General knowledge of mathematics in grade five

A math joke 1. Once, her mother patiently inspired her to do arithmetic: "Ya Ya, have you learned to do subtraction?" Come on, let's see, how much is 4 MINUS 2? ""it's already two o'clock, mom. "

"That's right, good boy. So, what about 5 MINUS 5? " "Five minus five, minus five.

"Ya ya muttered," I won't, mom. "

"Son, you can't! Think about it, for example, you have five coins in your pocket, but suddenly, all five coins fall out. Tell me, what else do you have in your pocket? " Ya Ya blinked her eyes and said, "Did you drop it? Well, there is still a hole in my pocket! " "I always get 100 in arithmetic."

"That's because you learn well." "But I never listen in class."

"That's because you are smart. You will know to study hard when you come home from school." "Smart? A little, but after school, I am a person who deals with football. "

"Then you must have cheated in the exam." "I can't say that. I didn't copy books or peek at others. How can I be derailed? "

"Then what happened to you?" "I kicked Jim, the bookworm in front, in the chair." "If you don't, you won't. How can you be so naughty? "

"I kicked the first foot, and he stretched five fingers back with his hand." "What does this mean?" "The answer to the first question is 2+3."

"Oh ... what if you ask the 5*8 answer to the tenth question?" "It was after I kicked the tenth foot that he stretched out four fingers first and then clenched his fist immediately, so I knew the answer of 40." 3. The teacher announced the results: "Xiaohua scored 30 points, Xiaoming scored 20 points ..." Pig: I got 0 points! Dog: What should I do? Me too ... Pig: We both got the same score in the exam. Will the teacher think we cheated? Legend has it that one day, Zhuge Liang summoned his soldiers and said, "Which one of you chooses an integer from 1 to 1024 and keeps it in mind. I asked ten questions, only one' yes' or' no'.

After answering all ten questions, I will' calculate' the numbers in your mind. "ZhuGeLiangGang say that finish, a counselor stood up and said, he has chosen a good number.

Zhuge Liang asked, "Did you choose more than 5 12?" The counselor replied, "No." Zhuge Liang asked his advisers nine questions in succession, and all the advisers answered them one by one.

Zhuge Liang finally said, "The number you remember is 1." The counselor was surprised because he really chose this number.

Do you know how clever Zhuge Liang is? In fact, the method is very simple, that is, take half of 1024, and the tenth time is "1". According to this truth, you can find the required number by asking ten questions in a row.

3. Mathematical sayings 1. Wang Juzheng's Percentage China scientist Wang Juzheng has a proverb about experimental failure, which says, "There is still a 50% chance of success if you continue, or 100% failure if you don't do it." 2. Tolstoy's score When it comes to people's evaluation, Tolstoy compares people to a score.

He said: "A person is like a score, his practical ability is like a numerator, and his evaluation of himself is like a denominator. The larger the denominator, the smaller the value of the score. "

1, the essence of mathematics is its freedom. Cantor) 2. In the field of mathematics, the art of asking questions is more important than the art of answering questions. Cantor) 3. No problem can touch people's emotions as deeply as infinity, and few other concepts can stimulate reason to produce rich thoughts as infinity. However, no other concept needs clarification like infinity. Hilbert) 4. Mathematics is an infinite science. Hermanville 5. The problem is the core of mathematics. P.R. halmos 6. As long as a branch of science can ask many questions, it is full of vitality. No problem, indicating the termination or decline of independent development. Hilbert 7. Some beautiful theorems in mathematics have such characteristics: they are easy to sum up from facts, but the proofs are extremely profound. Gauss 3. Rybakov's Constants and Variables Russian historian Rybakov said in The Use of Time: "Time is a constant, but for diligent people, it is a' variable'. People who use' minutes' to calculate time spend 59 times more time than people who use' hours'. "

When talking about learning and exploration, Hua, a famous mathematician in China, pointed out: "To dare to do subtraction in learning is to subtract the parts that have been solved by predecessors and see if there are any unsolved problems, which need us to explore and solve." Edison, a great inventor, used a plus sign to describe genius. He said: "Genius = 1% inspiration +99% sweat."

