- •Unit 1: Fractals
- •Identify the stressed sound in each word as in the example.
- •Put the following words into the corresponding column according to the sound of the adjective or regular past ‘ed’.
- •Organize the information from the text in the form of a mind map or a flow chart. For example, types properties
- •Fractals
- •Work in pairs and see if you can remember the following words and phrases. Take turns to ask each other. Use the Mini-dictionary (unit 1) if necessary.
- •In the text, find one example of the passive infinitive, five examples of verbs in the passive voice.
- •Explain the meaning of the words and phrases below.
- •Find the words in the text which match the following definitions.
- •Match the words and phrases (1-10) from the text with their definitions (a-j).
- •Fill the gaps in the sentences with the correct words from the text. The first letter has been given.
- •Fill the gaps with the words given below.
- •Find and cross out extra words in the text. There are 10 unnecessary words.
- •Match the words in the left-hand column with the words in the right-hand column to make phrases from the text. Use each word only once. Translate the collocations into Ukrainian.
- •Put the phrases and words in the correct order to make meaningful sentences. The first word of each sentence starts with the capital letter.
- •Fill in the gaps with a suitable preposition.
- •Work in pairs. Look through the applications if fractal analysis below and put them into the corresponding row of the chart.
- •Put the words in brackets into the correct form.
- •One of the underlined parts of a sentence contains a mistake. Find it and correct.
- •Rewrite the sentences using the passive voice where possible. Omit the agent where it can be omitted.
- •. Put the verbs in brackets into the correct passive form.
- •Fill in ‘by’ or ‘with’.
- •Help your friend to translate the following sentences into English.
- •Discuss the following questions in small groups or pairs.
- •Prepare a short two-minute presentation for your classmates on one of the topics below. You may use the information from the unit or do some research on the Internet.
- •Translate the following sentences into Ukrainian for your friend’s poster.
- •Using the information from this unit and further reading section write your own short wiki entry about fractals. (up to 200 words).
- •Do the quiz to find out how much you found out about fractals. (Problem-Solving, unit 1)
- •Fractals
- •Fractal patterns spotted in the quantum realm
- •Fractals in the biological sciences
- •The common prepositions in english.
- •Passive voice
The common prepositions in english.
about |
beneath |
in front of |
since |
above |
beside |
into |
till |
across |
besides |
near |
through |
after |
between |
next to |
to |
against |
beyond |
of |
towards |
along |
down |
off |
under |
among |
by |
on |
underneath |
around |
during |
onto |
until |
at |
except |
opposite |
up |
before |
for |
out of |
upon |
behind |
from |
over |
with |
below |
in |
past |
without |
Passive voice
The passive is formed with the appropriate form of the verb “to be” followed by the past participle form of the main verb. Only transitive verbs (verbs which take an object) can be put into the passive. Intransitive verbs, like cry, die, arrive, disappear, wait, which often describe physical behaviour, cannot be used in the passive voice. |
Verb form |
Construction |
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Present simple |
am/is/are + pp |
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Present continuous |
am/are/is being + pp |
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Present perfect simple |
has/have been + pp |
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Past simple |
was/were + pp |
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Past continuous |
was/were being + pp |
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Past perfect simple |
had been + pp |
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Future simple |
will be + pp |
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Future perfect simple |
will have been + pp |
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Infinitive |
(to) be + pp |
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TENSES |
ACTIVE VOICE |
PASSIVE VOICE |
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Present Simple Present Continuous Past Simple Past Continuous Future Simple Present Perfect Past Perfect Future Perfect Present Infinitive
Perfect Infinitive -ing form Perfect -ing form |
He gives lectures. He is giving a lecture. He gave a lecture. He was giving a lecture. He will give a lecture. He has given a lecture. He had given a lecture. He will have given a lecture. He should give a lecture. He is going to give a lecture. He should have given a lecture. She remembers him giving a lecture. Having given the lecture,... |
Lectures are given. A lecture is being given. A lecture was given. A lecture was being given. A lecture will be given. A lecture has been given. A lecture had been given. A lecture will have been given. A lecture should be given. A lecture is going to be given. A lecture should have been given. She remembers a lecture being given. The lecture having been given,... |
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• Get is used in colloquial English instead of be to express something happening by accident. She'll get killed if she goes on driving like that. |
THE PASSIVE IS USED |
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• when the person who performs the action (agent) is unknown, unimportant or obvious from the context |
It is significant to understand that this formula could not have been discovered without computers. (unimportant agent) |
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• to emphasise the agent |
Her wedding dress was delivered to her by the dressmaker herself yesterday. |
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• to make statements more formal or polite |
My dress has been ruined. (more polite than saying ‘You have ruined my dress’.) |
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• when we are more interested in the action than the agent, such as in news reports, formal notices, instructions, processes, headlines, advertisements etc. |
Bicycle frames are made of steel or a chrome/molybdenum alloy. |
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CHANGING FROM ACTIVE INTO PASSIVE |
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• The object of the active verb becomes the subject in the passive sentence. The active verb changes into a passive form and the subject of the active verb becomes the agent, which is either introduced with "by" or is omitted.
