2001
Tieỏng Anh 4 Toaựn Tin - 2 CONTENT

LễỉI TệẽA 3
UNIT 1: MATHEMATICS 4
UNIT 2: WHAT IS A COMPUTER? 11
EXERCISES 12
UNIT 3: NUMBERS AND MATHEMATICS 16
UNIT 4: CHARACTERISTICS 22
EXERCISES 23
UNIT 5: STATISTICS 31
UNIT 6: MAINFRAMES 37
EXERCISES 38
UNIT 7: CALCULUS 44
UNIT 8: STEPS IN PROBLEM SOLVING 50
EXERCISES 52
UNIT 9: DISCRETE MATHEMATICS 56
EXERCISES 57
UNIT 10: PROGRAMS AND PROGRAMMING LANGUAGES 62
EXERCISES 63
GLOSSARY 70

Pre-reading:
1. Would you like to do science?
2. Which branch of science do you like?
3. You are studying mathematics, why do you like it?
Mathematics plays an important part of your lives. Today mathematics is of the great
use to many sciences, so more and more mathematical books are printed in many
languages, especially in English.
Anyone who works with any branch of science or technology needs to be able to talk
about numbers and shapes. Notice how following numbers and shapes are said in
English.

Numbers:
28% : Twenty-eight per cent.
10.3 : Ten point three

9
4
: Four ninths (four over nine)
4
2
: Four squared
5
3
: Five cubed
5
4
: Five to the power of four
1.623.457 : One million, six hundred and twenty-three thousand,
four hundred and fifty seven.


3

(Two x plus three y minus 2 equals three Z devided by four x)
Four basic operations of arithmetic are:Addition, subtraction, multiplication, division.
6 x 7 = 42 (six times seven is forty two)

The symbols and their expressions:
a. + (Plus) k. % (percent)
b. - (minus) l. > (is more than)
c. x (multiplied by) m. ∈ (is an element of)
d. : (divided by) n.
∞
(infinity)
e. = (is equal to) o.
3
(cube root)
f.
≈ (is equivalent to) p. (square root)
g.
≥ (is more than or equal to) q. x
2
(x squared)
h.
⊂ (is a subset of) r. x
3
(x cubed)
i. < (is less than) s. x
4
(x to the power four)
j.

AA
Pyramid
A’
C
A’
B

B
Tieáng Anh 4 – Toaùn Tin - 6 –

Teaching points:
Active: The simple present
Passive: The simple present
Suffix: - ion
(2) WORKING WITH VOCABULARY

A. Focus on the reading:
Arithmetic Lives
Equals Multiplication
Formulas Times
Dimensional Said
Plays Who
Choose the best words or phrases above for each sentence, if you need help, look
at the reading again (use each word only once)

7. _______ out of number today he is absent from lesson again.
8. Because we are students our _______ are different from theirs.
9. Some students don’t understand the term of _______ analysis.

UNDERSTANDING THE READING

A. Comprehension questions:
* Answer the questions about the reading:
1. Why are more and more mathematical books printed in English?
2. Why do scientists and technologists need to be able to talk about numbers and
shapes in English?
3. Why does mathematics play an important part of our lives?
4. Can you read: +2; -2 in English?
5. Can you do the algebraical maths: If 3a+4 is greater than 16, then a must be
a. greater than 4 c. equal to 4 e. greater than 3
b. less than 4 d. less than 5

B. Details: Write T if the sentence is true and F if it is False
1. Mathematics is necessary for us because it helps to research
2. Sciences need mathematics
3. Some branches of science don’t need mathematics
4. Two halves of a circle can be called semi-circle
5. A rectangle has four right angles
6. The symbol:
≥ can be read: more than or equal to

C. Main idea: Check b the two most important ideas from the reading
1. Some mathematics symbols
2. How to do maths
3. Mathematics and its use in our lives

Practice: Put the verbs in the correct forms, all the verbs are in simple present, either in
the active or in the passive
1. Complex algebraical fraction ________ by the same method used in arithmetic
(simplify)
2. The oldest villagers ________ to attend a meeting (invite)
3. They ________ science books in English (print)
4. English ________ in many parts of the world (speak)
5. The doctor ________ on the patient (operate)
6. She ________ from bad headaches (suffer)
7. She ________ in touch with her family by phoning home every Sunday (keep)
8. Wood ________ in water (not sink)
9. Three persons ________ in a car cash (injure)
10 Water ________ from the rivers by women and children (bring)
11. That film ________ on TV tonight (not show)

Tieáng Anh 4 – Toaùn Tin - 9 –
B. Word forms: Nouns
Sometimes verbs and nouns are the same forms; sometimes we can change
verbs to nouns by adding suffix.