6. dimitrov's symbol dimitrov, an internationally renowned worker movement activist, said in his evaluation of a day's work: "We should spend time thinking about what we have done in a day, whether it is' addition' or' subtraction'. If it is' addition', we will make progress; If it is'-',you have to learn from it and take measures. " 3. The aphorism written in Formula 7. Einstein Formula When talking about the secret of success, Einstein wrote a formula: A = X+Y+Z Y+Z.

And explained: A stands for success, X stands for hard work, Y stands for correct method, and Z stands for less empty talk. ""If you use a small circle to represent what you have learned and a big circle to represent what I have learned, then the area of the big circle is a little more, but the blank outside the two circles is our ignorance.

The bigger the circle is, the more ignorant faces its circumference contacts. "-Zhi Nuo Cauchy (A.L. Cauchy) People will die, but their deeds will last forever. People will die, but achievements will last forever.

Laplace (1749–1827) is not well known. What we don't know is infinite. C. Hermite1822–1901) Abel left mathematicians enough to keep them busy for 500 years. When commenting on Abel, he once said: "What Abel left behind can keep mathematicians busy for 500 years.

"Poursin (Poisson, Simé on1781-1840)" Life is only good for two things, discovering mathematics and TEAC.

2. Fifth grade mathematics interesting knowledge

Cleverly arrange 24 people in 6 columns and ask 5 people to be a column. Do you know how to arrange them? Eggs in the basket Put the eggs in the basket. Suppose the number of eggs in the basket increases by 1 time per minute. At this rate, the basket will be full in 12 minutes.

So, do you know when it is half a basket of eggs? Father and son: I know a child named Xiaolong. He loves learning very much and always asks me to give him questions. This day, he came to ask me questions again, and I said to him: There is a photo of our family with two fathers and two sons on it. Can you guess how many people are in the photo? Xiaolong guessed at once. Have you guessed? Chef Pancake Three customers came to a shop, eager to buy cakes to catch the train, and the limited time should not exceed 16 minutes.

Several chefs said there was nothing they could do, because it took five minutes to bake two sides of a cake, and two cakes could be put in one pot at a time, so it took 20 minutes to bake three cakes. Then there was the chef Lao Li, who said that it only took 15 minutes to think.

Do you know how to make a brand? .

3. Collect 20 math skills

The vertex angles are equal. 2. Pi is an irrational number.

3。 The sum of the internal angles of a triangle is 180 degrees 4.

The sum of the inner angles of a polygon is (number of sides -2)* 180 degrees 5. The sum of the outer angles of a polygon is equal to 360 degrees 6.

The image of a linear function is a straight line. 7。

The image of the proportional function is a straight line passing through the origin. 8。

The image of inverse proportional function is a hyperbola. 9。

The image of a quadratic function is a parabola. 10。

Same radix power multiplication, constant radix, exponential addition. 1 1。

Two parallel lines are cut by a third straight line and have the same angle. 12。

Two parallel lines are cut by a third line, and their inner angles are equal. 13。

Two parallel lines intersect with the third straight line, which complement each other. 14。

The three median lines of a triangle intersect at a point, which is called the center of gravity. 15。

The bisectors of the angles of a triangle intersect at a point, which is called the heart. 16。

The three heights of three sides of a triangle intersect at a point, which is called the center of gravity. 17。

The perpendicular lines of the three sides of a triangle intersect at a point, which is called the epicenter. 18。

Two triangles with the same base and height have the same area. 19。

1+2+3+……+n =( 1+n)* n/2 20 .Sin90= 1，Cos90=0，Sin0=0，Cos0= 1 .

4. Little knowledge of mathematics

Saturday, August 6th

I saw a puzzling math problem tonight. The topic is: 37 students want to cross the river. There is an empty boat at the ferry that can only take five people. How many times must they cross the river with this boat at least?

Careless people often ignore the "empty boat", that is, forget to have a gondola, so they can only take four people at a time. In this way, 37 people subtract one rowing classmate, leaving 36 students, 36 divided by 4 equals 9, and the classmate who worked as a boatman on the other side for the last time also landed 4, so it takes at least 9 trips.

Math diary III

Tuesday, August 9

In the evening, I saw a problem in the Olympiad Book: the number of apple trees in the orchard is three times that of pear trees. Master Lao Wang fertilizes 50 apple trees and 20 pear trees every day. A few days later, all the pear trees were fertilized, but the remaining 80 apple trees were not fertilized. Excuse me: How many apple trees and pear trees are there in the orchard?

