Bài Tập Hình Học Không Gian Lớp 11 Học Kì 1

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Quy tắc nhân vecto với 1 số

Cho vecto a và số thực k 0 ta được vecto $\overrightarrow{A}$ và số thực $k\neq 0$ ta được vecto $\overrightarrow{ka}$ có các tính chất sau:

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Vecto trong không gian là gì?

Một đoạn thẳng có hướng được gọi là vecto trong không gian với kí hiệu $\overrightarrow{AB}$, điểm A là điểm đầu, điểm B là điểm cuối.

Cho hình bình hành ABCD thì ta có:

$\overrightarrow{AC}=\overrightarrow{AB}+\overrightarrow{AD}$

2.2. Quy tắc 3 điểm đối với phép cộng vecto

Khi có 3 điểm A, B, C bất kì thì:

$\overrightarrow{AC}=\overrightarrow{AB}+\overrightarrow{BC}$

Hoặc $\overrightarrow{AC}=\overrightarrow{BC}+\overrightarrow{AB}$

$\overrightarrow{AB}+\overrightarrow{AD}+\overrightarrow{AA'}=\overrightarrow{AC'}$

Sự đồng phẳng của các vecto, điều kiện để ba vecto đồng phẳng

Vecto được gọi là đồng phẳng nếu trong không gian các giá của chúng song song với cùng một mặt phẳng.

Vecto c =k. Vecto a + l. Vecto b

Bài tập vận dụng về vectơ trong không gian lớp 11 (có lời giải)

Có hình lăng trụ ABC.A’B’C’, chỉ ra các vecto bằng nhau và có điểm đầu và điểm cuối là đỉnh của hình lăng trụ.

Áp dụng tính chất của hình lăng trụ, ta sẽ có:

Cho hình chóp S.ABCD, đáy ABCD là hình bình hành. Hãy chứng minh:

$\overrightarrow{SA}+\overrightarrow{SC}=\overrightarrow{SB}+\overrightarrow{SD}$

Bài giải: Khi O là tâm của hình bình hành ABCD ta sẽ có:

Tứ diện ABCD. Trên AD có M vecto AM = 3. Vecto MD. N trên BC sao cho vecto NB= -3. Vecto NC. CM: vecto AB, DC, MN đồng phẳng

Cho hình hộp ABCD.A’B’C’D, hãy chứng minh:

Có tứ diện ABCD. Gọi G là trọng tâm tam giác ABC.

$\overrightarrow{DA}+\overrightarrow{DB}+\overrightarrow{DC}=3\overrightarrow{DG}$

Áp dụng quy tắc 3 điểm ta có

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Bài tập trắc nghiệm vectơ trong không gian lớp 11 (có đáp án)

4 điểm A, B, C, D không thẳng hàng trong không gian O. Khi nào A, B, C, D có đầy đủ điều kiện để cấu thành nên hình bình hành?

S. ABCD, vecto SA= vecto a, vecto SB= vecto b, vecto SC= vecto c, vecto SD = vecto d

A. Vecto a +vectp c = Vecto b + Vecto d

B. Vecto a + Vecto b = Vecto c + Vecto d

C. Vecto a + Vecto d = Vecto b + Vecto c

D. Vecto a + Vecto b + Vecto c + Vecto d

Cho tứ diện ABCD, định nghĩa G là trọng tâm tứ diện ABCD khi:

$\overrightarrow{GA}+\overrightarrow{GB}+\overrightarrow{GC}+\overrightarrow{GD}=\overrightarrow{0}$

Khi đó khẳng định nào dưới đây là sai?

A. Trung điểm của IJ với I là trung điểm của AB và J là trung điểm của CD, giao nhau là G.

B. Đoạn thẳng nối trung điểm của AC và BD là G.

C. Trung điểm của AC và BD là G.

Câu 7: Ba vecto $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$, không đồng phẳng nếu?

A. Ba đường thẳng chứa vecto không cùng 1 mặt phẳng

B. Ba đường thẳng chứa chúng thuộc cùng 1 mặt phẳng

C. Ba đường thẳng chứa không cùng song song một mặt phẳng

D. Ba đường thẳng chứa vecto không cùng song song một mặt phẳng

Có tứ diện ABCD với trung điểm AB và CD là trung điểm của E và E. Có AB = 2a, CD = 2b, EF = 2c. M là điểm bất kỳ. Vậy MA2+MB2 là

Tọa độ điểm và vector trong không gian là những dạng toán quan trọng trong chương trình toán học THPT. Vì vậy bài giảng video dưới đây thầy Phạm Anh Tài sẽ cung cấp cho các em đầy đủ kiến thức về phần hình oxyz - Tọa độ điểm và vector, giải một số vì dụ và bài tập một cách chi tiết và dễ hiểu nhất để các em tự tin khi gặp dạng bài này.

