Fundamentals of mathematical information processing (beginner level) Task-Sanak book Authors: А.Zaripova, D. Ishtiryakova, A.Yamaev Editor: Adelya apa
Content 1. Data representations(tables, charts, plots, graphs) (10 tasks) 2. Graph theory (5 tasks) 3. Set theory (11 tasks) 4. Probability theory (4 tasks)
Data representations
Task №1 The table above is given. Answer the following questions: 1. How many teachers live in the Master’s house? 2. In which rooms can you conduct robotics lessons if you need 9 laptops for this, but do not need a projector? 3. In which rooms can you conduct gamedesign lessons if you need 7 laptops and a projector for this? Room Room type Residents Laptops Projector 1 Lobby - 6 Yes 2 Meeting room - 8 Yes 3 Educational center - 10 Yes 4 Kitchen - - - 5 Terrace - 13 No 6 Living room 7 - Yes 7 Living room 4 - No 8 Living room 2 - No Tablе №1 «Master’s house»
Task №2 The table above is given. Answer the following questions: 1. Which room did the selkeshes go to bed in later than the others? 2. Which room did the selkeshes woke up in before everyone else? 3. In which room did the selkeshes sleep for less than 9 hours? Room Bed time Wake up time 2 22:22 7:30 1 23:01 8:06 4 22:10 7:46 2 23:08 7:59 3 23:06 8:26 1 22:47 7:24 Tablе №2 «Sanak’s house №4»
Task №3 The table above is given. Answer the following questions: 1. Who wakes up later than Azaliya apa, but before than Adelya apa? 2. Who goes to the morning exercise more often than Almaz, but less often than Eileen? 3. Who doesn't drink tea for breakfast? Name Wake up time Morning exercise Breakfast Amir 8:00 3 times Porridge, tea, bread and butter Azaliya apa 8:05 1 time Tea, bread and butter Adelya apa 8:30 5 times Porridge and tea Almaz 8:10 4 times Porridge and bread Aylin 8:00 6 times Doesn't have brekky Tablе №3 «Morning of Sanak’s people»
Task №4 2,6 ч. 30 мин. 3 ч. 14,6% 9 ч. 12,5% Selkeshes' daily schedule Lessons Day event Pool Meal time Evening event Sleep Other 2,9 ч. Selkeshes' daily schedule is shown in the pie chart. Answer the next questions based on given information: 1. What percentage of sleep is in the schedule? 2. Which takes more time the lessons or the evening event? 3. Is it true that sleep and the other together take up more than half of the day? 4. How many hours do Day and Evening event make up together?
1 7 9 10 4 2 3 5 4 2 0 2 4 6 8 10 12 Tech.English Gamedesign Robotics Python FRONTEND DEVELOPMENT Lessons in Sanak boys girls Task №5 Some lessons in Sanak camp are shown in the bar chart. Answer the next questions based on given information: 1. How many boys are there on Python and Frontend lessons? 2. Which lesson do the most selkeshes attend? 3. Is it possible to send girls from robotics and English lessons to a competition where 9 people are needed in a team?
Task №6 5 7 6 4 4 6 3 5 3 2 4 1 0 1 2 3 4 5 6 7 8 Round 1 Round 2 Round 3 Round 4 Event «Start in» English songs Russian songs Tatar songs Selkeshes participated in the «Start in» dance event. There were 4 rounds and in which songs were plyaed English, Russian, Tatar languages. The number of songs is shown in the line chart. Answer the next questions based on given information: 1. How many songs were there in Tatar in all the rounds? 2. Which round played the most songs? 3. On which кщгтв did the sum of English and Russian songs play less than the others?
