I. Meeting and catching up in a straight line

Example 1. A and B both start from east and west at the same time. A travels 56 kilometers per hour and B travels 48 kilometers per hour. The two cars met at a distance of 32 kilometers from the midpoint of the two places. Q: What is the distance between east and west? (A key middle school junior high school examination questions in 2007)

1, an express train and a local train leave from Station A and bilibili at the same time in opposite directions. After the 6-hour rendezvous, the express train will continue to travel for 3 hours and then arrive in bilibili ... It is understood that the local train travels 45 kilometers per hour. How many kilometers are the two stops apart?

Party A and Party B walk from A and B to each other at the speed of 3km and 5km per hour respectively. After meeting, they walked on. If A departs from the assembly point and arrives at Line B in 4 hours, how many kilometers is there between A and B?

3. Two brothers leave home for school at the same time, and the distance is 1400 meters. My brother rides a bike 200 meters per minute, and my brother walks 80 meters per minute. On the trip, my brother met his brother who had just returned to school. How many meters did my brother walk from departure to meeting? How many meters is the venue from the school?

The distance between a and b is 38 kilometers. A and B start from two places at the same time and go in opposite directions. A travels 8 kilometers per hour, and B travels 1 1 km per hour. Go back to B as soon as A arrives at B, and B will go back to B as soon as B arrives at A, and meet you on the road a few hours later? How far is it from A when we meet?

5. Two cars, A and B, leave from A and B respectively at the same time. After five hours of meeting, they left separately. Three hours later, a car arrived at b, and at this time, b car was still 120 km away from a place. What are the speeds of A and B respectively?

Example 2. Two swimmers are swimming back and forth in a 30-meter swimming pool. The speed of A is 1 m per second, and the speed of B is 0.6 m per second. They started from both ends of the swimming pool at the same time and swam back and forth for 5 minutes. How many times have two people met during this time, if not counting the turning point? (A key middle school junior high school examination questions in 2006)

2. The train passes by, crosses the bridge, and the wrong car

Example 3. It takes 25 seconds for a bus to pass through a 250-meter tunnel and 23 seconds for a 2 10-meter tunnel. It is known that there is a truck in the same direction in front of the bus, with a length of 320 meters and a speed of 17 m/s. Find out when the train and truck meet and leave. (A key middle school in 2005 fifth grade last semester final exam questions)

Example 4. A PLA captain is 450m, and the speed is1.5m per second. How long does it take a soldier to walk from the end of the platoon to the head of the platoon at a speed of 3 meters per second, and then return to the end of the platoon immediately? (A key middle school junior high school examination questions in 2008)

1, Xiaoming sat on the moving train and saw the oncoming truck from the window, 6 seconds. Known truck length168m. Later, it took 12 seconds to see the train passing through a bridge 180 meters long from the window. How many kilometers does this truck travel per hour?

2. An army marched in a line of 65,438+0,200m. The correspondent on the other end of the phone had to contact the battalion commander at the front. He ran for six minutes and caught up with the battalion commander. In order to get back to the end of the line, he waited for 24 minutes where he caught up with the battalion commander. If he runs from the front of the line to the end, it only takes a few minutes.

3. A PLA unit dispatched 80 vehicles to take part in the field work, and on the way, it had to pass through a tunnel with a length of120m. If the length of each vehicle is10m, and the distance between two adjacent vehicles is 20m, how many minutes will it take for the motorcade to pass through the tunnel at a speed of 500m per minute?

The express train and the local train are going in opposite directions. The length of the express train is 50 meters, the length of the local train is 80 meters, and the speed of the express train is twice that of the local train. If it takes five seconds for a person sitting in the local train to see the express train pass through the window, how long does it take for a person sitting in the local train to see the local train pass through the window?

Three. Move between multiple objects

Example 5. There are three people: A, B and C. A walks 100 meters per minute, B walks 80 meters per minute and C walks 75 meters per minute. Now A starts from the East Village, and B and C start from the West Village at the same time. On the way, A meets B for 6 minutes, and A meets C again. So, what is the distance between the two villages?