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Trên đây toàn bộ kiến thức về vecto trong không gian thuộc chương trình Toán lớp 11 mà VUIHOC chia sẻ với các bạn học sinh. Hy vọng rằng, sau bài viết này, các em học sinh đã có thể nắm vững kiến thức về dạng bài vecto trong không gian và luyện tập một cách thuần thục. Để có thêm các thông tin bổ ích, các em hãy truy cập Vuihoc.vn nhé!

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Bài tập Tiếng Anh lớp 5 Học kì 1 có đáp án

Bài tập Tiếng Anh Unit 6, 7, 8, 9, 10 lớp 5

Bài tập Tiếng Anh lớp 5 Unit 6: How many lessons do you have today? (có đáp án)

Bài tập Tiếng Anh lớp 5 Unit 7: How do you learn English? (có đáp án)

Bài tập Tiếng Anh lớp 5 Unit 8: What are you reading? (có đáp án)

Bài tập Tiếng Anh lớp 5 Unit 9: What did you see at the zoo? (có đáp án)

Bài tập Tiếng Anh lớp 5 Unit 10: When will Sports Day be? (có đáp án)

Đề ôn luyện Tiếng Anh lớp 5 Học kì 1

PART 1. LISTENING (2.5p)Question 1. Listen and number. (0.5 p)

Question 2. Listen and tick. (1.0 p)

Question 3. Listen and circle. (1.0 p)

PART 2. READING AND WRITING (5.0 p)

Question 4. Read the text carefully. Tick (a) True or False.(1,25 pt)

Tom likes reading. On Sunday, he often stays at home and reads comic books. He like Case Closes very much. It is a Japanese story. The main character is a schoolboy called Jimmy Kudu. He often helps the police. He is good at his job. Jimmy Kudu is Tom’s favourite character because he is clever and brave.

1. Tom likes reading books in his free time

2.Case Closed is a Malaysian story.

3.The main character is Jimmy Kudo

5.Jimmy Kudu is clever and brave

Question 5. Fill in each gap with a suitable word from the box ( 1,25 pt ) .

friendly Science favourite week school

It is Wednesday today . Trung is at Hung Duong Primary(1)……….…. . . He has four lessons : Vietnamese , Maths , English and (2) …………………..Trung has English four times a (3)………………. Miss Hien is his English teacher . She is a kind and (4) …………….teacher . English is one of Trung’s (5)………………..subjects because he loves reading English short stories and comic books . Trung also likes chatting online with his foreign friends like Akiko , Tony , Linda and Peter .

Question 6. Fill in the blank with a suitable letter(0.5)

Question 7. Put the letters in the correct order to make correct words.(1pt)

Question 8. Reorder the words to make sentences .(1 pt)

1. pandas /saw/ two /at /the /She /zoo/.

…………………………………………………………………………..………………..

2. I /times /have /a /English /four /week/……………………………………….……………………………………………………….

3.are /the /your/ zoo /favourite/ animals/ What/ at/?……………………………………………………….............................................................

4.We/ learn/ friends /talk /English/ our /because /we/ to /with/ want/ foreign.

………………………………………………………………………………………………..

Question 1. Listen and number. (0.5 p)

Question 2. Listen and tick. (1.0 p)

Question 3. Listen and circle. (1.0 p)1 - a;

Question 4. Read the text carefully. Tick (a) True or False.(1,25 pt)

Question 5. Fill in each gap with a suitable word from the box ( 1,25 pt ) .

Question 6. Fill in the blank with a suitable letter(0.5)

Part 1. Listening (5 points ) ( 20 minutes )

Question 1. Listen and tick (1point)

Question 2. Listen and circle A,B or C (1point)

2. Mai learns English by ……………

3. Nam learns English by ……………

A. writing emails to his friends

B. talking with foreign friends

4. We learn English because we want to ……………

B. talking with foreign friends

C. writing emails to his friends

Question 3. Listen and number (1point)

Question 4: Listen and write T(True) or F(False): ( 1 point )

PART 2: READING AND WRITING(4 points ) (15 minutes)

Question 5. Look and read. Put a tick (P) or a cross (x) . (1p)

Question 6. Read and choose A, B or C (1point)

My name’s Tuan. I’m in class 5B, Quang Trung Primary School. My school year started in August. I go to school every day except Saturday and Sunday. I have four lessons a day. Today is Thursday. I have Maths, Vietnamese, Music and English. I have Maths and Vietnamese every schoolday. I have Music once a week and English four times a week. My favourite subject at school is English.