I am not intimidated by this question, but it can stimulate my interest. I think the apple tree is three times as big as the pear tree. If two kinds of trees are to be fertilized on the same day, Master Lao Wang will fertilize "20*3" apple trees and 20 pear trees every day. In fact, he only fertilizes 50 apple trees every day, which is 10, and the last 80 trees. Therefore, Master Lao Wang has been fertilizing for 8 days. 20 pear trees a day, 8 days is 160 pear trees. According to the first condition, there are 480 apple trees. This is to solve the problem with the idea of hypothesis, so I think the hypothesis method is really a good way to solve the problem.

Math diary IV

August 4th 1 1

I met another math problem today, and it took me a lot of effort to solve it. The topic is: there are 30 birds in two trees, and 4 birds fly away from the second tree first. At this time, tree A flew to tree B with three birds, and the birds on the two trees were just equal. How many birds are there in each tree?

As soon as I saw the topic, I knew it was a reduction problem, so I solved it by the method of reduction problem. But when I checked, I found something was wrong. I will do it again more seriously. I think there are as many as four missing, half of them are 13, and the restored B-tree is14; A tree is 16. The formula is: (30-4) ÷ 2 = 13 (only); 13-3+4 =14 (only); 30- 14 = 16 (only). The answers are: a tree 16 and b tree 14.

By solving this problem, I understand that no matter what I do, I should be careful, otherwise, even if I master the solution to the problem, the result will be wrong.

Tuesday, June 28th

At noon today, I was doing my math summer homework. Writing, unfortunately, I have a problem. I thought about it for a long time, but I couldn't figure out a way. The question is this:

There is a cuboid, the product of the front and the upper two areas is 209 square centimeters, and the length, width and height are prime numbers. Find its volume.

I saw it and thought: this question is really difficult! Only knowing the product of two surface areas, the volume must also know the length, width and height, but there is no hint at all. How does this start?

Just as I was scratching my head, a colleague of my mother came. He taught me to use the idea of equation to solve it first, but I am not very familiar with this method of equation. So, he taught me another way: list the numbers first, and then exclude them one by one. First, we listed a lot of numbers according to the requirements of the topic, such as: 3, 5, 7, 1 1, and then we began to exclude them, and then we found that only1and 19 were left. At this time, I thought: one of these two numbers is the length of the common side of the front of the cuboid in the question; One is the front of the cuboid, and the other is the division of the previous one.

Sum of side lengths (all lengths are prime numbers). So, I began to tell which number these two numbers were.

Finally I got the result, which is 374 cubic centimeters. My formula is: 209 =11*19 = 2+171* 2 *17 = 374 (cubic centimeter).

Later, I checked this problem with what I learned this semester: prime factor decomposition, and the results are exactly the same.

I am happier than anyone to solve this problem. I also understand the truth that mathematics is full of mysteries, waiting for us to explore.

5.5 grade mathematics knowledge

A math joke 1. Once, her mother patiently inspired her to do arithmetic: "Ya Ya, have you learned to do subtraction?" Come on, let's see, how much is 4 MINUS 2? ""it's already two o'clock, mom. "

"That's right, good boy. So, what about 5 MINUS 5? " "Five minus five, minus five.

"Ya ya muttered," I won't, mom. "

"Son, you can't! Think about it, for example, you have five coins in your pocket, but suddenly, all five coins fall out. Tell me, what else do you have in your pocket? " Ya Ya blinked her eyes and said, "Did you drop it? Well, there is still a hole in my pocket! " "I always get 100 in arithmetic."

"That's because you learn well." "But I never listen in class."

"That's because you are smart. You will know to study hard when you come home from school." "Smart? A little, but after school, I am a person who deals with football. "

"Then you must have cheated in the exam." "I can't say that. I didn't copy books or peek at others. How can I be derailed? "

"Then what happened to you?" "I kicked Jim, the bookworm in front, in the chair." "If you don't, you won't. How can you be so naughty? "

"I kicked the first foot, and he stretched five fingers back with his hand." "What does this mean?" "The answer to the first question is 2+3."

