December 2018 1 21 Report
Rozwiaz nierownosci:
a. (x^2-4)(x-3)>0
b. (x^2-9)(x+2)<0
c. (x-1)(x+3)(2-x)>0
d. (x-1)^2(x+1)^3(x-2)^4 mniejsze lub rowne od 0
e. (x^2-1)(x^2+x)(1-x) wieksze lub rowne od 0.
^2 oznacza 2 do potegi.
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1. ‘Whose is his house?’ ‘It is -_______ . A. our family B. our C. our one D. ours 2. How do you do? A. I’m fine, thanks B. How do you do? C. I do well. D. Hello, how are you 3. ‘Have you ever been to Scotland?’ yes, I ______ there last summer. A .have been B. went C. have gone D. was being 4. Last Sunday there were ______of people on the beach. A. one thousand B. thousands C. a great deal D. three thousands 5. Good afternoon sir. Can I help you? A. No, you can’t, thank you. B. Yes, I’m looking for a suit. C. Yes, you can very well. D. Yes, I’m looking a dress 6. A. How much is that radio? B. What do you want for that radio? C. How much costs that radio? D. What the price of that radio ? 7. I wanted ______the window. A.her to open B. that she open C. that she opened D. she to open 8. He asked her whether ______ London. A.she would like B. she liked C. had she liked D. if she liked 9. Joe didn’t tell us who ______ A.that poem was written by B. was that poem written by C. that poem was written D. that poem had written 10. Joe _______ the car- no one else has the key to the garage. A.must have taken B. must take C. had to take D. had to have taken 11. My wife has a _____ job at chemist’s. A.half-time B. spare-time C. part-time D. free-time 12. Mom won’t buy an ice cream ________. A.unless you are polite B. if you are polite C. unless you are impolite D. if you aren’t impolite 13. I’m too hot with this jacket on. A.Could I take it down? B. Can I put it off? C. Do you mind if I take it off? D. I’d like to put it away 14. I have passed my last exam. A. Many happy returns of the day. B. I’m happy for you. C. So what? D. It’s very kind of you. 15. Did you use to wear glasses at school? A. I got used to wear glasses. B. Yes, I did but I don’t now. C. Yes, I use to wear glasses at school. D. Yes, I wear glasses at school. 16_____ to your mother! A. Remind me B. Send my greeting C. Offer my respect D. Remember me 17. Do you know where………. ? A. did I put the keys B. put I the keys C. I put the keys D. I the keys put 18. How ___ is he? He is 1.85m. A. high B. short C. big D. tall 19. I like your hat, Jane. It really _____ you. A. passes B. suits C. shows D. matches 20. When you buy something you are usually given a _______. A. receipt B. bill C. recipe D. tip 21. When the fire broke out in the Louvre, at least twenty ______ paintings were destroyed . A. worthless B. valueless C. useless D. priceless 22. Mother was worried when she didn’t ___ Keith for a whole week. A. hear B. hear of C. hear from D. learn about 23. Andrew has a ____ in Music from Cambridge University. A. paper B. degree C. certificate D. mark 24. She wanted to complain about her boss, but she didn’t _____. A. risk B. courage C. dare D. attempt 25. A: ‘What is Peter like?’ A. A asks about Peter’s appearance. B. A doesn’t know what Peter likes. C. A doesn’t know what Peter wants. D. A doesn’t know how Peter is. 26. The children who knew French enjoyed the show. A. All the children knew French and that is why they enjoyed the show. B. Some children liked the show because they knew French- others didn’t C. Children don’t enjoy shows because they don’t know French D. None of these versions is correct 27. A:‘Am I ringing at a bed time?’ B: ‘Well, actually I’m just solving a maths problem. A. Although B is solving a maths problem now, B is happy that A is ringing B. It will be better if A rings some other time because B is solving a maths problem now C None of these versions is correct D. It is OK that A is ringing now because B is solving a maths problem now. 28. Shops do not usually close for lunch except in small towns. A. Shops never close for lunch in small towns. B. Shops are open at lunch time in small towns only. C. In big cities and small towns shops do not close for lunch. D. Shops rarely close for lunch in big cities. 29. A: ‘My soup is a bit salty.” B: ‘So is mine, I’m afraid.’ A. Both A and B like their soups because they aren’t too salty B. Both soups are too salty for A and B C. B thinks that his soup isn’t salty enough D. Neither A or B likes the soups because they aren’t salty enough 30. It took me twenty minutes by taxi to get to my room. A. Somebody took my taxi and I had to wait twenty minutes for the next one. B. There was no taxi, so I was in my room twenty minutes late. C. The ride lasted twenty minutes. D. I had to wait for the taxi in my room for twenty minutes. 31. He is called Ken for short. A. Ken calls him when he has little time. B. When we have a lot of time, we call him Ken. C. We call him Ken when we are short of time. D. Ken is the short version of his name and his friends can use it. 32. You really must have your house redecorated. A. I assume that you were obliged to redecorate your house. B. I assume that you redecorated your house yourself. C. Did you pay someone else to redecorate your house? D. It is my view that your house needs to be redecorated.