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• By + agent is used to say who or what did the action. The geometry of the fourth dimension - fractal geometry - was created almost singlehandedly by Mandelbrot. With + instrument /material is used to say what the agent used or after past participles such as coloured, crammed, crowded, filled, flavoured, packed etc. She was killed with a hammer. By + agent is omitted when the agent is unknown, unimportant, obvious from the context or referred to by words such as: someone, people, I, etc. They revealed the truth. – The truth was revealed. (‘by them’ is omitted) |
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• Verbs which take who objects (give, offer etc) form their passive in two ways; it is more usual to start the sentence with the person object, not the thing object. They offered Ann a bunch of flowers. – Ann was offered a bunch of flowers. (more usual than: A bunch of flowers was offered to Ann.) |
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• Verbs followed by a preposition (accuse of, take down etc) take the preposition immediately after them when turned into the passive. She took down the minutes of the meeting. – The minutes of the meeting were taken down. |
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• In passive questions with who, whom or which we do not omit by. Who gave you this information? – Who were you given this information by? |
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• Hear, help, make, see are followed by a to-infinitive in the passive. She made me work overtime. – I was made to work overtime. Note that hear, see, watch can be followed by a present participle in the active and passive. We saw her crying. – She was seen crying. |
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The verbs believe, expect, feel, hope, know, report, say, think etc are used in the following passive patterns in personal and impersonal constructions. |
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• subject (person) + passive verb + to –inf (personal construction) |
The police report that she is in France. She is reported to be in France. |
• it + passive verb + that-сlause (impersonal construction) |
It is reported that she is in France. |
Listening Script
UNIT 1
Some experiments have shown that looking at fractal patterns leads to the positive physiological changes in people. The experiments - which use eye-tracking equipment to examine how people look at the patterns, and quantitative electroencephalography (qEEG) and functional magnetic resonance imaging (fMRI) probing techniques to quantify the resulting brain activity - indicate that people are ‘hard-wired’ to respond to a specific form of fractal found in nature, one that reduces stress levels by up to 60%. This stress-reduction is triggered by a physiological resonance that occurs when the fractal structure of the eye matches that of the fractal image being viewed. The discovery that exposure to fractals automatically relaxes people holds crucial implications for society: the U.S. spends over $300 billion annually on stress-induced illnesses, and stress is increasingly blamed for disorders such as schizophrenia.
As society increasingly surrounds itself with urban landscapes, people risk disconnecting from this natural stress-reducer. Accordingly, researchers investigated people’s responses to paintings created by artists famous for capturing the essence of nature on their canvases. For example, the positive physiological responses of viewing Jackson Pollock’s poured paintings and Escher’s tessellations might explain their enduring popularity. The long-term goal is to collaborate with artists and architects to incorporate stress-reducing fractals into novel indoor and outdoor environments. These ‘biophilic’ fractals could be used in many applications, ranging from keeping astronauts calm on their long journeys into space to soothing anxious patients in dentist waiting rooms.