ION SAME FORM

Verbs Nouns Verbs Nouns
Subtract - Subtraction Play - Play
Communicate - Communication Change - Change
Act - Action Work -Work
Retract - Retraction Use - Use

Tieáng Anh 4 – Toaùn Tin - 10 –
CONTEXT CLUES
Choose the answer that is closest in the meaning to each word or phrase
underlined use context clue:
1. He knew it was a waste of time to
carry on studying archaeology and the moment he
started gaderning again
a. conitnue b. begin
c. finish d. start
2. It is very dry today will you help me
water the plants?
a. moisten b. wet
c. irrigate d. sprinkle
3. Can you please
tell me a little about yourself?
a. speak b. talk
c. say to d. explain
4. Do you
mind my turning the TV on now?
a. show b. disapprove
c. want d. like
5. The
enjoyable thing about travelling by train rather than by car is that you can sleep
or read during the journey
a. cheerful b. pleasurable
c. interested d. pleased
6. She had taken over the cooking at home for her father’s dinner parties and she had

and characters. The basic idea of a computer is that we can make the machine do what
we want by inputting signals that turn certain switches on and turn others off, or that
magnetize or do not magnetize the cores.
2. The basic job of computers is the processing of information. For this reason,
computers can be defined as devices which accept information in the form of
instructions called a program and characters called data, perform mathematical and/or
logical operations on the information, and then supply results of these operations. The
program, or part of it, which tells the computers what to do and the data, which provide
the information needed to solve the problem, are kept inside the computer in a place
called memory.
3. Computers are thought to have many remarkable powers. However, most
computers, whether large or small have three basic capabilities. First, computers have
circuits for performing arithmetic operations, such as: addition, subtraction, division,
multiplication and exponentiation. Second, computers have a means of communicating
with the user. After all, if we couldn’t feed information in and get results back, these
machines wouldn’t be of much use. However, certain computers (commonly
minicomputers and microcomputers) are used to control directly things such as robots,
aircraft navigation systems, medical instruments, etc.
4. Some of the most common methods of inputting information are to use punched
cards, magnetic tape, disks, and terminals. The computer’s input device (which might
be a card reader, a tape drive or disk drive, depending on the medium used in inputting
information) reads the information into the computer. For outputting information, two
common devices used are a printer which prints the new information on paper, or a
CRT display screen which shows the results on a TV-like screen.
5. Third, computers have circuits which can make decisions. The kinds of decisions
which computer circuits can make are not of the type: ‘Who would win a war between
two countries? or ‘Who is the richest person in the world?’ Unfortunately, the computer
can only decide three things, namely: Is one number less than another? Are two
numbers equal? and, Is one number greater than another?
6. A computer can solve a series of problems and make hundreds, even thousands,

information to do so.
_______ 2. All computer accept and process information in the form of instructions
and characters.
_______ 3. The information necessary for solving problems is found in the memory
of the computer.
_______ 4. Not all computers can perform arithmetic operations, make decisions,
and communicate in some way with the user.
_______ 5. Computers can still be useful machines even if they can’t communicate
with the user.
_______ 6. There are many different devices used for feeding information into a
computer.
_______ 7. There aren’t as many different types of devices used for giving results
as there are for accepting information.
_______ 8. Computers can make any type of decision they are asked to.
_______ 9. Computers can work endlessly without having to stop to rest unless there
is a breakdown.

Tieáng Anh 4 – Toaùn Tin - 13 – 3. Locating information
Find the passages in the text where the following ideas are expressed. Give line
references.
_________1. Computers accept information, perform mathematical and/or logical
operations then supply new information.
_________ 2. All computers have three basic capabilities.
_________ 3. A computer is a machine that can be made to operate by receiving
signals.
_________ 4. A computer cannot work without being told what to do.
_________ 5. A computer can make three types of decisions.

program memory medium

Tieáng Anh 4 – Toaùn Tin - 14 – CRT display
1. Every computer has circuits for performing arithmetic operations, operating
_____________ or magnetized _____________.
2. A ___________ with a screen is normally referred to as a __________ unit.
3. A computer is a ___________ that processes information in the form of
__________ and ______________ and can store this information in a
_____________.
4. Card readers, tape drives, or disk drives are different _______________ for
inputting information.

