ENGLESKI – PREDAVANJA MATHEMATICS READING BASIC FORMULAE FORMULA (Sg) – FORMULAE/FORMULAS (Pl) BASIC MATHEMATICAL PROCESSES: Sign
Noun
Verb
+ (plus)
addition
add
- (minus)
subtraction
subtract
multiplication
multiply
division
divide
X (multiplied by/ times) 2 (divided by) 4
= (equals/is/ is equal to) TYPES OF BRACKETS
brackets
square brackets
curly brackets
LETTERS ABC – capital letters, ex. capital A, capital B, capital C. def – small letters, ex. small d, small e, small f. FRACTIONS 1 2
2
3
one half
1
two thirds
1
3 8
one third
1 one fourth 4
one eighth
3 three sixteenths 16
3
4
three fourths
READ OUT THESE FORMULAE 1.
X
2. x y
ab Capital X is equal to a plus b divided by c c A x plus y is capital A by a minus b a b
3. I a n 1d Capital I is a plus open brackets n minus one close brackets times d 4. V IR Capital V is capital I multiplied by capital R 5.
1 1 1 one by u plus one by v is equal to one by f / 1 over u plus 1 over v is equal to 1 over f u v f
6. v u at v equal u plus a times t 7. Ft mv mu Capital F times t is m multiplied by v minus m multiplied by u 8.
1 M 1 over capital R is minus captal M over capital E times l R El
9.
dQ q d times capital Q over d times z is minus q dz
1
ENGLESKI – PREDAVANJA 10. E T P c e capital E is capital T plus capital P minus c plus e MORE SYMBOLS AND VALUES:
x
2
x to the power of two ( x to two/ x squared)
3
x to the power of three (x to three/ x cubed)
n
x to the power of n (x to n)
x x
x
x
n 1
x to the power of n minus one
n
x to the power of minus n
x square root of x 3
x cube root of x
n
x
th
n
root of x
READ OUT THESE VALUES AND EQUATIONS:
20cms
1
98.3kms
twenty centimeters multiplied by s to the power of minus one 2
ninety eight point three kilometers multiplied by s to the power of minus two
3
thirty three centimeters to the power of three
33cm
2
four point thirty nine centimeters squared
4.39cm
31
nine point one times ten to the power of minus thirty one
9.1x10
x
x
1 2
x to the one half
3 4
x to three forths 2
a 1 b2
open brackets a plus b to the one half, close brackets, all that squared/squared/to the power of two
xy 3
square root of x multiplied by y
x a 2
cube root of open brackets x minus a to the power of two, close brackets
PRACTICE READING THESE EXPRESSIONS: 1.
2.
p
x x
p/q
1
x
q
x to the power of minus p is equal one over x to the power of p
p
x
p
x to the power of p over q is qth root of x to the power of p
2
ENGLESKI – PREDAVANJA 3.
x a x ax a 2
2
x squared minus a to two equal open brackets x plus a, close brackets multiplied by open brackets x minus a, close brackets
4. y ae
kx
5. x
y is equal to a times e to the power of k times x
nx mx 1
x is equal to open brackets n multiplied by x subscript 1 plus m multiplied by x
2
mn
subscript 2, close brackets over m plus n
6. y y y 2 2 1
x
y x x x 1 1
1
y minus capital y subscript 1 is equal open brackets capital y subscript 2 over capital x squared minus capital y subscript 1 over capital x to the power of 1 close brackets, multiplied by open brackets x minus capital x subscript 1
2
x y z a b c 2
7.
2
2
2 2
x to two over a to two plus y to two over b to two plus z to two over c to two is 1
1
y1 y2 z1Z 2
8. d x x 2 1 2
2
2
1
d equal square root of open square brackets, open brackets x
subscript 1 minus x subscript 2 close brackets to the power of two plus open brackets y subscript 1 minus y subscript 2 close brackets to the power of two plus open brackets z subscript 1 minus z subscript 2 close brackets to the power of two close square brakcets 9.
b a 1 e 2
2
2
x y
10.
