
- •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
Simple closed figures
Geometry studies figures in the … and on the … . The main geometric notions are the … of a point and a line. A point is an exact … in space. A line consists of … of points. Lines form line …, rays and angles. A line segment includes … and all points … them. A ray is a line segment extended in one … .
Drawing two … originating from the same endpoint we get an … . The common point of the two rays is the … of the angle. Angles separate the plane into three distinct … of points: interior, …, and the angle. The letter naming the vertex of an angle is the … letter in naming of each angle.
A … angle has a measure of 90°. An … angle has a degree measure less than 90°. An … angle has a degree measure greater than 90°.
A simple closed figure is any figure drawn in a … in such a way that … never crosses or intersects itself and encloses … of the plane. Every simple closed figure … the plane into three distinct sets of point. The … of the figure is the sets of all points in the part of the plane enclosed by the figure. The … of the figure is the set of point in the plane which are outside the figure. And finally, the simple … figure itself is still another set of points.
A simple closed figure formed by line segments is called a …. Each of the line segments is called a … of the polygon. Polygons may be classified according to the … of the angles or the measure of the … . Triangle can be … . The sides of such triangle all have the same linear measure. An … triangle has two sides of the same measure. A right triangle has … right angle. A right triangle has two … and a …. A hypotenuse is a side opposite to the … angle.
A parallelogram is a quadrilateral whose opposite sides are …. So the set of all parallelograms is a … of all quadrilateral. A trapezoidal has only two parallel … . They are called the … of a trapezoidal.
Task 8
Fill in the gaps:
Problems of Cosmic and Cosmetic Physics
L. Meitner was ___ 1 _____woman – physicist in Germany. The title____ 2 ____her dissertation seemed absurd to one of the____ 3 ____. In his article______ 4 _____ L. Meitner which he _______ 5 ____in a newspaper he ___ 6 ____the title and ____ 7 _____ "Problems of Cosmetic Physics". L. Meitner only ____ 8 _____and ____ 9 ______this a ___ 10 ____ joke.
1. a. one 2. a. to
b. first b. for
c. the first c. on
d. the one d. in
3. a. magazines 4. a. about
b. journalists b. through
c. articles c. at
d. stories d. according
5. a. is publishing 6. a. corrected
b. was publishing b. drew
c. published c. asked
d. publishes d. talked
7. a. said 8. a. laughed
b. wrote b. is laughing
c. went c. has laughed
d. brought d. was laughing
9. a. is calling 10. a. fun
b. was calling b. funny
c. will call c. more funny
d. called d. more fun
Task 9
Can you help with geometry test?
Task 10
Now read the text and solve the problems.