's dress and shoes. ( justify the answer).
(5 points) Snow White distributed mushrooms to the seven dwarfs. Each next dwarf received one more mushroom than the previous one, and together they received 707 mushrooms. How many mushrooms did the last gnome get? ( justify the answer).
(5 points) Jack can buy a bottle of Pepsi for $ 3. An empty bottle can be returned for $ 2. How many bottles of Pepsi can Jack drink with $ 10? ( justify the answer).
(6 points) Let the expression a ¤ b denotes the sum of digits in a product a · b . Find what equals (15 ¤ 10) ¤ (15 10) ?.(justify the answer).
(6 points) In April of a certain year, three Sundays fell on odd numbers. What day of the week was April 20th? ( justify the answer).
(6 points) From the basket of eggs they took half of the total number of eggs, then another half of the remainder, then half of the new remainder, and finally half of the next remainder. As a result, there are 10 eggs left in the basket. How many eggs were originally in the basket? ( justify the answer).
Annex 1
MKOU SOSH number 10
school round olympiad in mathematics
7th grade
solutions
100 = (7 7 + 7: 7) (7: 7 + 7: 7), 100 = 777: 7 - 77: 7 there may be other options
1) 25 9 = 225 (l) - total age of 9 people
2) 45 11 = 495 (l) - total age of 11 people
3) 225 + 495 = 720 (l) - total age of 20 people
4) 720: 20 = 36 (l) average age of 20 people
Answer: 36 years old. there may be other solutions
On the 1st day, the snail will rise to 4 dm, at night it will go down to 1 dm. On the 2nd day it will rise to 5 dm, at night it will go down to 2 dm. On the 3rd day it will rise to 6 dm, at night it will go down to 3 dm. On the 4th day it will rise to 7 dm, at night it will go down to 4 dm. On the 5th day, it will rise to 8 dm, at night it will go down to 5 dm. On the 6th day it will rise to 9 dm, at night it will go down to 6 dm. On the 7th day, it will rise to 10 dm. The answer is 7 days.(maybe a graphical solution too)
1) 120 · 240 = 28800 (cm²) - the area of the plywood sheet
2) 20 45 - 900 (cm²) - plate area
3) 28800:900 = 32
Answer: 32 plates
Moscow
Chicago
Petropavlovsk-Kamchatsky
12-00
03-00 (i.e. Moscow - 9:00)
03-00
12-00 (i.e. Moscow + 9 hours)
03-00 - 9 hours = 18-00
18-00 - 9 hours = 09-00
03-00
The answer is 9 o'clock in the morning
Boys girls
12 8
1 week +1 +2
13 10
2 week +1 +2
14 12
3 week +1 +2
15 14
4 week +1 +2
16 16
Answer 32 club members
Anya Valya Natasha
White dress not white green blue
White shoes not white i.e. blue green
Let x - mushrooms received by the 1st dwarf, x + 1 - 2nd, x + 2 - 3rd, x + 3 - 4th, x + 4 - 5th, x + 5 - 6th, x + 6 - 7th, then
98 + 6 = 104 mushrooms
The last dwarf got 104 mushroom answer
School round of the Olympiad in mathematics 4th grade 2013-2014 academic year year
Surname, name ________________________________________________
Class______________
Tasks.
- How much does it get when you add the largest odd two-digit number and the smallest even three-digit number? _________________________________.
- 240 students from Moscow and Orel arrived at the tourist camp. There were 125 boys among the arrivals, of which 65 were Muscovites. There were 53 girls among the students who arrived from Orel. How many students came from Moscow? _________________________________________________________________________________________________________________________________________________.
- What is the sum of the numbers shown in the picture twice?
- Place the brackets so that the equality is correct: 15 - 35 + 5: 4 = 5
- A square plot of land (length of a side of a square is 40 m) consists of 16 square beds. To irrigate the area between some of the beds, it is necessary to lay a pipe from the place shown by point A. This pipe, 100 m long, should divide the area into 2 equal parts. Show me how to lay the pipe.
- The two sisters have 36 years of age. How old is each if 1/2 of one is equal to 1/4 of the other? ______________________________________________
______________________________________________________________________
- Crack the code!
Each letter of the alphabet is represented by a number:
A - ____; E- ______; Y _ ____; O- _____; Y - ____; NS - _____; NS - ______;
B - ____; Yo - _____; TO - _____; NS- _____; F - _____; SCH - _____;
V - ____; F - ____; L - _____; R - _____; NS - _____; B - ______; I AM - ______;
G - ____; З - _____; M - _____; WITH - _____; C - _____; NS - _____;
D - ____; AND - ____; H - _____; T - _____; H - _____; B - ______.
A) Try to determine these numbers (find the code) if the word GID is written as 6, 12, 7, and the word SON is written as 21, 18, 17.