2
2
b to two is a to two multiplied by open brackets 1 minus e to two close brackets
2 gx 2 fy c 0
x to two plus y to two plus 2 times g times x plus 2 times f times y plus c is 0 GEOMETRY
DIMENSIONS: NOUN
ADJECTIVE
height
high
width
wide
length
long
depth
deep
thickness
thick
ASKING ABOUT DIMENSIONS:
1
-
How high/wide/long is object A?
-
-
What is the height/width/length of object A? -
Object A is 5cm high/wide/long. The height/width/length of object A is 5cm.
-
Object A is 5cm in height/width/length.
-
Object A has a height/width/length of 5cm.
moguc primer na ispitu – OBRATITI PAZNJU!!!!!!
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ENGLESKI – PREDAVANJA SHAPES AND BODIES: NOUN
ADJECTIVE
square
square
rectangle
rectangular
triangle
triangular
circle
round/circular
semi-circle
semi-circular
oval
ovular
cube
cubic
prism
prismatic
pyramid
pyramidal
ball/sphere
spherical
hemisphere
hemispherical
cone
conical
cylinder
cylindrical
exemple: 1. The are circular pins for live and neutral. 2. The slot has got a flat base with one side rounded over to form a semi-circle. 3. This one has rectangular blades for live, neutral and earth. 4. It has a cylindrical slot to receive the earth pin. 5. The pins are arranged in linear configuration. 6. They`re laid out in triangular conficuration. DESCRIPTION (TALKING) what are you talking about, what shape is it, what king of material is used to manufacture.... I will now tell you (describe) about shape of....., material of..... STRUCTURING DESCRIPTIONS -
Starting what object is being described
-
Starting what are the segments of the description
-
Describing shape, dimensions, material
-
Explaining the use and functioning of the object h – external, inner
circular
d – internal, outer
diameter radius circumference (obim kruga)
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ENGLESKI – PREDAVANJA -
A is a solid wooden block 5cm high, 10cm long and 4cm width.
-
A is a solid wooden block. It has a height of 5cm, a length of 10cm and a width of 4cm.
-
A is a solid wooden block having a height of 5cm, a length od 10cm and a width of 4cm.
disk, cylinder, coinlike, round plate.. This is a round plate, made of plastic, which has a height of 0.25cm and the radius of 20cm hollow, shallow, empty inside.... This is a hollow cylinder, made of copper, which has a length of 0.75cm, inner diameter of 0.08m and outer diameter of 0.02m. DESCRIPTION OF LINES AND ANGLES
vertical
horizontal
sharp/acute
normal/perpendicular
rightangle
obtuse
parallel
90 reflex angle 180 outer
DESCRIPTION OF TRIANGLES
equalsided/equilateral
obtuse
rightangle
diagonal line
isosceles(jednakokraki)
crossing(common)/intersecting(scientific, formal)
axis(Sg) of symmetry/axes(Pl)
DIAGRAMS (BLOCK DIAGRAMS AN CIRCUITS) description definition:
This is a....
components:
It consists of... It comprises... It is made of... It is compriset of.... It is assembled of... Its part are (the following) Its constituent elements/parts are 5
ENGLESKI – PREDAVANJA connections between components: ...is/are connected with/to ...is/are linked to in series in parallel the function of each component:
is used for... is used to... the function of.... is to...
*names of block diagrams* A – arial, antenna
L1 – inductor
C1 – variable capacitor
E – earth
D1 – diode
C2 – capacitor
R1,2,3 – resistor
IC,2 – operational amplifer
C3 – potentiometer
Q1 – transistor NPN
Q2 – transistor PNP
LS1 – loud speaker
OV – supply rail exemples: This is a block diagram of a radio. It consists of an arial... They are connected in series. The antenna is used to receive signals. The function of the tuner is t adjust the frequency of waves. Detector then detects useful signals. AF amplifies the signals. After that, the volume control adjust the amplitude of the basic signals. Finally, the signal is sent to the loud speaker systems, which converts the signal from electrical into mechanical waves. PROCESS DESCRIPTION sequence words:
first/firstly, second/secondly, the first step, next, following, that, afterwords, further on, in the end, finally...