1, Party A and Party B go from A to B, and Party C goes from B to A. They start at the same time. A cycling speed is 8 kilometers per hour, and C cycling speed is 10 kilometers. Five hours later, A and C meet, 1 hour later, B and C meet. Find the speed of B.

2. The walking speeds of Party A, Party B and Party C are 30m, 40m and 50m per minute respectively. A, B are in place A and C are in place B, walking in opposite directions at the same time. Party C meets Party A 10 minutes after meeting Party B. How many meters is there between A and B?

3. Party A, Party B and Party C should go in groups of three. A walks 60 meters per minute, B walks 50 meters per minute and C walks 40 meters per minute. A starts from A, B and C start from B. After A and B meet, 15 minutes later meets C, thus finding the distance between A and B. ..

4. Ring problem and clock problem

Example 6. Two people, A and B, ride bicycles from the same place on the ring road at the same time, with their backs to each other. It is now known that it takes 70 minutes for A to walk once. If A and B meet 45 minutes after departure, how many minutes does it take for B to take a trip?

1. The circular track of the stadium is 400 meters long. Xiao Gang and Xiao Hua are on the same starting line of the track and start in opposite directions at the same time. Xiaogang runs 152 meters per minute, and Xiaohua runs 148 meters per minute. A few minutes later, they met for the third time.

2. Party A and Party B run towards each other around the circular runway at a uniform speed, starting at both ends of the circular diameter. If they start at the same time and meet for the first time when A runs 60 meters, and meet for the second time when B is 80 meters short, what is the length of the runway?

Example 7. The clock now shows 10 hour. Then, how many minutes later, the minute hand and the hour hand coincide for the first time; How many minutes later, the minute hand and the hour hand coincide for the second time?

1. When does the hour hand and minute hand of a clock form a right angle between four o'clock and five o'clock?

Grandpa goes out for a walk at 7: 00 pm. When he went out, the hour hand and the minute hand were in a straight line. When he came back, the hour hand and the minute hand coincided. How long has grandpa been out for a walk?

The hour hand and minute hand of a clock are between 4 and 6, and the "5" on the clock face is right in the center of the hour hand and minute hand. What time is it now?

Xiao Liang aimed at his watch at nine o'clock in the evening. Arrived at school at 8 am and was late 10 minutes. Then how many minutes does Xiao Ming's watch lose every hour?

Verb (abbreviation of verb) is a problem of running water.

1. When the ship is sailing in the river, the downstream speed is12km/h and the upstream speed is 6km/h.. How many kilometers per hour is the ship speed and how many kilometers per hour is the water speed?

The speed of the ship in still water is 265,438+0 kilometers per hour. The ship sailed upstream from city A for 8 hours and arrived at city B, with a distance of 1.44 km. How many hours does it take for this ship to return from B to A?

A ship is sailing at the speed of 20 kilometers per hour in calm water. It takes 12.5 hours to get the distance between two docks in a river with a flow speed of 4 kilometers per hour.

5, a ship, the first time sailing 56 kilometers downstream, 20 kilometers upstream, * * * need 12 hours; The second time, at the same time, I sailed 40 kilometers downstream and 28 kilometers upstream. Find the speed of the ship in still water.

Exclusion principle (3)

1. How many * * * in an integer not exceeding 20 are multiples of 2 or multiples of 3?

There are 23 members in a class. There are 20 boys in this class. How many more girls are there in this class than boys who are not league members?

There are 25 people who get 90 points in math in one class. There are 2 1 person with a language score of 90 or above; There are at least one of the two subjects, and there are 38 people over 90. How many people scored above 90 in both subjects?

As shown in the figure, a square with a side length of 2 and a square with a side length of 3 are placed on the desktop. How big is the area they cover?

5. A piece of paper with an area of 7 and a square piece of paper with a side length of 2. Put these two pieces of paper on the table, covering an area of 8. What is the overlapping area of two pieces of paper?

6. There are 65,438+000 passengers, of whom 65,438+00 know neither English nor Russian, 75 know English and 83 know Russian. How many people know both English and Russian?