B) Try to read the phrase with this code: 16 18 15 18 7 8 26
17 3 27 12 17 3 13 7 20 23 6 23 34 21 22 20 3 17 12 26 23
Answer: _________________________________________________________________
________________________________________________________________________
_________________________________________________________________________
- The sum of two numbers is 715. One number ends in zero. If you cross out this zero, you get the second number. Find these numbers.
- One watch is 25 minutes behind, showing 1 hour 50 minutes. What time does the other clock show if it runs 15 minutes?
__________________________________________________________________________
__________________________________________________________________________
- Three friends - Vera, Olya and Tanya went to the forest to pick berries. For picking berries they had a basket, a basket and a bucket. It is known that Olya was not with a basket or a basket, Vera was not with a basket. What did each girl take with her to pick berries?
Vera - ________________, Tanya - ________________, Olya - ___________________.
Grade 4 Answers
- 199 (1 point)
- For the task - 4 points
1) 240-125 = 115 girls from Moscow and Orel
2) 115-53 = 62 girls from Moscow
3) 65 + 62 = 127 children from Moscow
- 16+19=35 47+16=63 47+19=66
or
16+19+47=82
Among the numbers presented in the picture are uniquely twice
depicted numbers 16 and 19. Their sum is 35.
Since the number 41 during deformation turned out to be very similar to the number 47, we also decided to count it. (5 points)
- 15- (35 + 5): 4 = 5 (2 points)
- There are two options:
(4 points + 2 points for an additional answer option. Maximum - 6 points)
- The total age is 36 years. Let's say one part is X, then we make the equation: 2X + 4X = 36.
We solve the equation:
6X = 36,
X = 6.
Now we multiply 6 by 2 (since the age of one sister is 2X), we get 12. 12 is the age of one of the sisters.
Next, we find the age of the other sister. 6 times 4 (4X), we get 24.
(Only answer - 1 point. Correct answer and solution - 4 points).
- A)
A-3 E - 8 Y - 13 O - 18 U - 23 W - 28 E - 33
B-4 E - 9 K - 14 P - 19 F - 24 Sh - 29 S - 34
H-5 F - 10 L - 15 R - 20 X - 25 b - 30 Z - 35
G-6 W - 11 M - 16 S - 21 C - 26 Y - 31
D-7 I - 12 N- 17 T - 22 H - 27 L - 32
B) the phrase: " Well done, start another page»
.
The number of points is 5 for each stage of the assignment. Total - 10 points.
- Answer: 650 + 65 = 715 (2 points)
- 1 hour 50 min + 25 min = 2 hours 15 min
2 hours 15 minutes + 15 minutes = 2 hours 30 minutes
(2 points)
- Vera was with a basket, Olya - with a bucket, Tanya - with a basket. (2 points)
Preview:
1. Grandma baked pancakes. The grandson came home from school and immediately began to eat them. While he ate three pancakes, grandmother had time to bake only two. When the grandson came home from school, there were 12 pancakes on the plate. How many pancakes did the grandson eat if he left when there were only 7 pancakes on the plate?
2. When in New York it is 5 o'clock in the morning, in Kiev - noon. When it's 5 am in Kiev, it's noon in Tokyo. What time is it in New York when it's 5 am in Tokyo?
3. Swap the two digits to get the correct equality:
2012= 1719 + 275
4. A bottle, glass, jug and jar contains milk, lemonade, kvass and water. It is known that water and milk are not in a bottle, but a vessel with lemonade is between a jug and a vessel with kvass, in a jar there is neither lemonade nor water. The glass is located between the jar and the container with milk. How are these fluids distributed throughout the vessels?
5. There are 28 children in the class. Of these, 15 go to the drawing circle, 12 go to dances and 5 people go to both circles. How many children in this class are not in any of these clubs?
6. The freight train is 1 km long and travels at a speed of 50 km / h. How long will it take to complete a 1 km tunnel? (Express your answer in minutes and seconds.)
7. When your parents were children, milk was sold in liter and half liter glass bottles. Empty milk bottles could be taken to the store at a price of 20 kopecks. and 15 kopecks. respectively. Kolya went to the store without money, taking with him empty bottles - 6 liter and 6 half liter. The store had draft milk for 22 kopecks. per liter. Kolya decided to turn in some of the bottles, and pour the milk he bought with the money he had received into the remaining bottles. What is the most milk he can bring home?
8. It takes 1 gram of paint to paint a 2x2x2 wooden cube. How much paint does it take to paint a 6x6x6 wooden cube?
9. A square plot of land (length of a side of a square is 40 m) consists of 16 square beds. To irrigate the area between some beds, it is necessary to lay a pipe from the place indicated by the dot. This pipe, 100 m long, should divide the section into 2 equal parts. Show me how to lay the pipe?
Preview:
DISTRICT OLYMPIAD IN MATH (4 CLASS)
ANSWERS TO TASKS
- 15 pancakes. 2 points. Only answer : 1 point; correct answer with a drawing, explanation, solution: 2 points.