VALUES: I have a five dollar bill. There are four star hotels It is a 47kΩ resistor Two 47kΩ resistors contour (kontura) SENTENCES RELATIVE PROUNOUNS FOR DEFINING SENTENCE: Who – for people Which – for thingd Whose – for people anda things (oznacava priadnost) Which – addicional information about the subject or the object To – reason why something is done
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ENGLESKI – PREDAVANJA PARAGRAPH (ANALYTICAL PARAGRAPH) The basic structural unit of both written and spoken formats Nucleus piece of thinking, convevs one idea and explains it -Structuce of paragraph- topic sencence (defining sentence) - syppirting sentences - closing sentence 1. (definition), 2., 3., 4. (supporting sentences), 5. (closing sentence) DEFINING SENTENCE The basic kind of tehnical definitions relies on the premise of Aristotelian logic, namely, A=B+specific characteristics. In this kind of defining, start with naming the subject, then state the class to which it belongs then specify the main distingvushing feartures of the subject. The subject + general classification + its specific characteristics that differentiate it from the rest of the general class. Exemple1: A
=
A generator is a device that transforms mechanical into electrical energy. B
My concept
+
specific
{= je is u recenici
+ je that u recenici}
categorization
Topic
logic group Exemple2:
An OS is a kind of software that belongs to the group of system software that is used to integrate the basic function that enable both the development and execution software. A generator is a device that transforms mechanical into electrical energy. Concept in question – generator General class that belongs – device Specific characteristics – it transforms mechanical into electrical energy Use the PRESENT SIMPLE TENSE Use the UNDEFINITE ARTICLE A/AN USEFUL PHRASES Is/are
Can/be defined as
Can/be called as
.....known as
.....refered to as
.....used to
Can/be termed as
Have/exhibit/display/show the capacity to/the property of SUPPORTING SENTENCE Supporting sentences are at least two sentences that come after the paragraph opening sentence. They can be elaborations on constituent parts or functions of the device or item in question, defined in the first sentence. The supporting sentences present facts, details, examples of the concept that the paragraph is about.
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ENGLESKI – PREDAVANJA CLOSING SENTENCE Closing sentence summarizes the idea of the defining sentence by simply restating it, and if possible gives an example of the use of the concept. Exemple from the class – all students A cell phone is a device which is used to communicate. It consists of a display, mask, battery, keyboard, circuit board, SIM card. The display is used for us to watch information. The mask protects the internal parts and makes the phone more beautiful. The battery provides energy. The keyboard allows us to input information. Circuit board sontain radio, antenna, and a processing unit. SIM card is a stand-alone component that holds user`s identification. Cell phone is a practical, handheld device for communication. IF CLAUSES – CONDITIONAL CLAUSES A sentence structure that has an economy of meaning. Frequently used in science. Expresses the degree of probability that something will happen. Contains two sentences: If – clause expressing condition The main clause expressing possible result. There are three basic types: first, second, third. There is also Zero Conditional, a subtype of the First Type. There are also mixed types. ZERO CONDITIONAL If you heat water up to 100 degrees C, it boils. If + Present Simple + Present Simple. The meaning - If the condition is fulfilled, the probability that the outcome will happen is 100%. - used for scientific, natural facts. (There is no chance that if the condition is fulfilled something else other than stated happens.) FIRST CONDITIONAL If you manage to complete the experiment, you will get the better mark. If + Present Simple + Future Simple The meaning – If the condition is fulfilled, the probability that the outcome will happen is highly probable, about 90%. (If the condition is fulfilled, the predicted result will surely happen.) SECOND CONDITIONAL If the scientists could see an atom, they would know more about it. If + Past Simple + would The meaning – this is a present situation, and in the present the situation is completely impossible. Yet, the future is open. (The scientists cannot see an atom now, maybe in the future they will.) 8