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Dlaczego -1 do potęgi 2015 wynosi -1 ?
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Jak obliczyć 10 do potęgi log5. Wynik to 5, ale nie rozumiem dlaczego.
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1. Jeżeli 0 stopni < alfa < 90 stopni oraz tg alfa= 2 sin alfa, to cos alfa ile się równa ? 2. Wyrażenie 3*sin^3 alfa*cos alfa + 3*sin alfa*cos^3 alfa może być przekształcony do postaci: a. 3 b. 3*sin alfa*cos alfa c. 3*sin^3 alfa*cos^3 alfa d. 6*sin^4 alfa*cos^4 alfa 3. Dla każdego kąta alfa, spełniającego warunek 0 stopni < alfa < 90 stopni, wyrażenie 2*sin*cos^2 alfa / 1+cos^2 alfa - cos^2 alfa jest równe: a. cos alfa b. sin alfa c. 2*sin alfa d. cos^2 alfa 4. Kąt alfa jest ostry oraz 3*sin alfa - pierwiastek z 3*cos alfa = 0. Wtedy ile równa się tg alfa.
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Odpowiedz na pytania po angielsku w minimum czterech zdaniach. 1. Describe the last time an illness spoilt your plans. 2. What advice could the pharmacist give the customer ? 3. Describe the last time when you had to do something despite being ill. 4. Do you believe in natural medicine ? Why ? Why not ?
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1. Ciąg (an) określony jest wzorem an= -2+12/n dla n≥1. Równość an= 4 zachodzi dla jakich n ? 2. Liczby 2,-1,-4 są trzema początkowymi wyrazami ciągu arytmetycznego (an), określonego dla liczb naturalnych n≥1. Jaki jest wzór ogólny tego ciągu ?
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Zadanie 9 w załączniku.
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Wartość wyrażenia: log na dole pięć u góry 0,04 - 1/2 log na dole 25 u góry 1 jest równa. Proszę o podanie wzorów do obliczania logarytmów.