- 15 o'clock in the afternoon. 2 points.
- 2012 = 171 7 + 2 9 5 1 point.
- The bottle is lemonade
The glass is water
Jug - milk
Bank - kvass. 3 points. Only answer : 1 point; correct answer with reasoning in the form of a diagram, table: 3 points.
- 6 children. 3 points. Only answer : 1 point; correct answer and solution: 3 points. 1) 15 + 12 = 27 2) 27 - 5 = 22 3) 28 - 22 = 6 (d.) - do not attend any circles.
- 2 min 24 s 3 points. Only answer : 1 point; correct answer and solution: 3 points.
- 5 liters of milk in liter bottles. 4 points.
Only answer: 1 point; correct answer and solution: 3 points.
15 × 6 + 20 × 1 = 110 (kopecks)
22 × 5 = 110 (kopecks) From this it follows: the boy needs to hand over 6 half-liter and 1 liter bottles; with the money received, pour 5 liters of milk into the remaining liter bottles.
- 9 g of paint. 4 points. Only answer : 1 point; correct answer and solution: 4 points.
(2 × 2) × 6 = 24- S cubes measuring 2 × 2 × 2
(6 × 6) × 6 = 216 –S 6 × 6 × 6 cubes
216: 24 = 9 - the area of the cube has increased so many times, which means that 9 times more paint will be required. 1 × 9 = 9 (g)
- 4 points + 2 points for the second correct answer.
Total: 28 points.
Preview:
Primary School Mathematics Olympiad School Tour
"Not a single mentor should forget that his main duty is to accustom pupils to mental work, and this duty is more important than the transfer of the subject itself."
K. D. Ushinsky
Participation in the Mathematical Olympiad promotes creative development, increased creative activity in children, and also contributes to the development of cognitive activity of younger students: perception, representation, imagination, attention, memory, thinking, speech.
I offer tasks for training the mind.
Assignments for students of 2 grades
1. Draw how you can get 15 out of 4 sticks without breaking them?
2. Two girls went to the park, they met five more friends. How many girls went to the park? Circle the correct answer: 7, 5.2
3. Kitten Woof received gifts for his birthday: cakes and cupcakes instead of 7 pieces, pies and cupcakes - 9, and cakes and pies -6. How many gifts were there?
4. There are 10 fingers on the hands. How many fingers are there in 10 hands? Write an answer.
5. For the preparation of firewood, 3 logs were taken. How many logs were there if 15 cuts were made?
6. There were four birds perched on a tree. Two more birds flew to them. The cat crept up and grabbed one bird. How many birds are left on the branch? Circle the correct answer: 3,5,4, none.
7. Using only addition, write down the number 28 using five twos.
8. There are as many barefoot boys on the lawn as there are girls with shoes on. Who is more on the lawn - girls or barefoot children?
9. Milk, yogurt and kefir were poured into a glass, mug and cup. There is no kefir in the mug. There is no kefir or yogurt in the cup. What was poured where? Write an answer.
Cup -------: Cup ----------: Cup ---------:
10. The square, inside which the smaller square is cut, must be cut into four equal parts. Find at least three solutions to this problem and draw them.
11. Need to pack several books. If you link them in two, then there will be one extra book, if three, then two books, if four, there will be three books. Find the smallest number of books to pack. Write an answer.
12. In the house, the Mouse lives above the Frog, but below the Hare, and the Rooster lives below the Frog.
Write down who lives on which floor.
13. On one side of the scale there are 5 identical apples and 3 identical pears, on the other side there are 4 identical apples and 4 identical pears. The scales are in balance. Which is lighter: an apple or a pear? Write an answer.
14. There were 9 books on the shelf. After they took several books from the shelf, 4 books remained on it. How many books were taken from the shelf.
15. The tailor has a piece of cloth about 16 meters from which he cuts off 2 meters every day. After how many days will he cut the last piece? Write an answer.
16. After 9 cars left the parking lot, 8 cars remained there. How many cars were parked first?
17. There were 7 large and 8 small buttons in the box. They took 9 buttons from the box. How many buttons are left in the box?
18. Five years ago Sasha was 4 years old. How old is Sasha now?
19. Indicate numbers consisting only of hundreds and ones:
a) 596.
b) 604.
c) 830.
d) 905:
20. Indicate a series of numbers in descending order:
a) 935, 928, 876, 729.627.604.564.357.
b) 357,564,604,627,729,876,928,935.
21. Maxim bought 9 new brands. After placing several stamps in the album, he had 3 stamps left. How many stamps did Maxim put into the album?
22. There were 9 green and 5 red apples in the basket. They took 10 apples from the basket. How many apples are left in the basket?
