- •Навчальний посібник
- •First term
- •Second term
- •Mathematics as a science
- •Mathematics
- •Task 17
- •Isaak Newton
- •Age problem
- •Self-assessment Be ready to speak on the topic "Mathematics as an independent science" using the following as a plan:
- •Check your active vocabulary on the topic:
- •Translate into English and be ready to give illustrative examples:
- •Fill in the gaps using a word from the list:
- •Arithmetic operations
- •Four basic operations of arithmetic
- •Two Characteristics of Addition
- •Self-assessment
- •Rational numbers
- •Rational and irrational numbers
- •Rational and irrational numbers
- •What is a number that is not rational?
- •Self-assessment
- •Properties of rational numbers
- •Properties of rational numbers
- •Properties of rational numbers
- •Reciprocal Fractions
- •Reducing Fractions to Lowest Terms
- •A Visit to a Concert
- •Self-assessment
- •Geometry
- •Meaning of geometry
- •Points and Lines
- •The history of geometry
- •Strange figures.
- •Measure the water.
- •Self-assessment
- •Simple closed figures
- •Simple closed figures
- •Simple closed figures
- •Problems of Cosmic and Cosmetic Physics
- •How to find the hypotenuse
- •Geometry Challenges
- •Self-assessment
- •Functional organization of computer
- •Computers
- •An a is a b that c
- •Find the numbers
- •Hundreds and hundreds
- •Tasks for self-assessment
- •Computer programming
- •Now read the description below. Do you like it? Why/Why not?
- •Instruction, instruct, instructed, instructor
- •Programming languages
- •Testing the computer program
- •Genius’s answer
- •A witty answer
- •The oldest profession
- •Tasks for self-assessment
- •Additional texts for reading
- •Read the text and summarise the main ways of expressing numbers in English.
- •Expressing numbers in english
- •Expressing millions
- •Ways of expressing the number 0
- •Fractional numbers
- •Writing full stops and commas in numbers
- •A short introduction to the new math
- •Algorithm
- •Mathematical component of the curriculum
- •Some facts on the development of the number system
- •The game of chess
- •Computers in our life
- •Is "laptop" being phased out?
- •The Main Pieces of Hardware
- •Text 10
- •Programs and programming languages
- •Text 11
- •All about software Categories of applications software explained
- •Systems Software
- •Applications Software
- •All the Other 'Ware Terminology
- •Malware
- •Greyware
- •Text 12
- •Advantages and disadvantages of the internet
- •Advantages
- •Disadvantages
- •Text 13
- •Text 14
- •Thinking about what we’ve found
- •Meta-Web Information
- •Text 15
- •Computer-aided instruction
- •Text 16
- •Teacher training
- •Іменник Утворення множини іменників
- •Правила правопису множини іменників
- •Окремі випадки утворення множини іменників
- •Присвійний відмінок
- •Практичні завдання
- •Артикль
- •Вживання неозначеного артикля
- •Вживання означеного артикля
- •Відсутність артикля перед обчислюваними іменниками
- •Вживання артикля з власними іменниками
- •Практичні завдання
- •Прикметник
- •Практичні завдання
- •Числівник
- •Практичні завдання
- •Займенник Особові займенники
- •Присвійні займенники
- •Зворотні займенники
- •Вказівні займенники
- •Питальні займенники
- •Неозначені займенники
- •Кількісні займенники
- •Практичні завдання
- •Прийменник
- •Дієслово
- •Неозначені часи indefinite tenses
- •Теперішній неозначений час the present indefinite tense active
- •Вживання Present Indefinite Active
- •Майбутній неозначений час the future indefinite tense active
- •Практичні завдання
- •Did you have a meeting yesterday?
- •I had an exam last week.
- •I didn't have an exam last week. Did you?
- •Тривалі часи дієслова continuous tenses
- •Теперішній тривалий час The present continuous tense active
- •Минулий тривалий час The past continuous tense active
- •Майбутній тривалий час The future continuous tense active
- •Практичні завдання
- •Перфектні часи perfect tenses
- •Теперішній перфектний час The present perfect tense active
- •Минулий перфектний час The perfect past tense active
- •Майбутній перфектний час The future perfect tense active
- •Практичні завдання
- •Узгодження часів sequence of tenses
- •Практичні завдання
- •Модальні дієслова modal verbs
- •Практичні завдання
- •Типи питальних речень question types
- •Практичні завдання
- •Пасивний стан дієслова passive voice
- •Практичні завдання
- •Check yourself
- •Читання буквосполучень
- •Читання голосних буквосполучень
- •Читання деяких приголосних та їхніх сполучень
- •Irregular verbs
- •Indefinite Tenses
- •Continuous Tenses
- •Perfect Tenses
- •Perfect Continuous Tenses
- •List of Proper Names
- •Sources of used materials
- •Contents
Age problem
Once there lived a clever king. One day a scientist came to him and surprised him with his knowledge. He amused the king by telling him many things that were new and interesting. Finally, the king wanted to find out the age of the scientist but the did not want to ask him.
"Professor," said the king, "I have an interesting problem for you. Think of the number of the month of your birth, but don’t tell me." The scientist was 60 years old, and his birthday was in December. So he thought of 12. "All right," he said. "Multiply it by two," said the king. "I have done it." "Add 5." "I have". "Now multiply by 50." "Yes." "Subtract 365." "OK." "Add your age." "Done." "Add 115." "Yes." "And now," said the king, "tell me result." "Twelve hundred and sixty," answered the scientist. "Thank you," said the king. "You were born in December and now you are sixty years old." "How do you know that?" asked the scientist. "From your answer," replied the king. "Oh!" the professor said laughing, "That is a polite way to find out one’s age."
Can you find out your friends’ age in the same way?
Self-assessment Be ready to speak on the topic "Mathematics as an independent science" using the following as a plan:
1. What is mathematics?
What can mathematics express?
How can mathematics help scientists?
What do we benefit from the results of mathematical research every day?
When did mathematics become a field on its own right?
Who first developed mathematical knowledge?
What branches of mathematics were the only mathematical disciplines until the 17th century?
What do you know about scientific research in the end of 18th and beginning of the 19th centuries?
Name several well-known mathematicians and say what they are famous for?
What role does the invention of computer play in science?
Science, technology and mathematics. What can you say about their interplay in modern life?
Check your active vocabulary on the topic:
Number System Measure Quantity Equation Interaction Terminology Analysis (pl analyses)
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Algebra Geometry Calculus Rigorous Equivalence To summarize Gravity Relativity Applied
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Invention Phenomenon(phenomena) Technology To calculate To compute Notion Сomplex Arithmetic |
Translate into English and be ready to give illustrative examples:
арифметика алгебра геометрія обчислення точний еквівалентність, рівність підсумовувати, складати тяжіння, сила тяжіння відносність, теорія відн.
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прикладний винахід явище, феномен техніка, технічні та прикладні науки, технологія обчислювати, обрахуватити рахувати, підраховувати поняття, уявлення, ідея складний, комплексний
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число, цифра, номер система, метод вимірювати, міра кількість, величина рівняння взаємодія термінологія аналіз
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