Focus: Contextual reference

Transitional markers are words used to link ideas together so that the text is
smoother to read. When pronouns such as it, they, them, I, he, she, which, who,
whose, that, such, one and demonstrative adjectives such as this, that, these and
those, are used as transitional markers, they refer to a word, or words, mentioned
earlier in the sentence or paragraph. Their function is to take your thoughts back to
something that has already been mentioned. Thus they serve as synonyms or
substitutes. Other words which are often used to refer backwards are the former,
the latter, the first, second, etc., the last.
Sample paragraph
A computer like any other machine, is used because it does certain jobs better and
more efficiently than humans. It can receive more information and process it faster
then any human. The speed at which a computer works can replace weeks or even
months of pencil-and-paper work. Therefore, computers are used when the time

Exercise 2
Now look back at the text ‘What is a computer?’ and find out what the words in
bold typeface refer to.
1. that operate switches (p. 1)
electronic circuits___
2. which accept information (p. 2) __________________
3. or part of it (p. 2) __________________
4. which tells the computers (p. 2) __________________
5. which prints the new information (p. 4) __________________
6. which shows the results (p. 4) __________________
7. which can make decisions (p. 5) __________________
8. It can find the solution (p. 6) __________________
9. it has no originality (p. 6) __________________
10. tells it what to do (p. 6) __________________

Tieáng Anh 4 – Toaùn Tin - 16 – UNIT 3: NUMBERS AND MATHEMATICS It is said that mathematics is the base of all other sciences, and that arithmetic,
the science of numbers, is the base of mathematics. Numbers consist of whole
numbers (integers) which are formed by the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 and
by combinations of them. For example, 247- two hundred and forty seven- is a
number formed by three digits. Parts of numbers smaller than 1 are sometimes
expressed in terms of fractions, but in scientific usage they are given as decimals.

Tieáng Anh 4 – Toaùn Tin - 17 – 5. Name the common arithmetical operations. Using actual numbers, give
examples of each.
6. What are the two number-systems commonly used throughout the world?
7. Give examples of numbers in the binary system.
8. What are the advantages of each system?
9. Name some other branches of mathematics.
10. What branch of mathematics is very useful to the ordinary citizen? Why?

II. Word study
Synonyms
Find words in the passage which mean approximately the same as:
1. entire __________ 2. simpler ____________
3. usually __________ 4. in the place of ____________
5. widely __________ 6. be put to use in ____________
7. lastly __________ 8. continually ____________
9. discover __________ 10. kind, sort ____________
11. system of measurement _________________________
12. action of trying to do something _________________________
13. cause someone to make a mistake by
giving wrong or incomplete information _________________________

Word building
∗ Use the suffix –ion, -ment, -ity to form nouns from the following words:
add calculate simple equip
subtract isolate able adjust
divide explain available improve
multiply measure stable move

6.The scale in which numbers are expressed by combination of two digits 0 and1
is called _____________.
7.In the field of mathematics, __________ and ____________ are considered to
be specialized extensions.
8.In the binary scale 3 is _______________ as 011.
9.Algebra and geometry are ______________ of mathematics.
10. The branches of mathematics are _____________used in both natural and
social sciences.

III. Revision
Use correct prepositions to complete these sentences.
1.Parts of numbers smaller than 1 are represented _________ fractions, but in
scientific usage ______________ decimals.
2.It’s not easy to find proportion __________ pairs of numbers.
3.The ten-scale is used ____________ the world.
4.Some countries use systems of weights and measurements based ________
other scales.
5.Another scale ____________ general use is the binary one.
6.Some mathematical extensions are being applied ___________ an increasing
range of activities.
7.In computer science, people use some other scales _________ the ten one.

IV. Structure study

Tieáng Anh 4 – Toaùn Tin - 19 – A. It preparatory subject
Study the example:
It’s easy to perform various mathematical operations.

Exercise
Complete these sentences with –ing form or –ed form. The first letter(s) of the
participle are given each time.
1. I’m starting a new job next week. I’m quite ex___________ about it.
2. The s___________ jewelry was recovered.
3. Success in one’s work is a sa___________ experience.