7. A school organizes chess competitions, which are divided into three groups: Go, China Chess and Chess. There are 42 participants in Weiqi, 5 1 person in China and 30 in chess. There are 65,438+03 people who take part in Weiqi and China chess competitions at the same time, 7 people who take part in Weiqi and chess competitions at the same time, and 65,438+065,438+0 people who take part in China chess competitions at the same time, among which 3 people take part in all three chess competitions. How many people are there in the chess game?

8. As shown in the figure, put three squares with sides of 6, 5 and 2 on the desktop. Ask them what area they cover.

9. A class of students have red, yellow and blue balls in their hands. There are 34 red balls, 26 yellow balls and 8 blue balls/kloc-0. Among them, there are six people with red, yellow and blue balls in their hands. There are 9 people who have only red and yellow balls, 4 people who have only yellow and blue balls and 3 people who have only red and blue balls. So how many people are there in this class?

Of the natural numbers from 10 to 100,

(1) How many numbers are not divisible by 6 and 10?

(2) How many numbers are divisible by at least one of 2, 3 and 5?

1 1, from 1 to 200, how many natural numbers are not divisible by any of 2, 3 and 5?

12, one day in midsummer, 10 students went to a cold drink shop and handed the waiter a cold drink demand statistics: coke, sprite and juice for five people each; Three people want coke and sprite; Two people want coke and juice; There are two people who want sprite and juice; Only 1 person wants all three. Prove that there must be 1 of them who didn't want any of these three drinks.

13. 100 the results of the survey of students' extracurricular activities are as follows: 32 students participated in the math group; 20 people take part in the English group and 45 people take part in the biology group. Among them, 15 people participated in both the math group and the biology group; There are 7 people in English group and math group; 10 people participated in the English group and the biology group. There are still 30 people who have not participated in any of the above subject groups.

(1) Find out the number of participants in all three topic groups.

(2) Fill in the corresponding number of students in eight areas of venn diagram. Among them, A, B and C represent the number of students participating in math, English and biology groups respectively. The number of 100 students surveyed is i.

Special lecture on the competition of the principle of inclusion and exclusion

14. How many natural numbers from 1 to 1000 are not divisible by 5 or 7?

15. How many natural numbers from 1 to 100 are not divisible by 2, 3 and 8?

16. A class of students took the exams in mathematics, science and chemistry, with 30 excellent students in mathematics, science and chemistry, 28 excellent students in mathematics, physics and chemistry, 20 excellent students in mathematics, physics and chemistry, 16 excellent students in all three subjects 17. Q: How many people are excellent in at least one of mathematics, science and chemistry?

17. There are 48 students in the class, among whom 27 can swim, 33 can ride bicycles and 40 can roller skate. Q: How many students can do at least all three sports?

17. On a hot summer day, several children went to a cold drink shop, and each of them ordered at least one cold drink. Six of them asked for popsicles, six for soda and four for Sprite. As long as there are three popsicles and soda, as long as there are no popsicles and sprite, as long as there are 1 soda and sprite; All three have 1 person. Q: * * * How many children went to the cold drink shop?

18. All the students in a class took part in sprint, swimming and basketball tests. Four students failed to achieve excellent results in these three items, and the rest of the students each achieved excellent results in at least one item. The number of students who have won excellent projects is as follows:

Ask how many students there are in this class.

Fill in the blanks: (basic training)

1, 3.85 cubic meters = () cubic decimeter 4 liters 40 ml = () liters.

2. Weld a cubic frame (excluding joints) with 48cm long iron wire. The surface area is () square centimeters and the volume is () cubic centimeters.

3. Fill in the appropriate unit name in brackets:

The volume of an eraser is about 8 (), and a classroom accounts for about 48 ().

The volume of the automobile fuel tank is 30 (), and the length of each step is about 60 ().

There are () odd numbers and () even numbers among natural numbers within 4.20 (including 20).

5. In14,6, 15 and 24, () is divisible by (), and () and () are prime numbers.

6. The largest two-digit number that can be divisible by 2, 3 and 5 at the same time is (), and the prime factor to decompose it is ().