Task №7 Plot the graphs of the functions knowing b and k: L) 𝑦 = 4𝑥 + 6 A) 𝑦 = 2𝑥2 − 8 B) 𝑦 = 5 − 3x3 Task №8 Plot the graphs of the functions knowing b and k: L) 𝑏 = −1; 𝑘 = 4 A) 𝑏 = 3,5; 𝑘 = 8 B) 𝑏 = −12; 𝑘 = −4,7
Task №9 L) Find the value of the 𝑦 function 𝑦 = 1 3 𝑥 − 3 when x = −2; 7; −11 A) Find the value of the 𝑦 function 𝑦 = −1,5𝑥 + 2 when x = 1; −9; 18 B) Find the value of the 𝑦 function 𝑦 = 7𝑥 + 2,5 when x = 5; −4; 10 Task №10 L) Find the value of the 𝑥 function 𝑦 = 1 3 𝑥 − 3 при y = 4; −5; −13 A) Find the value of the 𝑥 function 𝑦 = −1,5𝑥 + 2 при y = 2; 7; −9; B) Find the value of the 𝑥 function 𝑦 = 4𝑥 + 2,5 при y = 5; −4; 10
Graph theory
Task №1 After the football match, Ildar aby and Rashit aby decided to walk around the forum with the guys. Their route was as follows: 1) Bilyarsk shop 2) Vegetable garden 3) Stage 4) Café 5) SeletStore 6) Café 7) Stage 8) Football field 9) Bilyarsk shop Draw a graph of the route. Is it open or closed? Explain the answer.
The chess tournament is going on. Alan Sanak is playing with Alan Atilla. The graphs show the walks of the Sanak participants' moves. Find order and dimension of the following graphs. Task №2 a) b)
Task №3 Ruslan aby likes to go to the forum in different ways. Below are the different variants for its walks. Among them find a trail and a path? Сircle them and write down the walk. Also write their type.
Task №4 Psychologist Camilla apa conducted a "Tree" training, where a tree was drawn and 30 people numbered on it. Camilla Apa conduct one 3 times. Draw one large graph with 30 vertices and with different colors highlight the answers of the selkesh on it, which are presented below. Use directed graph for highlighting. a) 4-7-12 b) 1-3-28 c) 16-11-2 d) 14-6-19 e) 9-12-5 f) 8-21-30
Come up with stories and based on it task for the following graphs: Task №5 a) b)
Set theory
What kind of sets presented below belong to? (finite, infinite, empty) L) ∅ A) ሼ… hugs, aidamans′ love for children,evening event Task №1 Task №2 Do the following assignment: L) Write a set of female selkeshes of 7 elements in curly brackets A) Write a set of male selkeshes of 5 elements in paranthesis B) Write a set of male aidamannar of 5 elements in brackets
Write which subsets each set contains and depict it. А – set of the Selet’s camp bases B – set of the beds in the room №2 of the house №3 C – set of the houses on the territory of the Fansar base D – set of bolts inside the beds E – set of the rooms in the Fansar’ s house №3 Task №3 Task №4 There is a lunch in Sanak camp and it consists of the set 𝑆 = ሼsoup, rice, fish, cucumber, a piece of
Task №6 Task №5 The team of female aidamans consists of the set N = Aisylu apa, Azaliya apa, Camilla apa, Ilmira apa Which subsets do not belong to the set N? L) A = Aisylu apa, Adelya apa A) B = Azaliya apa, Ilmira apa B) C = Camilla apa, Aisylu apa, Ilmira apa, Radmila apa Determine the cardinality of each set L) A = Diana, Karim. Amir, Masha, Camilla A) B = Timur, Matvey, Azaliya, Eilin, Kira, Timur, Musa B) C = Aidar, Ilsiya, Rostislav. Anna, Ramin, Ilsiya, Said, Ramazan, Ramin, Karim
Task №7 Two sets are given: A = music, Rashit aby, rhythm, morning exercise, DJ B = meeting,rhythm Riles, groups, time, news, bashzhiteks Execute the following operations for these sets: L) Union A) Intersection B) Absolute complement Task №8 Two sets are given: A = Ilgiza apa, Zarina apa, table, Vladik aby, WI − FI, lesson, IT B = breakfast, Ruslan aby, IT, Gulnaz apa, Bulat aby, camp, Zarina apa What operations are executed on them if L) C = IT, Zarina apa A) C = Ilgiza apa, table, Vladik aby, WI − FI, lesson B) C = breakfast, Ruslan aby, Gulnaz apa, Bulat aby, camp