23. Solve the problem. Find the correct answer from the three options offered. In the school lot, you need to plant 16 rows of trees, 6 in each row. A quarter of these trees have already been planted. How many trees are left to plant?
1) 24 trees.
2) 96 trees.
3) 72 trees.
4) 35 trees.
24. The length of the rectangle is 6 cm, the width is 3 times less. What is the sum of the lengths of the sides of the rectangle?
a) 14 cm.
b) 18 cm.
c) 16 cm.
25. Of the three options, find the correct answer: 1 | 5 the proportion of the entire fabric is 30 meters. How much fabric is on a roll?
a) 6 meters.
b) 150 meters.
c) 30 meters.
Assignments for students of 3 grades
1. The squirrel asked the hare 6 tasks. For each correct solution to the problem, the hare received 3 carrots, and for each incorrect squirrel, it took 2 carrots. How many hare did the hare decide correctly if he received 8 carrots?
2. Solve the problem: You made bouquets of 24 red and 18 white roses. Each bouquet contains 3 red and 3 white roses. What is the largest number of bouquets you can make?
3. The dog is chasing a rabbit, which is 180 m away from it. The dog jumps 3 meters every time the rabbit jumps 1 meter. How many jumps does the dog have to make to catch up with the rabbit?
4. Between some digits 123456789 put the addition signs so that you get 99. Find three ways to solve this problem.
5. Calculate in a convenient way: 7846x329: (168-84x2) x 921 =
6. Establish the rule according to which a series of numbers is composed, and continue it by writing down three more numbers: 3,5,9,17,33.
7. Fly-Tsokotukha found money and bought a samovar, pretzels and sweets with it. The samovar and pretzels cost 48 blamziks. For pretzels and sweets, Mucha paid 3 blamziks. Moreover, sweets are more expensive than pretzels. How many blamziks is the money found by Fly-Tsokotukha?
8. In a three-digit odd number, the sum of the digits is 3. It is known that all three digits are different. Find this number.
9. The girl drew two straight lines. On one she marked 2 points, and on the other - 3. There were 4 points in total. How did it happen? Draw your answer.
10. How many times will the area of a square increase if each side of it is doubled? Give a numerical example.
11. Establish a rule according to which a series of numbers is composed, and continue it by writing down 3 more numbers: 3,5,9,17,33, ..., ..., ...
12. 3 boxes of chocolates and 5 boxes of cookies cost 1,350 rubles, and 3 boxes of sweets and 8 boxes of cookies cost 1,800 rubles. How much is 1 box of cookies and 1 box of chocolates.
13. Second-graders need to plant one row of apple trees. The length of this row is 30 m, the distance between the apple trees is 3 m. How many apple trees should be prepared for planting?
14. In the village of Prostokvashino, Uncle Fyodor, the cat Matroskin, the dog Sharik and the postman Pechkin are sitting on a bench in front of the house. If Sharik, sitting on the far left, sits between Matroskin and Fyodor, then Fyodor will be on the far left. Who is sitting where?
15. Write down all the numbers from 1 to 100 in a row. How many times has the number 5 been written?
16. 17 tables and several wardrobes were bought for the school, for a total of 2,716 rubles. The table cost 56 rubles, and the wardrobe cost as much as 9 tables. How many cabinets have you bought?
17. How to write the number 100 using five digits 5 and mathematical action signs?
18. The hostess raised chickens and rabbits. In total, they have 35 heads and 94 legs. How many chickens does the mistress have and how many rabbits?
19. Write an expression whose value is 54 using the numbers 1,2,3,4,5.
20. Arrange the signs of arithmetic operations and parentheses so that the correct equality is obtained. 1 2 3 4 5 = 18
21. From town to village, the distance between which is 32 km, a cyclist left at a speed of 12 km / h. And from the village to the city at the same time a pedestrian came out at a speed of 4 km / h. Which of them will be further from the city in 2 hours?
22. One old collector had 25 tin soldiers, which were made from an old tin spoon weighing 123 grams. 24 soldiers were the same: they did not differ from each other. But the 25th soldier turned out to be one-legged. It was cast last, and the olive was a little short. What is the mass of the last soldier?
23. The city bus had 5 empty seats. At the stop no one got out, but 7 people entered. There are only 2 empty seats left. How many of those who entered are left to stand?
24. Three high school soccer teams compete. Each team plays one game with two others. How many games must be played?
25. A third-grader Denis faced a problem at the end of August: 1 eraser, 2 pencils and 3 notebooks cost 38 rubles. 3 rubber bands, 2 pencils and 1 notebook cost 22 rubles. How much does a set of eraser, pencil and notebook cost?
Assignments for 4th grade students
1. The box contains white, black and red cubes. Only 50 pieces. There are eleven times more whites than blacks. There are fewer reds than whites, but more blacks. How many red cubes are in the box?
2. Put 8 bags in a row. The weight of the first bag is 88 kg, and the weight of each next one is 8 kg less than the previous one. Find the mass of all the bags.