7, 5□ When () is filled to the maximum, this number can be divisible by 3, and the divisor of this number is ().

8. If A is divisible by B, the greatest common divisor of A and B is (), and the least common multiple of A and B is ().

9. It is known that A = 2× 2× 3× 5 b = 2× 5× 7, the common prime factor of A and B is (), and their greatest common divisor is ().

10, a 2-meter-long rectangular steel, cut into two sections along the cross section, and the surface area is increased by 0.6 square decimeter. The volume of this rectangular steel is () cubic decimeter.

Second, judgment: 5 points

1, nonzero natural numbers are either prime numbers or composite numbers. ( )

2. The multiple of a number must be greater than its divisor. ( )

3. The product of two prime numbers must be a composite number. ( )

Application of engineering problems

[Example 1] For a project, team A 12 days completed the task, team B 15 days completed the task, team A completed it alone, and the rest were completed by both parties. How many days did it take to complete the task?

[Example 2] For a project, it takes 20 days for Team A to do it alone and 30 days for Team B to do it alone. Now the two teams cooperate for a few days, and the remaining B team 10 days will be completed. How many days did Team A and Team B cooperate?

[Example 3] A job takes 6 days by myself and 8 days by team B. Now that team C has completed all the projects, the rest are completed by teams A and B. How many days does it take to complete the task?

Example 4: A pool has three water pipes, A, B and C. Opening the first pipe can fill the empty pool within 6 hours, opening the second pipe can fill it within 4 hours, and opening the third pipe can fill it within 12 hours. How many hours does it take to fill an empty pool with three pipes at a time?

All-true simulation test questions for the sixth grade entrance examination

Class; Name: Achievements:

First, Chinese Pinyin. (10)

1, look at pinyin and write words.

zǔnáo bào Yuàn qáng miècíng báng dǐng jáng zhàn gu fu páI

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

2. Word formation of polyphonic words.

Ley ()

Hit {spray {

plum

Second, Chinese characters. (10)

1, look it up in the dictionary. The phonetic order of the word "Lu" is syllable; With the radical search method, what you want to search is the Ministry, and its name is. The definition of "shoes" in the dictionary is: ① shoes; 2 practice, step on; Three steps. Choose the correct answers for the following words according to the meaning (only fill in the serial numbers): A, walking on thin ice () B, Zheng Ren buying shoes () C, walking lightly ().

2. Write words according to different meanings.

Red: ① Red ② Honesty, Loyalty ③ Naked ④ Empty.

Ming: ① Ming, ② Open, don't hide, ③ Know, know, ④ One year or tomorrow.

Thorough: ① detailed and thorough; ② customs clearance.

Third, words. (13)

1. Complete the following idioms and classify them according to the prompts.

① Qianshan is a () ② uneasy () ③ giving up () is a person ④ () angry.

⑤ Scary () ⑤Lust, ⑤ No (), No () and No ().

Express inner activities:

Describe the natural scenery; Show spiritual quality;

2. Choose words to fill in the blanks. Cherish and cherish

(1) We need () our own school supplies to cultivate the virtue of thrift from an early age.

Teacher Wang often gives us lessons in spite of illness and never pays attention to his health.

Appear.

(1) On the night of National Day, the whole country was filled with festive atmosphere.

(2) Since the "Strive to Be a Living Lei Feng" activity was launched, there have been many good deeds on campus ().

Gently, quietly, quietly, slightly, slowly, gradually, thickly and tightly.

She sat there quietly with a book in her hand. I was embarrassed to disturb her, so I slowly pushed open the door and came to her side. Later, she looked up and saw me, () smiled, stood up and () shook my hand.

Fourth, sentences. (12)

1, write sentences as required.

(1) Extended sentence: The sun has risen.

(2) Abbreviation: A group of ragged trackers trudged.

This mountain is really high. The mountain is so high that it will soon penetrate the sky.

It is really hot today. It's really hot today,

(4) Change it into an exclamatory sentence: We live happily today.