Task №9 Three sets are given: A = pool, Nikita aby, wi−fi, forum, Pavel aby, Camilla apa B = DJ, blue, team, pool,camp,morning exercise bashzhiteks C = music, Camilla apa, pool,Nikita aby, morning exercise, DJ Draw the images for the operations below. Use Euler Circles. Also, give the final answer by enumerating. a) A ∩ B b) C/B c) (A ∪ C)/(B/A) d) B ∪ C ∩ A e) A ∪ C/(B/C) f) (C/A)/(B/A) ∪ C g) (A/B) ∪ (B ∩ C)
Task №10 How many elements are there in the Cartesian product of the sets below. Use the appropriate theorem L) A = Ruslan aby B = Zarina apa, Ilgiza apa, Camilla apa A) A = Irek aby, Kamil aby, Vladik aby, Nikita aby B = Aisylu apa, Azaliya apa, Camilla apa, Ilmira apa B) A = Askar aby, Pasha aby, Ildar aby, Bulat aby B = Gulfiya apa, Sveta apa, Kristina apa, Adelya apa,Sveta apa C = Adelya apa, Camilla apa, Rashid aby, Karina apa, Gulnaz apa Task №11 Determine the Cartesian product of two sets. Show the result in the form of a table A = laptop, phone. keyboard, code B = selkesh,aidaman,bashzhitek
Probability theory
Task № 1 There are 8 people in the team of aidamans: Irek aby, Aisylu apa, Kamil aby, Azaliya apa, Vladik aby, Camilla apa, Nikita aby and Ilmira apa. Every morning, the children are woken up by one of the aidamans. Irek aby, Aisylu apa, Azaliya apa, Camilla apa wear glasses, the rest of the team does not. Tomorrow it will be a man whose name begins with the letter A or I and he will wear glasses. What is the probability that it will be Aisylu apa or Irek aby? Task № 2 The event "Tabigat Tavyshy" choir consists of 5 rounds and is led by Askar aby and Ildar aby. What is the probability that the first and second rounds will be announced by Ildar Aby?
Task № 3 Task № 4 One more participant is needed for the streetball match. The following selkesh want to participate: Masha(152 cm), Said(164 cm), Amir(180 cm), Renal(140 cm), Azamat (174 cm) Daniel (156 cm), Saidash (146) and Zilya (162 cm). What is the probability that the selected person will be male or above 175 cm? Express it as a percentage. Before going to bed, Raisa apa conducts thermometry among children. Usually she does this in the house, canteen or in front of the assembly hall. What is the probability that thermometry will take place in front of the conference hall or in the canteen today? Express the answer in approximate percentages
Answers 1. Data representations 1. 1)13; 2) Educational center and terrace 3) Meeting room and Educational center 2. 1) 2 room 2) 1 3) 2 3. 1) Almaz 2) Adelya apa 3) Almaz and Eileen 4. 1) 37,5% 2) evening event 3) true 4) 6,5 5. 1) 14 2) Robotics and Python 3) No 6. 1) 22 2) 3) 7. You have to do it yourself 8. You have to do it yourself 9. L) -4; -2/3; -20/3 A) 0,5; 15, 5; -25; B) 37,5; -25,5; 72,5; 10. L) 7/3; -2/3; -10/3; A) 0; -3,(3); 7,(3); B) 0,625; -1,625; 1,875; 2. Graph theory 1. Closed 2. a) order = 5 ; dimension = 6 b) order = 6 ; dimension = 9 3. Trail: 1-2-3-4-2-1; (closed or circuit) path: 0-1-2-3-6-7 (open) 4. You have to do it yourself 5. You have to do it yourself
Answers 3. Set theory 1. Empty, infinite, finite, 2. Come up with your own elements L) A) B) 3. D ∈ B ∈ E ∈ C ∈ A 4. L 5. A 6. L) 5 A) 6 B) 8 7. L) C = music, Rashit aby, rhythm, morning exercise, DJ, meeting,rules, groups, time, news, bashzhiteks A) C = rhythm B) C = U/A ∪ B 8. L) intersection A) A/B B) B/A 9. You have to do it yourself 10. L) 3 A) 16 B) 80 11. You have to do it yourself 4. Probability theory 1. 2/3(66,67%) 2. 2/3 3. 1/4 4. 3/4(75%)
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