1. Tuan’s shool started in……….

2. He has Maths, Vietnamese, Music and English on ……...

3. He has Vietnamese and ………… every schoolday.

Question 7. Look and read. Put a tick (P) True or False (1point)

There are some events in Tim’s school every year. He is going to take part in the school music festival next month. Tim and his classmates are practising hard for this event. He’s going to play the violin. Lisa and Linda are going to play the pianos. Bill is going to play the drums. Some girls and boys are going to sing English songs. The school music festival is really an interesting event.

Question 8. Choose a word from the box and fill in the blanks (1point)

Last Sunday, my class went to the zoo. It was a sunny day. We saw a lot of wild (0) animals. Big tigers (1)________ loudly. A baby elephant (2)________ water with its trunk. It looked happy. Three (3) ________ were so noisy on the tree. The (4) ________ moved so quietly. In the end, we had a lot of fun at the penguin show. It was a great trip to the zoo.

Question 9: Reorder the words to make the sentences. (1 point)

saw/ I/ tigers/ two/ the/ at the zoo.

2. writes/ and/ new words/ He/ them aloud/ reads

3. I think/ visit/ I’ll/ tomorrow/ the moutains

4. went to/ I / yesterday/ Mai’s / party/ birthday

5. you/ Where/ go/ did/ on holiday?

PART 3: SPEAKING (1 point ) ( 5 minutes )

PART 1: LISTENING ( 20 minutes)

Total: 40 questions = 10 marks →Each right question is given 0,25 mark.

Question 1 : Listen and tick (1point) ( Track 24)

Question 2. Listen and circle A,B or C (1point) ( Track 20)

Question 3. Listen and number (1point) ( Track 53)

Question 4: Listen and write T(True) or F(False): ( 1 point ) ( Track 8)

1. She can talk with Tom and Linda in English.

2. Her foreign friends sometimes can’t understand her.

3. She can’t sing English songs.

4. She wants to be an English teacher.

PART II: READING AND WRITING (15 minutes)

Questions 5: Look and read. Put a tick (√) or a cross (x) in the box: ( 1point)

Question 6. Read and choose A, B or C (1point)

Question 7. Look and read. Put a tick (X) True or False (1point)

0. Tim is going to join a school music event.

1. The music festival will be next month.

2. Tim is going to play the violin in the event.

3. Two girls are going to play the drums.

4. Some of the girls and boys are going to dance.

Question 8. Choose a word from the box and fill in the blanks (1point)

Question 9: Reorder the words to make the sentences. (1 point)

1.He writes new words and reads them aloud.

2.I think I’ll visit the mountain tomorrow.

3.I went to Mai’s birthday party yesterday.

Question 1. Listen and number .

Question 3. Listen and complete:

1. I have three:…………………, Maths and English.

2. She is …………………….. The story Mai An Tiem

Question 4. Read and Circle the odd one out.

Question 5: Read and circle the correct answer.

1. What _______ you do at the zoo yesterday?

2. Did they enjoy the birthday party? – No, I ________

3. When will Sports Day ______?

4. How did you get to Ha Noi? – I went _______ train.

Question 6. Match the sentences

1.What’s your address ? a. I always do morning exercise

2.What’s the village like ? b. twice a week

3.What do you do in the morning ? c. It’s small and quiet

4.How often do you have English ? d. It’s 81 Tran Hung Dao Street

Question 7: Read and tick ( √ ) true ( T ) or false ( F).

Hi, My name is Nam. I live with my family in Ho Chi Minh City. My family has four people: my father, my mother, my sister and I. I go to school by bike every day except Saturday and Sunday. In the morning I always get up at 6:00 and do morning exercise. I brush my teeth twice a day. Then I eat breakfast and ride a bicycle to school at 6.30 am. My school starts at 7:00 . It takes me for 10 minutes to school.