ENGLESKI – PREDAVANJA THIRD CONDITIONAL If the scientists had known about this solution earlier, they would have solved the problem by now. If + Past Perfect + (would + have + Past Participle) The meaning - this is a past situation, so the entire situation is definitely impossible. This is a kind of guessing what would be if the past was different. (The scientists did not know, and nothing can be changed.) IF CLAUSES - PRACTICE 1. block of ice/heat/above 0ºC/melt → If you heat the block of ice above 0 degrees C it melts. /zero 2. north pole/magnet/bring near/south pole/another magnet/poles/attract/each other → If you bring near north pole of the magnet to the south pole of another magnet they will attract each other poles /first 3. end of copper bar/heat/heat/travel/along/bar → If you heat one end of the copper bar the heat will travel along the bar. /first 4. electric current/pass/along/conductor/conductor/become/hot → If electric current passes along the conductor, the conductor will become hot. /first 5. tensile force/ apply/ metal wire/ length/ increase → If you apply tensile force to the metal wire, the length will increase. /first 6. rectangular metal block/ heat/ volume / increase → If you heat rectangular metal block, its volume will increase. /first 7. liquid/heat/it change/ to a gas → If you heat liquid it changes to a gas. /zero 8. gas/ cool/ it change/ to a liquid → If you cool gas it changes to a liquid. /zero 9. current /pass/ through a wire/ it set up/ a magnetic field around the wire → If current passes throught a wire it sets up a magnetic field around the wire. / first 10. force apply/ to a body/ there be/ an equal and opposite reaction → If you apply force to a body there is equal and opposite reaction. /zero 11. wire cut/ a magnetic field/ it /transmit/ equally throughout the fluid → If you cut a wire in a magnetic field it transmits equally throughout the fluid. /zero PASSIVE VOICE IBM makes computers.
- active sentence
Computers are made by IBM.
- passive sentence
Subject
Verb Object
Object of the active sentence becomes subject of the passive sencence Verb is split into TO BE + PAST PARTICIPLE 9
ENGLESKI – PREDAVANJA TO BE (number and tense) /* singular/plural, is/are, was/were*/ PAST PARTICIPLE (meaning) /* -ed (regular verbs), III column (irregular verbs) Exemple: They make(write) programs.
Programs are made(written) by them.
PASSIVE THROUGH TENSES (USEFUL FOR ENGINEERS) Make is/are made Is/are making is/are being made Made was/were made Was/were made was/were being made Will make will be made Can make can be made Exemple: 1.
Each instrument is recorded (record) using a microphone. The sound is fed (feed) to a mixing desk.
The recording level is controlled (contol) and the EQ is adjusted (adjust) by the sound engineer. The output is recorded (record) on a multitrack. The sounds from the multitrack are mastered (masters) back through the mixer. The tape is remixed (remix) until the musicians are happy with the sound. Special effects can be added (add) on the mixing desk. The remixed tape is mastered down (masters down) to produce a master tape. This can be used (use) to produce copies in many different formats. 2.
Microprocessors (make) are/are being made of silicon.
3.
Call centres (use) are used to deal with telephone enquiries.
4.
In recent years, most mobile phones (equip) are/have being equipped with Bluetooth.
5.
GPS (develop) was developed in 1970s as a military navigation system.
6.
Sorry about the mes – the computer (replace) is being replaced at the moment.
7.
In the near future, the Internet (access) will be accessed more frequently from PDAs and mobile
phones than from desktop computers. 8.
I had to use my laptop this morning while my PC (fix) is being fixed.
Questions in passive voice: Programs are made by them.
Are programs made by them?
Where/why/how are programs made?
