a) Cac tia nang mat troi tao voi mat dat mot goc xap xi bang 34 va bong cua mot thap tren mat dat
dai 86m Tinh chieu cao cua thap (lam tron den met) (trong hinh b)
b) Tinh chieu cao cua mot cot thap, biet rang luc mat troi o do cao 500 ( nghia la tia sang cua mat
troi tao voi phuong nam ngang cua mat dat mot goe bang 500) thi bong cua no tren mat dat dai
96m.

c) Mot cot den cao 7m co bong tren mat dat dai 4m. Hay tinh goc (lam tron den phut) ma tia sang
mat troi tao voi mat dat (goc a trong hinh c).
d) Mot khuc song rong khoang 250m. Mot chiec do cheo qua song bi dong nuoc day xien nen phai
cheo khoang 320m moi sang duoc bo ben kia. Hoi dong nuoc da day chiec do lech di mot goc bang
bao nhieu do? (góc a trong hinh d)

Chứng minh giá trị các biểu thức sau không phụ thuộc vào giá trị
của các góc nhọn α.
a) A = cos⁴α + 2cos²α . sin²α + sin⁴a

b) B = sin⁴α + cos²α . sin²α + cos²α

c) C = 2(sin α - cos α )² - (sin α + cos α )² + 6sin α . cos α

d) D = (tan α - cot α )² - (tan α + cot α )²

e) E = 4 cos² α + (sin α - cos α)² + (sin α+ cosα)² + 2(sin² α -cos² α)

f) F = \(\dfrac{1}{1+sin\text{α}}\)+\(\dfrac{1}{1-sin\text{α}}\)-2 tan²α

Rewrite the sentences below using the word(s) given

Question 1: Keep silent or you’ll wake the baby up.

→If............................................................................................................................................

Question 2: Stop talking or you won’t understand the lesson

→ If ..................................................................................................................................................

Question 3: I don’t know her number, so I don’t ring her up.

→ If ..................................................................................................................................................

Question 4: I don’t know the answer, so I can’t tell you.

→ If ..................................................................................................................................................

Question 5: We got lost because we didn’t have a map.

→ If ..................................................................................................................................................

Question 6: Susan felt sick because she ate four cream cakes.

→ Had ..............................................................................................................................................

Question 7: Without this treatment, the patient would have died.

→ Provided that ................................................................................................................................

Question 8: He lost his job because he was late every day.

→ Had it ...........................................................................................................................................

Question 9: Peter is fat because he eats so many chips.

→ Supposing that .............................................................................................................................

Question 10: Robert got a bad cough because he started smoking cigarettes.

→ But for ..........................................................................................................................................

Question 11: I'm sorry that I didn't finish my homework last night.

→ I wish ...........................................................................................................................................

Question 12: The child will die if nobody sends for a doctor.

→ Unless...........................................................................................................................................

Question 13: We didn't go because it rained.

→ If it hadn’t ....................................................................................................................................

Question 14: You may get hungry on the train, so take some sandwiches.

→ In ..................................................................................................................................................

Question 15: My husband didn't leave the car keys, so I couldn't pick him up at the station.

→ If my husband ..............................................................................................................................

Question 16: She didn't hurry, so she missed the train.

→ If ..................................................................................................................................................

Question 17: If the work is finished by lunchtime you can go home.

→ Get ...............................................................................................................................................

Question 18: It's a pity I didn't take my doctor's advice.

→ I wish ...........................................................................................................................................

Question 19: We didn't go on holiday because we did not have enough money.

→ If we .............................................................................................................................................

Question 20: You can't visit the USA unless you have a visa.

→ If you ..............................................................................................................................................        

Choose ONE suitable word in the box to complete each of the sentences below

case       even       long       on       only    otherwise   supposing       unless    

  whether             but      without           as         else      condition      provided      

Question 1: You should vote _______ if you don't know who to vote for.

Question 2: You can go on _______ that you come back before 10.

Question 3: The government had to reduce the tax or _______ there would have been a nationwide strike.

Question 4: I'll enter the competition _______ if you do it with me.

Question 5: It's my money, so I'm going to buy a new car _______ or not you agree with me.

Question 6: _______ I told you the truth, would you ever tell anyone?

Question 7: He would have arrived on time for the interview _____ for the traffic jam.

Question 8: It doesn't matter how slowly you go as _______ as you do not stop.

Question 9: You can print as many copies as you want _______ that they are intended for personal use

Question 10: I'll tell you _______ condition you don't tell anyone.

Question 11: The concert will be cancelled _______ we sell more tickets.

Question 12: I'll take some snacks in _______ we get hungry along the way.

Question 13: He prepared all the materials for the meeting last night. _______, he would have had to

come to the office early today.

Question 14: ________ the mercy of the landlord, he couldn’t stay in this house.

Question 15: So long _______ you work hard, the boss will increase your salary some day.

 Give the correct form of the verbs in the brackets to complete the sentences

Question 1: If you take my advice, you ________ (be) happy.

Question 2: What would you do if you ________ (be) me?

Question 3: If you ________ (lend) me some books, I will give them back in two weeks.

Question 4: I ________ (send) her a letter if I had found her address.

Question 5: She ________ (not/steal) the bread if she hadn't been hungry.

Question 6: If she ________ (come) here, I will tell her about the film.

Question 7: I will be unhappy if you ________ (leave) me.

Question 8: If you hadn't been so crazy, you ________ (not/buy) this expensive house.

Question 9: If the sun ________ (shine), I will go to the beach.

Question 10: If I ________ (win) the lottery, I would leave my country.

Question 11: If I see him, I ________ (give) him a gift.

Question 12: If I had a typewriter, I ________ (type) it myself.

Question 13: If I had known that you were in hospital, I ________ (visit) you.

Question 14: You could make better progress if you ________ (attend) class regularly.

Question 15: If I ________ (know) his telephone number, I’d give it to you.

Question 16: If you ________ (arrive) ten minutes earlier, you would have got a seat.

Question 17: If he worked more slowly, he ________ (not make) so many mistakes.

Question 18: I shouldn’t drink that wine if I ________ (be) you.

Question 19: If I __________ (find) a cheap room, I will stay a fortnight.

Question 20: A lot of people ________ (be) out of work if the factory closed down.