After school, I often do my homework with my friends. Then I go to English club to improve my speaking skills. In the evening I sometimes watch TV and I always watch my favourite programme “English for Kids” after 8.pm.

Question 8 . Read and write the word in each gap.There is one example.

Question 9. Put the words in order.

1.will / the countryside / I / in / be.

2.Ha Noi /She /floor/ on/ the/ lives/second / of /Tower.

3.hard /they/ the/ are/ contest/ practicing/ for/ singing/.

4.did / on / go / where / holiday / you ?

II. Talking about a familiar object.

Give some story book and ask some question

3. Who is the main character?

1. What subjects do you have today?

2. Do you like English? Why/ why not?

3. What’s your favourite subjects?

1. I will be in the countryside.

2. She lives on the second floor of Ha Noi tower.

3.They are practicing hard for the singing contest.

Task 1. Listen and circle (0,5pts)

Task 2. Listen and tick. ü (1pt)

Task 3. Listen and complete (1pt)

Morning windmill afternoon sandcastles cruise

A: What will we do in the (1) morning?

B: We’ll build some (2) ___________.

A: What will we do in the (3) ___________?

B: We’ll visit a small (4) ___________.

A: Will we (5) ___________ around the islands?

Task 5. Read and do the tasks (1.5pts):

Nam lives in TienGiang. Every morning, he gets up early. He often walks to school. Yesterday was Sunday. Nam gets up late. He did not do morning exercise. He did not have breakfast. He went out for lunch with his family. In the afternoon, he went swimming with his father. He did not listen to her favorite music, but he watched the program of “English for Kids” on TV. In the evening, he had no homework. He went to bed early.

B. Read the passage again and answer the questions:

1. Where does Nam live? He lives in TienGiang.

2. What day was it yesterday?_____________________________________________.

3. Who did he go swimming with?___________________________________________.

4. Did he stay up late last night?___________________________________________.

Task 6. Look and write letters (1 pt).

Task 7. Answer the questions (0,5pts)

1. What’s your hometown like? _____________________________________________

2. What will you do at the weekend? _________________________________________

Task 8. Write about your learning English (1 pt)

1. How do you practice speaking English?

________________________________________________________________

2. How do you practice reading English?

________________________________________________________________

3. How do you practice writing English?

________________________________________________________________

5. Read and do the tasks (1.5pts):

2. he went swimming with his father.

6. Look and write letters (1 pt).

7. Answer the questions (0,5pts)

1. It is beautiful/quiet/small….

8. Write about your learning English (1 pt)

3. I write message or email to my friends…

Task 1. Listen and match. There is one example:

Task 2. Listen and tick (ü) A, B or C. There is one example.

Task 3. Listen and tick (ü) the correct pictures. There is one example.

Task 4. Listen and tick (ü) Right or Wrong.

PART II. READING AND WRITING Task 1. Look and write the correct words. There is one example.

Example: It’s a fairy tale about two sisters. The Story of Tam and Cam_____

1. It’s a story about an animal and a bird. _________________________

2. It’s a fairy tale about a princess and seven short men. ___________________

3. It’s a story about a Vietnamese hard-working man. ___________________

4. It’s a Japanese story about a magic cat. ________________________

Task 2. Read and tick (ü) True or False. There is one example (0).

Vy likes English very much. At school, she has English four times a week. She often speaks English with her classmates. Sometimes, she talks with her foreign friend, Amy. They are happy because they can understand each other. Vy usually reads English comic books in her free time. At home, she practises listening by watching cartoons on TV. Vy wants to learn English well. She thinks English is necessary for her future.

Task 3. Read and number the sentences in the correct order. The conversation begins with 0.

Binh: Great! I’ll buy and read it tomorrow!

Hien: Who is the main character?

Binh: What are you reading, Hien?

Hien: I’m reading The Legend of the Watermelon. The story’s very interesting.

Binh: It’s Mai An Tiem. He’s a brave and clever man.

Task 4. Look and read. Fill each gap with one word from the box. Write the word next to the number. There is one word that you do not need. There is one example (0).

Hi Joe, Are you enjoying your (0) summer holiday? This summer I’m staying at (1)______________. I’m (2)________________ a lot of story books. I didn’t have enough time to read them during the school year. Yesterday I went to the (3)____________ and bought a lot of story books. The characters in these books are great people. I like them very much. I’ll write more about my (4) ___________ in the next letter.

Write and tell me about your summer. Hoa

2. Snow White and the Seven Dwarfs

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