DESCRIBING GRAPH TRENDS Curve – kriva Verb +
adverb
Increase steadly
Climb
slightly
Rise
Go up
gradually
Decline sharply
steeply
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ENGLESKI – PREDAVANJA Dip
suddenly
Steadly
dip
Drop
fast
Sudden
drop
Fall
quickly
Fast
fall
Go down gradually Adjective + noun Slight
increase
Gradual
rise
The curve climbs slightly.
There is a slight increase of the curve.
READING GRAPHS -
identify the graph
-
read the coordinates
-
identify the various curves
-
read each curbe exemple:
This is a graph that shows.... The vertical axis represents.... The horizontal one stands for.... There are ..... curves that indicate..... The first curve shows....
The first quadrant shows the characteristics of the diode when it is a forward biased. When the voltage is increased, at first the current doesn`t flow. When the voltage reaches about 600mV there is a slight increase of a current. The current countinues to rise as the voltage increases but eventually a point is reached when the diode would be destroyed by heat.The third qaudrante shows what happens when the diode is reversed biased. There is almost no voltage. The diode is therefore a good rectifier. It conducts in one direction and almost not at all in the other.
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ENGLESKI – PREDAVANJA However, there is high leakage of reverse current. This leakage current is flowing until what is known as breakdown voltage. At this point there is sudden rise in reverse current. This sudden increase is called the Zener effect. Exemple: This graph shows the trends on the sales of music formats. Some of these formats are outdated, and the graph shows the apperence and rise of new one. The sample was taken in UK. The vertical coordinate shows number of sold cipoes in millions. The horizontal one presents the time observe. There are four curves , one for LPs, the other for singles, the third of cassettes, the forth for CDs. The trend of singles: in the year from 1983 to 1984 there is a slight increase of sales, from about 76 to 78 million copies. After that, there is a period from 1984 to 1988 of a steady decline to aproximatly 60 million copies. ARTICLES a/an
the
kada se pominje prvi put koristi se a, svaki sledeci put kada se pominje isto the kada je nesto generalno (uopsteno) nema clan odredjeno neodredjeno
a/an
one original of a/an just exemple: A book – singular
The book is very nice.
Books – plural
The books are very nice.
a/an
the
one
particular
just any
defined
unknown
exact
unintruduced
known
exemple: A controller is a device. – representative of a class (predstavnik vrste) exersize: Linux is an operating system and it was initially created as a hobby by a young student, Linus Torvalds. Version 1.0 of the Linux Kernel was released in 1994. The Kernel, at the heart of all linux systems is developed and its source code is freely available to everyone. Apart from the fact that it`s freely distributed, ϕ Linux`s functionality, adaptability and robustness has made it the main operating systems. More than a decade after its initial release, Linux is being adopted worldwide, primarily as a server platform. This operating system can also be incorporated directly into ϕ microchips in a process called ϕ embedding.
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ENGLESKI – PREDAVANJA COLLOCATIONS A collocation is a pair of words that are often used together. receive, transmit, demodulate SIGNAL distribute, compress, stream, decode, playback, watch, copy, protect CONTENT CONTENT provider, maker exersize 1. A lot of content makers are concerned that their programs are being copied illegally. 2. It is important for a national broadcaster to be able to transmite signal to every part of the country. 3. MPEG techniques make it possible to distribute content into much smaller files. 4. A PC media player can decode the content in MPEG, wmv and MP3 files. 5. Digital rights management allows film makers to protect content to a certain extent. 6. Most TV viewers still need an aerial pointing in the right direction to receive sihnal from the national broadcaster. 7. A CRT creates images from the demodulate signal it receives from the antenna. 8. As broadband capacities have increased, it has become easier to distribute content across networks in IP packets. VERBS ALLOW/PREVENT allow
prevent
allow to work
prevent from working
exemples: 1.
. … there’s a setting on the GPS that allows/prevents it to detect the movement.
2.