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Zadanie 1. (2,5 pkt) Przeczytaj poniższy tekst. Uzupełnij luki 1.1.-1.5., przekształcając podane w nawiasie wyrazy w taki sposób, aby otrzymać logiczny i gramatycznie poprawny tekst. Wymagana jest pełna poprawność ortograficzna wpisywanych wyrazów. Za każdą poprawną odpowiedź otrzymasz 0,5 punktu. Easter Island is one of the world's most 1.1. ______________ (SPECTACLE) and enchanting archaeological sites. It is also one of the most remote places on earth - the nearest inhabited island is Pitcairn, which is over 1200 miles to the west. The island lies 1.2. ______________ (APPROXIMATE) 2500 miles off the coast of South America, and 2000 miles away from Tahiti, in the middle of the Pacific Ocean. It appears, that the original 1.3. ______________ (SETTLE) came from one of the islands of Polynesia, some time between 400-600 AD. They brought tools, food, plants and animals - with the apparent desire of beginning a new life. Perhaps they were a small clan that had fought with their neighbours and lost the 1.4. ______________ (DECIDE) battle. Perhaps they were explorers looking for their next 1.5. _______________________ (CONQUER). Or perhaps they were simply lost at sea - we'll probably never know. Transformacje Zadanie 2. (2,5pkt) Wykorzystując wyrazy podane w nawiasach, uzupełnij każde z poniższych zdań tak, aby zachować znaczenie zdania wyjściowego (2.1.-2.5.). Nie zmieniaj form wyrazów podanych w nawiasach. Wymagana jest pełna poprawność ortograficzna i gramatyczna wpisywanych fragmentów zdań. Za każdą poprawny odpowiedz otrzymasz 0,5 punktu. 2.1. I'm sure Tim didn't send that e-mail. (HAVE) Tim __________________________________ that e-mail. 2.2. Anne couldn't sing or dance. (UNABLE) Besides __________________________, Anne couldn't dance either. 2.3. Very few tickets are left, so book now! (HARDLY) Book now, because _________________________________ left! 2.4. Our house has been burgled twice this year. (HAD) We have _________________________________ twice this year. 2.5. Anne soon recovered from her cold. (LONG) It didn't __________________________________ from her cold.
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1. Brad Pitt is (tak znanym aktorem) ............. that even you must have heard about him. 2. I cannot undersatnd (dlaczego nam nie wolno) ................ to leave the building now. 3 Janice is not answering the phone; she (może pracuje) ................ in the garden. 4 Clive felt sick because he (zjadł za dużo) ........... chocolete. 5 Our plane (wystartował) .................. half an hour late because of the dense fog. 6 Mrs Davies did not insure her car, ( co ja kosztowało) ............. over 2000 in repair bills when she had an accident. 7 I hope that (wszyscy rozumieją) ............. the importance of security precautions. 8 Martha (nie mogła napisać) ............. this text; her English is not good enough. 9 It's a mystery (dlaczego on jest tak złym kierowcą) ................ after so many years behind the wheel. 10 Jeff's uncle suggested (żeby poszukał) ............ another place to practise the drums. 11 I'm planning to take up gardening when I (przejdę na emeryture) ................... 12 You'll have to read these books if you want to (przygotować się do) .................... your examination. 13 Martin was fined because he (zaparkował) ................ his car in the no-parking zone. 14 Sorry, all (te informacje są) .................... strictly confidential. 15 Here is my telephone numer (na wypadek, gdybyście) ................ need any more information. 16 How long (masz) .......... this wreck of a car > 17 This session is my toughest so far; I have an examination (co drugi dzień) ................ 18 But (gdyby nie pomoc przyjaciół) ......... Patrick would be in serious trouble. 19 I'd rather (żeby pan nie dzwonił do) ............... my daughter any more. 20 You offer sounds (bardzo interesująco) ................. 21 (Niepotrzebnie się martwiliście) .................. about Jimmie, he is all right. 22 They promised in the garage that the car (będzie gotowy) ......... after lunch, but when I came, they were still working on it. 23 What's wrong with Jane and Tommy ? They (nie rozmawiają ze sobą) ............ since yesterday. 24 I talked to the manager and he agreed to give me (wolny dzień)............. 25 Jordan suggested (żeby zaprosić) .................. all the children from the neighbourhood. 26 I can't find my gloves anywhere. I (może zostawiłam) ............ tchem in the office. 27 You'll get fired unless (zaczniesz ciężej pracować) ........... 28 The police blocked the main road, (co spowodowało) ............. serve traffic jams. 29 Someone (musiał zostawić) ....................... the front door unlocked last night. 30 Susan is very musican but (żaden z ) ............ her twin sons has any musical talent. 31 (Nigdy mnie nie potraktowano) ............. with such disrespect. 32 I have no idea (która była godzina) ................... when Sylvia called me. 33 Your mother's cake always (smakuje tak dobrze) .............. that I can't help eating too much. 34 (Im dłużej żyję, tym mniej) ............ patience I have for irrensponsible people.
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