Tieáng Anh 4 – Toaùn Tin - 20 – 4. The te_____________ villagers ran for their lives.
5. I found myself in an em_____________ situation last night.
6. A da_____________ earthquake occurred recently.
7. I elbowed my way through the cr____________ room.
8. Why do you always look so b____________? Is your life really so b________?
9. No one lives in that d__________ house except a few ghosts.
10. Parents have a la___________ effect on their children.

C. Revision: Passive Voice
Exercise:
(a) Make the following sentences Passive thus eliminating the unspecified
doer of the action and emphasizing the object or the main verb.
1. People apply mathematics in many different activities.
2. People use the binary scale in electronic computers.
3. People from the square of a number by multiplying the number by itself.
4. In the binary scale, people express numbers by combination of 0 and 1.
5. People usually use decimals rather than fractions for scientific purposes.
6. People develop new products everyday.
7. People call mathematics ‘the language of science’
8. People use the decimal system even in countries with non-decimalized systems

chemicals and equipment.
6. A combination of two elements forms a chemical compound.
7. The ordinary citizen often requires an elementary knowledge of statistics.
8. Economists also use mathematics.
9. Every type of scientist requires a knowledge of statistics.
10. Scientists use accurate systems of measurements.
11. Philosophers employ specialized extensions of mathematics.
12. Physicists also use probability theory.

(c) Make up sentences similar to the ones given in Exercises (a) and (b)
above, and then change them from Active to Passive.

Tieáng Anh 4 – Toaùn Tin - 22 – UNIT 4: CHARACTERISTICS
1. Computers are machines designed to process, electronically, specially prepared
pieces of information which are termed data. Handling or manipulating the information
that has been given to the computer, in such ways as doing calculations, adding
information or making comparisons is called processing. Computers are made up of
millions of electronic devices capable of storing data or moving them, at enormous
speeds, through complex circuits with different functions.
2. All computers have several characteristics in common, regardless of make or
design. Information, in the form of instructions and data, is given to the machine, after
which the machine acts on it, and a result is then returned. The information presented
to the machine is the input; the internal manipulative operations, the processing; and
the result, the output. These three basic concepts of input, processing, and output occur

computer has no known limit on the kinds of things it can do; its versatility is limited
only by the imagination of those using it.
5. In the late 1950s and early 1960s when electronic computers of the kind in use
today were being developed, they were very expensive to own and run. Moreover,
their size and reliability were such that a large number of support personnel were
needed to keep the equipment operating. This has all changed now that computing
power has become portable, more compact, and cheaper.
6. In only a very short period of time, computers have greatly changed the way in
which many kinds of work are performed. Computers can remove many of the routine
and boring tasks from our lives, thereby leaving us with more time for interesting,
creative work. It goes without saying that computers have created whole new areas of
work that did not exist before their development.

EXERCISES

1. Main idea
Which statement or statements best express the main idea of the text? Why did you
eliminate the other choices?
_______ 1. Computers have changed the way in which we live.
_______ 2. All computers have an input, a processor, an output and a storage device.
_______ 3. Computers have decreased man’s workload.
_______ 4. All computers have the same basic hardware components.

2. Understanding the passage
Decide whether the following statements are true or false (T/F) by referring to the
information in the text. Then, make the necessary changes so that the false
statements become true.
________ 1. All information to be processed must be prepared in such a way that the
computer will understand it.
________ 2. Because of the complex electronic circuitry of a computer, data can be

1. which are termed data (paragraph. 1) ________________
2. or moving them (paragraph. 1) ________________
3. the machine acts on it (paragraph. 2) ________________
4. they are stored on (paragraph. 3) _________________
5. it is not a single-purpose machine (paragraph. 4) _________________
6. the kinds of things it can do (paragraph. 4) _________________
7. of those using it (paragraph. 4) _________________
8. they were very expensive to own (paragraph. 5) _________________
9. Moreover, their size and reliability (paragraph. 5) _________________
10. that did not exist (paragraph. 6) _________________

5. Understanding words
Refer back to the text and find synonyms (i.e. words with a similar meaning) for the
following words.
1. called _______________
2. tremendous _______________
3. ideas _______________
4. react _______________
5. take away _______________

Tieáng Anh 4 – Toaùn Tin - 25 – Now refer back to the text and find antonyms (i.e. words with an opposite meaning)
for the following words.
6. taken away _______________
7. wide _______________
8. limited _______________
9. immovable _______________
10. after _______________

b. If you don’t know the meaning of a computer term, you cannot always
__________ an all-purpose dictionary for the answer.
c. Computers can do mathematical operations quickly and ____________.