(5) Change it into a rhetorical question: Plum blossom's fearless character is amazing.

(6) Write a sentence with three consecutive actions:

(7) Divide the following sentences into two sentences. The teacher asked the students to express their opinions.

① ②

(8) Combine the following two sentences into one sentence. Grandma told me. I should be careful when crossing the road.

(9) Change the word order in the sentence so that the meaning of the sentence remains unchanged.

Example: The steed gallops on the grassland.

The horse galloped on the grassland. On the grassland, horses gallop.

A Chinese book is on the teacher's desk.

(10) Read the sentence and write a coherent sentence with related words.

I found that more than 60 meters ahead is the enemy's frontier position, not only can you see barbed wire and

On the breast wall, you can also see bunkers and bunkers, and even hear the enemy talking.

Recall the content of the text and fill in the blanks. (5 points)

The swallow has gone. Willow withered,; Peach blossoms are thanks.

Fill in the appropriate idioms and poems on the lines.

My uncle is a man of learning. He (reads a lot) often (quickly). Sometimes he forgets to eat and sleep in order to study. I also often travel to the motherland (famous scenic spots), which is really ""(a poem in Lu You's Reading on a Winter Night).

Sixth, accumulation and application. (6 points)

1, about ancient poetry.

(1) In Long song, the poem widely read by people is:

(2) in the poem "The Yellow River was recaptured by the imperial army", the poem expressing the poet's ecstasy is:

(3) The title of the poem "Looking at Dongting from afar, there are green snails in the silver plate" is:

This poem uses a new rhetorical device.

2. To judge whether it is true or false, tick "√" or "×" in brackets.

(1) The author of Xiuzi is Lu You, a poet in the Tang Dynasty. ( )

(2) "resourceful" and "resourceful" are synonyms. ( )

(3) The little match girl is a fairy tale; The lesson of "serving the people" is argumentative; The lesson "the poor" is a story. ( )

(4) There are two pronunciations of "evil"-* *, which can be pronounced as "e" or "e". ( )

(5) "She and I seem to be getting old." This is a figurative sentence. ( )

(6) "I won't know you." And "How could I not know you?" Have the same meaning ()

(7) The pronunciation of Zi in Liezi is different from that in Son. ( )

(8) There are 10 paintings in "Dou" * * * and "Er", and the radical search method is used to search. ( )

(9) "It rains heavily." This is a complete sentence. ( )

(10) Xiuzi and Both Banks of the Yellow River were recaptured by the imperial army have different expressions and feelings. ( )

The dashes in (1 1) and "Sesame Blossoms Are Rising" are the same as those in "This is the last day of the year-New Year's Eve". ( )

(12) The word "disciple" in the sentence "The eldest disciple is sad" means "only". ( )

(13) Cang Kejia's poem Some People was written in memory of Li Dazhao. ( )

Eight, reading comprehension, complete the exercise. (20 points)

1, reading in class.

The railway has to pass through many high mountains, so it is necessary to dig tunnels, among which Juyongguan and Badaling tunnels are the most arduous projects. Juyongguan Mountain is high and the rock stratum is thick, so Zhan Tianyou decided to adopt the method of simultaneous excavation from both ends to the middle. The spring water at the top of the mountain seeped downward, and the tunnel was full of mud. There was no water pump on the construction site, so Zhan Tianyou took the lead in carrying buckets to drain water. He often eats and lives with the workers and never leaves the construction site. Badaling Tunnel is 1 100 meters long, which is three times as long as Juyongguan Tunnel. He discussed with the old workers and decided to adopt the intermediate sinking method. First, drill a shaft down from the top of the mountain, then dig both ends separately, and both ends will be constructed at the same time, which shortens the construction period by half.

(1) Divide this passage into three layers with "∨" and write the meaning.

First floor:

Second floor:

The third floor:

(2) Draw the schematic diagrams of Zhan Tianyou, Juyongguan and Badaling tunnels.