3. The princess cut 128 violets, 192 daisies and 160 peonies in her garden. What is the largest number of the same bouquets she can make of all cut flowers to present to her friends? How many daisies will there be in each such bouquet?
4. The school mathematics Olympiad was attended by 7 students aged from 7 to 12 years, inclusive. It is known that: Maxim is older than Seryozha; Sasha is older than Vasya, but younger than Vanya; Anya and Natasha have the same age, less than Vanya's, but more than Sasha's: Zhenya is older than both Natasha and Vanya. How old is everyone?
5. Using the numbers 3,5,7, write down all two-digit numbers that can be made, provided that the numbers in the record will not be repeated. List all these numbers, find the sum in a rational way.
6. There are four children in a big friendly family: they are 5,8,13 and 15 years old, and their names are Tanya, Yura, Sveta, Lena. How old are each of them, if one girl goes to kindergarten, Tanya is older than Yura, and the sum of Tanya and Sveta's years is divisible by 3?
7.Using the numbers 1,2,3, write down the three-digit number that is divisible by 7.
8. The mass of three boxes of cookies is equal to the mass of two boxes of chocolates. What is the weight of five boxes of chocolates if the cookie box weighs 12 kg?
9. Sister Alyonushka had 18 nuts. After she gave her brother Ivanushka a few nuts, she had 12. How many nuts did Alyonushka give to brother Ivanushka?
10. It takes 12 minutes to cut a log into 3 pieces. How long does it take to cut a log into 6 pieces?
11. Grandmother sews handkerchiefs in the shape of a square with a side of 25 cm. Every day she sews the same number of handkerchiefs. How many handkerchiefs does she sew a day if she used up 3 square meters of fabric in 8 days?
12. A collective farmer brought 100 eggs to the market. She sold 15 eggs to one buyer, 30 to another. How many eggs did the third buyer buy if the collective farmer has 35 eggs left?
13. The train carriage accommodated 30 football players and 22 hockey players. Moreover, 10 of the players were hockey players at the same time. How many people were accommodated in the carriage?
14. The age of the grandmother is expressed in the smallest 3-digit number, which is recorded in different numbers. How old is grandmother?
15. Sasha has 180 rubles. If she gives half of her money to Zhenya, then they will have the same amount of money. How much money does Zhenya have?
16. Oksana wrote down a 3-digit number, subtracted 1 from it and got a 2-digit number. What number did Oksana write down?
17. Find the pattern and continue the numbers: 2,5,14,41, ...
18. A notebook is cheaper than a pen, but more expensive than a pencil. Which is cheaper: a pencil or a pen?
19. Vanya lives above Petya, but below Senya, and Kolya lives below Petya. On which floor of the four-story building does each of them live?
20. Alice and the White Rabbit left the Rabbit's house together at noon and went to the Duchess's reception. Halfway through, Rabbit remembered that he had forgotten his gloves and fan, and returned home for them. As a result, Alice came to the Duchess 5 minutes before the start of the appointment, and Rabbit was 10 minutes late. Alice and Rabbit walked at constant and equal speeds. What time was the appointment with the Duchess?
12-10
12-15
12-20
12-25
12-30
21. Tatiana draws colored balls: first blue, then red, then black, then yellow, again blue, red, black, yellow, etc. What color will the seventeenth ball be?
Blue
Red
Green
Black
Yellow
22. To the mouse 20 steps to the mink. Cat to mouse 5 jumps. In one jump of the cat, the mouse makes 3 steps. One jump of the cat is equal to 10 steps of the mouse. Will the cat catch up with the mouse?
23. The teacher has 6 cards with numbers 1,2,3,4,5 and 6. The teacher explained that using them, you can make two three-digit numbers, for example, 645 and 321. Denis made these numbers so that their difference turned out to be the smallest of all possible. What is this difference equal to?
24. There were flower pots on three windows. On the first 2 pots, on the second 3, on the third 5. How do you rearrange one pot of flowers so that the two windows have the same number of flowers?
25. Petya walked to the station at a speed of 30 m / min and was already at a distance of 560 m from the house when the father and the dog followed him. The father walked at a speed of 50m / min, and the dog ran at a speed of 100m / min. Having reached Petya, she immediately turned back, ran to her father, then back to Petya, and so non-stop until the father caught up with his son. Which way did the dog go?
Preview:
Regional Olympiad in Mathematics
1 2 34 567 = 100
1 2 34 567 = 100
1 point for each case
Total - 2 points
1 point
1 point
3 points
4 points
5 points
5 points
5 points
4 points
4 points
Regional Olympiad in Mathematics 2009
the answers
1. Without changing the location of the digits, put the addition sign between them so that the sum is equal to 100. If necessary, consider any two adjacent digits as a two-digit number. Complete the task in two different ways.