. … an alarm sounds to warn you, and allows/prevents the boat from drifting unnoticed.
3.
. … and enables/ensures that you don’t lose track of where you were, which then enables/ensures you
to turn round and come back to the same point. The core function of your GPS receiver is to allow you to locate your precise geographical position. To enable the device to function, it receives at least three signals simultaneously from the GPS constellation – 30 dedicated satellites which allows receivers to function anywhere on earth. To enable extremely precise positioning and prevent errors from occurring due to external factors, this device is designed to receive four separate signals (enhanced system accuracy). TENSES AND COMPARISON 1. Digital radio sets are becoming (become) less and less popular. 2. More and more people are listening (listen) to radio over the Internet. 3. Laptops are getting cheaper (cheap). 4. Handheld devices are becoming more sophisticated (sophisticated). 5. Battery life is getting (get) longer (long). 6. In some areas, VoIP is talking (take over) from PSTN. 7. Mobile broadband speeds are increasing (increase) dramatically. 13
ENGLESKI – PREDAVANJA TENSES1: Abraham Graham Bell invented the telephone in 1878. He was a Canadian whose family immigrated/was/originated/came from Scotland. Since then, telephone systems increased/have improved dramatically, in the UK alone there are how over 24 million lines. Formerly. the UK system was analogue. Many changes were made/have appeared/have happened in recent years. Almost the entire UK netwoek is now digital. Fibre optic cables are replacing/have replaced/exchange/inherited the old copper lines. Previosly, telephone exchanges were using/used banks of electromagnetic relays from switching. Today, they are computer-contolled units. The new network is fast and reliable, allowing users access to many other communications services. TENSES2: Many changes were made in telephone design in recent years. Formerly, telephones _____________ rotary dials. A pulse _______________ each dialed number. Now, push-button is used for dials. Each button has a different audiofrequency tone. This is called/is known as multi-frequency dialing. Also, the bandset ______________. Old models had carbon microphones, which ________________ inexpensive and robust but noisy. Today moving-coil and electrical devices replaced the old microphones. Advances in tehnology _______ additional features to be added to phones. Most now _______________ memories to store frequently used numbers. Some telephone manufactures screens using LCDs which allow users to see latest dialed number and shows the duration of calls. MAKING COMPARISONS 1. The term ‘processor’ as the same meaning/is the same as (the same) the CPU. 2. Laptops are as powerful (the same) as microcomputers. 3. Some companies use the same disks as conventional filling systems for storing data. 4. A computer virus is similar to/like a virus in human body. 5. Many word-processing programs are similar in that they share certain common functions. 6. A mainframe is more powerful and more expensive (expensive) than a microcomputer. 7. Learning to use a computer is less/more difficult than learning to program. 8. A fax board costs as much as/the same as/less than/not as much as a fax machine. 9. Unlike factory-sealed software, pirated versions may contain viruses. 10. Desktop publishing is a form of electronic publishing. COLLOCATIONS exersize: Macth one word on the left with a partner on the right. 1. high definition
a) Internet radio
2. read and write
b) disc
3. play
c) videos and music
4. tune in to
d) television
5. broadband
e) data
6. optical
f) your favourite sites 14
ENGLESKI – PREDAVANJA 7. browse
g) compatible
8. fully backward
h) access
1-d; 2-e; 3-c; 4-a; 5-h; 6-b; 7-f; 8-g exersize: -
I have a program that monitors both incoming and outcoming mail and also blocks spam.
-
With a webcam you can add video to online chats and instant messaging. Simply instal the software
included, plug the webcam in your PC, and start having video conferences. -
This software enables you to burn CD and DVDs containing any data files.
-
I use a media player to stream audio and video files from the Web; I can play them directly.
-
This program allows us to perform video conferencing in real time, without any delay.
-
We have decided to make the material publicly/widely/freerly available on the Web.
-
I often log on to my Internet bank account to make payments; I never forget to log off.
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