(3) Zhan Tianyou has adopted different working methods according to different terrains, thus,

2. Reading after class.

Bees and ants

People love bees and praise their hard work. Painters have painted many honey-picking pictures, poets have written many poems praising bees, and even children who have just learned to speak sing "Our life is sweeter than honey ..."

Ants are jealous of bees, and there is always a doubt in their hearts: bees leave work early in the morning, and so do we;

Bees go home in the dark, so do we. We do no less work than bees, nor slower than bees, which is lovely.

Is it too biased for children to praise bees but not us? The ant thought about it, but still couldn't figure it out.

One day, an ant climbed onto a branch for food. When he saw a little bee buzzing around collecting honey, he looked up and said angrily, hey, honey, let me ask you a question.

What's the problem? The little bee said, Go ahead.

"Do you think we ants are hardworking?"

"Like us, you are busy all day, of course you are hardworking!"

"Then why do people only praise you and never praise us?"

The little bee thought for a moment and smiled and said, "Well, I think this question is not difficult to answer, because your hard work is for yourself, and our hard work is for people ..."

The ant was persuaded, so he was no longer jealous of bees.

(1) Find three words with similar meanings from the text and write them down.

(2) Contact the context and understand the words.

Jealousy:

Completely believe:

(3) Why do ants envy bees? Draw the relevant sentences in the article with "—".

(4) What do you think after reading this story? Please write it down below!

IX. Additional questions

1, complete the sentence according to the example: the meaning of life lies in giving, not taking. If you are a big tree, cast a shadow; If you are a clear spring, you will nourish one side of the land; If you are.

2. Read the examples provided and introduce a scene or a cultural relic with words with horizontal lines:

Huangguoshu Waterfall is not as long as Lushan Waterfall, but it is much wider than it, so it looks extraordinary and magnificent.

The monitor wrote a famous poem on the message to the teacher.

Praise her persuasiveness and subtly let her classmates receive education and make continuous progress.

4. Yesterday afternoon, Teacher Zhang assigned a math thinking question. At night, I racked my brains and couldn't figure it out. Just when I was "_ _ _ _ _ _ _ _ _ _ _ _ _ _", my father came to give me a hand. After listening to his advice, I was suddenly enlightened. It is really "_ _ _ _ _ _ _ _ _ _ _ _ _ _"

5. Our teacher often quotes two poems "_ _ _ _ _ _ _ _ _ _" by Su Shi, a famous poet in Song Dynasty, and emphasizes that exercise is the release of mind and emotion, writing methods should be eclectic, and language should have its own personality.

6. When Grandpa was 70th birthday, friends and relatives came to congratulate him. Everyone wishes grandpa "happiness as the East China Sea and longevity as the South Mountain". Grandpa sighed: "_ _ _ _ _ _ _ _ _ _ _ _ _ _" I quickly stopped grandpa's words: "_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Grandpa smiled and touched my head: "Only you can be loquacious."

7. Teacher, do you still remember me-a "naughty boy" who made you pay countless efforts and sweat. A wrinkle in the corner of your eye was born for me, and the silver hair on your head is a little white to me. "_ _ _ _ _ _ _ _ _ _", this poem is not about your dedication to burning yourself and illuminating others. Who else can you praise?

8. Spring rain, how many people praise you at all times and in all countries. "_ _ _ _ _ _ _ _ _ _" This is a beautiful sentence by the great poet Du Fu describing your coming to the world. You have come, like smoke, quietly, weeping willows spit out new buds under your comfort, bamboos are jointing under your moisture, and seedlings are shining under your bath. ...

9. Use the symbol "/"to draw a pause in the sentence of the advertising language. Good medicine, good medicine. -Drug advertisements

10, use the word "Yan" to match with the following words respectively.

Subject () Knowledge () Situation () Wording ()

1 1, "Xiang Xiang He" is from a historian of the Han Dynasty. Lian Po is the one in the title.

2. Complete the sentence and use the word corresponding to "so". Lian Po was unconvinced.

3. If underlined in "I am invincible in Lian Po", you should read it with contempt, pride, anger and excitement.

The underlined words in What Can He Do to Lin Xiangru should be read with contempt, pride, anger and excitement.

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