1 + 2 + 34 + 56 + 7 = 100
1 + 23 + 4 + 5 + 67 = 100
1 point for each case
total - 2 points
2. Write in digits a number consisting of 22 million 22 thousand 22 hundred and 22 units.
1 point
22 024 222
3. What four digits should be deleted from the number 4921508 so that the resulting three-digit number is as small as possible?
1 point
cross out the numbers 4,9,2,5.
number: 108
4. King Pea has 7 sons, each of his sons has 7 sons, and each grandson of King Pea has two daughters. How many great-granddaughters does King Pea have?
1) 7 * 7 = 49 (grandchildren)
2) 49 * 2 = 98 (great-grandchildren)
3 points
5 ... Six of them pull the turnip: the grandfather is twice as strong as the grandmother, the grandmother is twice as strong as the granddaughter, the granddaughter is twice as strong as the Bugs, the bug is twice as strong as the cat, the cat is twice as strong as the mouse. How many mice do you need to call so that they themselves pulled out the turnip?
The strength of the cat = the strength of 2 mice
Strength of the Bug = strength of 4 mice (2 * 2)
Granddaughter's strength = 8 mice strength (4 * 2)
Grandma's strength = 16 mice's strength (8 * 2)
The power of the grandfather = the power of 32 mice (16 * 2)
1 + 2 + 4 + 8 + 16 + 32 = 63 mice
4 points
6. A steamer and a boat departed from the pier simultaneously in one direction at speeds of 24 km / h and 15 km / h, respectively. After 4 hours the steamer ran aground. After taking off from the shallows after a while, he caught up with the boat an hour later. How long did the steamer stand aground?
1) 4 + 1 = 5 (h) - the steamer was in motion
2) 24 ∙ 5 = 120 (km) - the distance covered by the steamer (the boat passed the same amount)
3) 120: 15 = 8 (h) - the boat was on the way
4) 8-5 = 3 (h) - the time that the steamer was aground
Answer: The steamer was aground for 3 hours.
5 points
7. Three teams scored 285 points at the Olympiad. If the team of school №24 scored 8 points less, and the team of school №44 - 12 points less, the team of school №77 - 7 points less, then all of them would have scored equal points. How many points did the teams of schools # 24 and # 77 score together?
1) 8 + 7 + 12 = 27 (b)
2) 285-27 = 258 (b)
3) 258: 3 = 86 (b)
4) 86 + 7 = 93 (b)
5) 86 + 8 = 94 (b)
6) 93 + 94 = 187 (b)
Answer: 187 points were scored by the teams of school # 77 and # 24 together.
5 points
8. If the side of a square, the perimeter of which is 36 cm, is reduced by 3 times, then you get the width of a rectangle, the perimeter of which is 22 cm. Find the length of this rectangle and calculate the area.
1) 36: 4 = 9 (cm) - side of the square
2) 9: 3 = 3 (cm) - the width of the rectangle
3) 3 * 2 = 6 (cm) - 2 widths
4) (22-6): 2 = 8 (cm) - the length of the rectangle
5) 8 * 3 = 24 (cm)
Answer: 24 square centimeters is the area of a rectangle.
5 points
9. The lynx eats 600 kg of meat in 6 hours, and the tiger 2 times faster. How long will it take for them to eat this meat together?
1) 600: 6 = 100 (kg) - lynx eats in 1 hour
2) 100 * 2 = 200 (kg) - a tiger eats in 1 hour
3) 100 + 200 = 300 (kg) - together for 1 hour
4) 600: 300 = 2 (h)
Answer: the lynx and the tiger will eat this meat in 2 hours.
4 points
10. 5 diggers dig 5 meters of a ditch in 5 hours. How many diggers can dig 100 meters of a ditch in 100 hours?
If in five hours five diggers dig 5 m of a ditch, then in 100 hours in a time 20 times longer) the same five diggers will dig a ditch 20 times longer, that is, 100 m of a ditch.
Answer: 5 diggers.
4 points
Preview:
Mathematics Olympiad assignments for grade 3 with answers
- To put a fence on the side of the land, the farmer had to dig in 25 posts every 150 centimeters. How long was the fence?
Solution:
The fence can only be installed between two adjacent posts.
It turns out that the last pillar does not have a pair, which means the number of pillars through which the mesh can be pulled:
25 - 1 = 24
Now let's find out the length of the fence:
24 x 150 = 3600 (centimeters) = 36 (meters)
Examination:
(25 - 1) x 150 = 3600 (centimeters) = 36 (meters)
Answer: The length of the fence for the land plot will be 36 meters.
- The dragonfly flies at a speed of 10 m / s. How many kilometers will it fly in 1 hour?
Solution: 1 hour = 3600s 3600 10 = 36000 (m) or 36 km
Answer: a dragonfly will fly 36 km in an hour.
