Grammar focus: Present Perfect and Past Simple

Present Perfect

Past Simple

Already Just Never Ever Yet Have/has + past participle ? Have/has - haven’t/hasn’t Use this tense for a past action where no specific time is mentioned or understood. Yes, I’ve just bought it. Have you ever seen this film? She has already done it. We haven’t paid the phone bill yet. He’s been to Berlin = He has visited Berlin and come back He’s gone to Berlin = He is in Berlin now Yesterday Last (day, week, year) Two days ago In 1945 V+ ed ? Did - didn’t Use the past simple, when a specific time in the past is mentioned or understood between the speakers We bought it last year. Yes, it arrived this morning

A Underline the correct form (Present Perfect/Past Simple).

Alex So, where shall we go for a conference devoted to modern trends in Algebra?
Lidia I don’t know exactly... There are some but in different places. Have you ever 1 been/gone to Kharkov?
Alex Yes, 2 I’ve been / I went there twice.
Lidia I didn’t know that. When 3) have you been/did you go there?
Alex The year after I 4 have finished /finished university.
Lidia What about Dnepropetrovsk?
Alex 5 I’ve already been / I already went there, too.
Lidia Yes? Who 6have you been / did you go with?
Alex With my colleague and friend Dima. But we only 7 have been/went to open the conference. Let’s go there.
Lidia No, let’s go somewhere else to participate in the conference and see some new sights...

B Complete the dialogues with the correct form of the verbs in brackets (past simple and present perfect).

A: 1 Have you taught (you / teach) Algebra abroad before, Mr Ben?

B: Yes, I 2_____ (teach) from 2001 to 2003 in Italy, and I 3____ (just / come back) from a six-month job in Moldova.

A: How long 4_____ (you / be) an Algebra teacher?

B: For eight years. Before that I 5_____(be) a state school teacher for two years.

A: Do you have any post-graduate qualifications?

B: I 6_____(start) a part-time MA at Donetsk National University a year ago, but I 7_____(not finish) it yet.

A: How long 8 _____ (you / be) married, John?

B: Ten years. Anna and I 9 _____ (have) our anniversary last month.

A: Where 10 ____ (you / meet) Anna? At work?

B: No, we 11 ____ (go) to the same school. We 12 _____ (know) each other since we were five years old. What about you?

A: I’m divorced. I 13 _____ (get) divorced last year.

B: How long 14 ____ (you / be) married?

A: Only three years.

B: So you’re on your own now?

A: Yes, but I 15 ____ (just / meet) someone new.

We’re going out this weekend.



Read the text and do the tasks below it.


Early in the 17th century it was suggested to simplify long computations by presenting all real positive numbers as powers of some particular number.

The exponents of these powers called logarithms, were arranged in tables and in accordance with the principles of exponents multiplication was replaced by addition, division by subtraction, involution by a single simple multiplication, and evolution by a single simple division.

The exponent of the power to which a fixed number (called a base) must be raised in order to produce a given number is called the logarithm of a given number.

Most logarithms are endless decimals. The integral part of a logarithm is called the characteristic, the fractional or decimal part – the mantissa.

The logarithm of the product of two or more numbers is equal to the sum of their logarithms.

Log (mn) = log m + log n

The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor.

Log (m/n) = log m – log n

Involution by logarithms. The logarithm of a number is equal to the logarithm of a number multiplied by the index of the power.

 = a log m

Evolution of logarithms. The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the required root.

Log  = (log m) / a


In pairs, look at the highlighted words and phrases. Try to guess what they mean from the context. Then check with your dictionary or teacher. Work out the list of the terms involved, make a kind of glossary.

2. In the text find the definition of:

a) Logarithms

b) the characteristic

c) the mantissa


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