"Oh ... what if you ask the 5*8 answer to the tenth question?" "It was after I kicked the tenth foot that he stretched out four fingers first and then clenched his fist immediately, so I knew the answer of 40." 3. The teacher announced the results: "Xiaohua scored 30 points, Xiaoming scored 20 points ..." Pig: I got 0 points! Dog: What should I do? Me too ... Pig: We both got the same score in the exam. Will the teacher think we cheated? Legend has it that one day, Zhuge Liang summoned his soldiers and said, "Which one of you chooses an integer from 1 to 1024 and keeps it in mind. I asked ten questions, only one' yes' or' no'.

After answering all ten questions, I will' calculate' the numbers in your mind. "ZhuGeLiangGang say that finish, a counselor stood up and said, he has chosen a good number.

Zhuge Liang asked, "Did you choose more than 5 12?" The counselor replied, "No." Zhuge Liang asked his advisers nine questions in succession, and all the advisers answered them one by one.

Zhuge Liang finally said, "The number you remember is 1." The counselor was surprised because he really chose this number.

Do you know how clever Zhuge Liang is? In fact, the method is very simple, that is, take half of 1024, and the tenth time is "1". According to this truth, you can find the required number by asking ten questions in a row.

3. Mathematical sayings 1. Wang Juzheng's Percentage China scientist Wang Juzheng has a proverb about experimental failure, which says, "There is still a 50% chance of success if you continue, or 100% failure if you don't do it." 2. Tolstoy's score When it comes to people's evaluation, Tolstoy compares people to a score.

He said: "A person is like a score, his practical ability is like a numerator, and his evaluation of himself is like a denominator. The larger the denominator, the smaller the value of the score. "

1, the essence of mathematics is its freedom. Cantor) 2. In the field of mathematics, the art of asking questions is more important than the art of answering questions. Cantor) 3. No problem can touch people's emotions as deeply as infinity, and few other concepts can stimulate reason to produce rich thoughts as infinity. However, no other concept needs clarification like infinity. Hilbert) 4. Mathematics is an infinite science. Hermanville 5. The problem is the core of mathematics. P.R. halmos 6. As long as a branch of science can ask many questions, it is full of vitality. No problem, indicating the termination or decline of independent development. Hilbert 7. Some beautiful theorems in mathematics have such characteristics: they are easy to sum up from facts, but the proofs are extremely profound. Gauss 3. Rybakov's Constants and Variables Russian historian Rybakov said in The Use of Time: "Time is a constant, but for diligent people, it is a' variable'. People who use' minutes' to calculate time spend 59 times more time than people who use' hours'. "

When talking about learning and exploration, Hua, a famous mathematician in China, pointed out: "To dare to do subtraction in learning is to subtract the parts that have been solved by predecessors and see if there are any unsolved problems, which need us to explore and solve." Edison, a great inventor, used a plus sign to describe genius. He said: "Genius = 1% inspiration +99% sweat."

6. dimitrov's symbol dimitrov, an internationally renowned worker movement activist, said in his evaluation of a day's work: "We should spend time thinking about what we have done in a day, whether it is' addition' or' subtraction'. If it is' addition', we will make progress; If it is'-',you have to learn from it and take measures. " 3. The aphorism written in Formula 7. Einstein Formula When talking about the secret of success, Einstein wrote a formula: A = X+Y+Z Y+Z.

And explained: A stands for success, X stands for hard work, Y stands for correct method, and Z stands for less empty talk. ""If you use a small circle to represent what you have learned and a big circle to represent what I have learned, then the area of the big circle is a little more, but the blank outside the two circles is our ignorance.

The bigger the circle is, the more ignorant faces its circumference contacts. "-Zhi Nuo Cauchy (A.L. Cauchy) People will die, but their deeds will last forever. People will die, but achievements will last forever.

Laplace (1749–1827) is not well known. What we don't know is infinite. C. Hermite1822–1901) Abel left mathematicians enough to keep them busy for 500 years. When commenting on Abel, he once said: "What Abel left behind can keep mathematicians busy for 500 years.

"Poursin (Poisson, Simé on1781-1840)" Life is only good for two things, namely, discovering mathematics and teaching.

6. Knowledge points of mathematics in the fifth grade of primary school

1 5 or less. Understand the meaning of music score; *2. Think and use formulas to calculate the surface area and volume of cuboids and cubes.