- What number should 87912 be divided by to get the same five-digit number written in the same digits, but in reverse order?
Solution: 87912: x = 21978
X = 4
Check: 21978
4
87912
Answer: x = 4
- Put the signs and, if necessary, parentheses in the examples so that you get the given results:
A) 300 20 10 4 = 334
B) 300 20 10 4 = 154
Solution:
A) 300+ 20+ 10+ 4 = 334
B) 300: 20 10+ 4 = 154
- Two dozen times three dozen. How many tens did it turn out?
Solution: 2030 = 600 = 60d
- Write down all two-digit numbers so that the tens and ones of each number add up to 8.
Answer: 17,26,35,44,53,62,71,80
- Write down what numbers they are:
1) The sum of the digits of a two-digit number is equal to the largest single-digit number, and the number of tens is two less than this sum. This number is ___________________.
Answer: 72, because. 7 + 2 = 9, and 7 is 2 less than 9.
- The sum of the digits in a two-digit number is equal to the smallest two-digit number, and the tens digit is four times less than the ones digit. This number is _______________.
Answer: 28, because. 2 + 8 = 10, and 2 is 4 times less than 8.
8. A square with a side of 6 cm was bent from a piece of wire. Then they unbent the wire, and bent a triangle with equal sides out of it. What is the length of a side of a triangle?
Solution: 6 4: 3 = 8 (cm)
Answer: 8cm.
9. Three sisters found 47 mushrooms. When one sister gave her friend 6 butter, the other
Solution: 1) 6 + 2 + 3 = 11 (gr.) - given by the sisters. 4) 12 + 6 = 18 (gr.) - 1 sister found.
5) 12 + 2 = 14 (gr.) - found by 2 sister.
2) 47-11 = 36 (gr.) - remained with the sisters.
3) 36: 3 = 12 (gr.) - each became. 6) 12 + 3 = 15 (gr.) - found by 3 sister.
Check: 18 + 14 + 15 = 47 (gr.)
10. Divide the clock face into two parts with a straight line so that the sums of the numbers in these parts are equal.
Solution: in one part there will be numbers: 10,11,12,1,2,3 (sum 39)
In the other part there will be numbers: 9,8,7,6,5,4 (sum 39)
11. Crossword "Measure"
- The smallest measure of mass is 1 ... gram
2.100 kg = 1 ... centner
3.1000 g = 1 ... kilogram
4.10 q = 1 ... ton
- 10 cm = 1 ... decimeter
- 100 cm = 1… meter
- 1000 m = 1 ... kilometer
- The length of the line is its ... the length
Olympiad in mathematics (round 1) pupils ___ grade 3 ___ ____________________________________________________________________________
1. Two tens multiplied by three tens. How many tens did it turn out? ______________
- Write down all two-digit numbers so that the sum of tens and ones of each number is 8: ________________________________________________________________
- Write down what this number is:
The sum of the digits of a two-digit number is equal to the largest single-digit number, and the number of tens is two less than this sum. This number is ___, because _____________________________
4. Put the signs and, if necessary, parentheses in the example so that you get the given result:
300 20 10 4 = 334
5. Three sisters found 47 mushrooms. When one sister gave her friend 6 butter, the other
2 boletus, the third - 3 porcini mushrooms, then each of them has an equal amount of mushrooms. How many mushrooms did each sister find?
_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
6. By what number should 87912 be divided to get the same five-digit number written in the same digits, but in reverse order?
_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________
7. The dragonfly flies at a speed of 10 m / sec. How many kilometers will it fly in 1 hour?
____________________________________________________________________________
- A square with a side of 6 cm was bent from a piece of wire. Then they unbent the wire, and bent a triangle with equal sides out of it. What is the length of a side of a triangle? _____________________________________________________________________________________________________________________________________________________________________________________________________________________
9. Divide the clock face into two parts with a straight line so that the sums of the numbers in these parts are equal.
10. Crossword "Measure"
- The smallest measure of mass is 1 ...
2.100 kg = 1 ...
3.1000 g = 1 ...
4.10 q = 1 ...
11. To put the fence on the side of the land, the farmer had to dig 25 posts every 150 centimeters. How long was the fence?
____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
III CLASS (17 * h)
City of Mysterious Numbers (2 hours)
Solving arithmetic puzzles. Recording numbers according to specified conditions.
City of Ordinary and Unusual Tasks (4 hours)
Solving problems - jokes. Solving tasks for ingenuity. Solving comparison problems. Solving problems - fairy tales. Solving problems related to quantities.
City of Mathematical Reasoning (2 hours)
Building statements. Solving logical problems.
TownGeometric « transformations"(3h)
Paintingfigures, nottearing offpencilfrompaper. Countgeometricfigures. Tangram.
TownRegularities (2 h)
Unravelingandcontinuationlogicalchainsandsquares. Solutionassignmentswithhelpcoloring.
TownMagicalmathematics (2 h).
« Crosses- noughts». Winningsituations. Mathematicalmagic tricks.
Expectedresults
TOthe endlearningpupilsIIIclassmay:
analyzeconditionentertaining, comictasks;
isolateessentialandthe necessarysignsobjectorprocessatthe decisiontasks;
abstract awayfromirrelevantsignsobjectorprocessatthe decisiontasks;
buildutterancesof the kind « IfA, thenV» andusetheiratthe decisiontasks;
applygraphicmethodsatthe decisiontasks;
isolatefamousgeometricfigures, incomingvcompositionmorecomplexobjects;
to followgivenconditionsforachievementsdeliveredgoals;
to plantheiractions;
applyreceivedknowledgevreallife.
Tasks for ingenuity. Grade 3
# 1. Lived in a swamp - there was a frog Kvakushka and her mother Kvakkvakushka. For lunch, Kwakkvakushka ate 16 mosquitoes, and Kwakushka 7 less, for dinner 15 mosquitoes, and Kvakushka 5 less. How many mosquitoes do frogs need per day if they do not eat breakfast.
No. 2. A mouse-noose and 2 frogs-frogs weigh the same as 2 mice - a burrow and one frog-frog. Who is harder: a mouse or a frog?
No. 3. Ryaba chicken laid several golden eggs. The grandfather and the woman began to share them. The grandfather says: "If we take 3 testicles, then one will remain." And the woman replied: "If we want 4 each, then one is not enough." The granddaughter came and said: "We have 8 eggs." Is the granddaughter right? How many eggs did Ryaba's chicken lay?
No. 4. When building a fence on a square plot in the village of Prostokvashino, the dog Sharik, the cat Matroskin and the little daw Khvatayka dug in the posts. On each side of the site, you need to dig in 6 columns. How many posts did the cat Matroskin, Sharik and Khvataika need to build the fence?
No. 5. A 12-meter cord was cut into 3 pieces of equal length. How many incisions did you have to make?
No. 6. Dunno had five whole pears, six halves and eight quarters. How many pears did Dunno have?
No. 7. Vanya laid out the pebbles on the table at a distance of 2 cm from one another. How many pebbles did he spread over 10 cm? Write an answer.
No. 8. There are chickens and piglets in the yard. A total of 5 heads and 14 legs. How many chickens are there and how many pigs are there? Write an answer.
No. 9. One hundred nuts were divided into five nuns. In the first and second, the total is -51 nuts, in the second and third - 44, in the third and fourth - 31, and in the fourth, 5 - 33. Find the number of nuts in each pile. Write an answer.
No. 10. A barrel full of honey weighed 12 kg. When half of the honey was eaten, the barrel began to weigh 7 kg. Write how much will it weigh when all the honey is eaten?
No. 11. There are poles along the treadmill. The start is given at the first pillar. After 12 minutes, the runner was at the fourth pillar. In how many minutes from the start will the runner reach the seventh pillar? (runner speed constant)
No. 12. Vova and Dima solved the problem in 10 minutes. How much time did each boy spend on solving the problem?
No. 13. Danila has 20 rubles in two pockets. When he transferred 6 rubles from one pocket to the other, the money in both pockets became equal. How much money (in rubles) was originally in each pocket?
No. 14. A pen is 15 rubles more expensive than a pencil. How many rubles are 5 pens more expensive than 5 pencils?
No. 15. The length of the log is 5 meters. In one minute, one meter is sawn off from a log, In how many minutes will the whole log be sawn?
No. 16. Anya, Borya, Vera and Gena are the best skiers of the school. To participate in the competition, you need to make a team of three skiers. How many ways can you create such a team?
No. 17. The goose weighs 2 kg. How much will he weigh if he stands on one leg?
No. 18. Misha has several soldiers, and Sasha has twice as many. Together the boys have 9 soldiers. How many soldiers does each boy have?
No. 19. Three birds were sitting on the tree, two more birds flew to them. The cat crept up and grabbed one bird. How many birds are left on the branch?
No. 20. Three were playing checkers. In total, 3 games were played. How many games did everyone play if everyone played equally?
Answers: (No. 1- 50 k; No. 2- equally; No. 3- 7 pieces of eggs; No. 4- 20 s; No. 5- 2 p; No. 6-10; No. 7- 6 k; No. 8- 3 chickens . 2 pores; No. 9 - in the first-33, in the second - 28, in the third - 16, in the fourth - 15, in the fifth - 18; No. 10 - 2 kg. No. 11 - after 24 minutes; No. 12. - 10 minutes; No. 13 - 16 and 4 rubles; No. 14 - 75 rubles; No. 15 - in 4 minutes; No. 16 - 4 ways; No. 17 - 2 kg; No. 18 - for Misha -3, for Sasha -6; No. 19 - none; no. 20oldest? Whohighest?