*3. Do statistics, learn to do statistics, and watch statistics! (All the above are very important, especially those with an asterisk) Do the questions. 1. Fill in the blanks. 1. Among natural numbers, the number that is neither prime nor composite is (), the smallest prime is (), and the smallest composite is ().

2. The prime factor of decomposition 120 is (). 3. Two prime numbers whose least common multiple is 60 are both composite numbers, namely () and ().

4.a and B are a pair of prime numbers, and a*b =36, so A and B are () respectively. 5. A three-digit number is the smallest natural number, the tenth smallest composite number and the hundredth smallest prime number in the unit, which is (). 6. Rectangular length 1 decimeter, width 8 cm, height 3 cm. Its surface area is () and its volume is ().

7. Make the largest cube frame with 48 cm long wire. Its surface area is () square centimeters and its volume is () cubic centimeters. 8. It is known that the triangle has an area of 24 square centimeters, a base of 8 centimeters and a height of () centimeters.

9. Saw a 2-meter-long cuboid wood into four sections on average, and the surface area increased by 48 square decimeters. The original volume of this wood is () cubic decimeter. 10. It is known that the area of a trapezoid is 36 square centimeters, the height is 4 centimeters, and the sum of the upper bottom and the lower bottom is ().

1 1. It is known that a number =3*3*5*7, b number =3*5*7* 1 1, and the greatest common divisor of a number and b number is (). 12. Fill in the following figures as required.

69102451091780 248 37 odd number () is divisible by 2 () even number () is divisible by 3 () prime number () is divisible by 5 () composite number () is divisible by 2, 3 and 5 (). 1. The sum of the sides of a cuboid is 84 cm, and the sum of the lengths of three sides from a vertex is 2 1 cm.

() 2.7.2 Divided by decimals, the quotient must be greater than 7.2. () 3. Two numbers without common divisor are called prime numbers.

() 3. Multiple choice questions. 1. If both m and n are natural numbers and m = 8n, then the least common multiple of m and n is ().

A, m B, n C, mn D, 82, in the following groups, the first number divisible by the second number is (). A, 36 and 0.9 B, 7 and 56 C, 54 and 27 D, 84 and 83. If the least common multiple of two natural numbers is 2 10 and their least common divisor is 14, then these two numbers are ().

A, 140 and 2 1 B, 42 and 70 C, 10 and 2 1 D, 14 and 354. If m ÷ m÷n = 13, m and n n are natural numbers, then m is n (. A. Minimum common divisor B. Maximum common divisor C. Maximum common multiple D. Minimum common multiple 5,99.999 The two decimal places reserved are ().

a . 99.99 b . 100 c . 100.00d . 100.06。 The sum of two adjacent natural numbers must be (), and the product must be (). A. odd number B. even number C. composite number D. prime number iv calculate

1. Calculation, simplify what can be simplified. 6.7 1*7.5 + 2.5*6.7 1 ( 3. 12 + 0.3 )÷[ ( 1-0.4 )÷0.2 ] 3. 14*625-3. 14*374-3. 14 [ 4 1 -(4.2+5.8 ÷ 5)] ÷ 0.93.4 ÷ 4.41+0.4 * 0.0512.5 * 3.2 * 0.25 *1.32. Direct

5.2-3+8 = 2.9+4. 1 = 1.05 = 8 * 0.5 = 3.29+8.9 = 2-3.6 = 8.8-0.8 = 4.8 ÷.6x-0.4 * 6 = 9.6 1 18-2 *(4. 1+x)= 55 4x+80 = 1609.6÷x = 0.8 4.8-x = 3 *(x+6

Five centimeters, three centimeters, five. Column calculation. 1. If you subtract 3.6 from a number, the difference is five times, which is exactly three times this number. Find this number.

2. The number of B is 3 times less than that of C, and the number of A is 4 times that of B. It is known that the number of A is 132. Find the number of c ... 3.2.5 Divide by the product of 64 1.44. What is the quotient? 5 times of a number is 48 less than the quotient of 40 divided by 5, so find this number.

(solve by equation) VI. Application problems. 1. Only column types are not counted.

(1) The construction team will build a 480m-long road, which is scheduled to be completed in 12 days. Actually, it was completed in 10 day. How many meters are actually built every day? Formula: _ _ _ _ _ _ _ _ _ _ (2) The average score of Xiaohua's first two math exams is 9 1, and the average score of the last three exams is 90.

Ask him the average score of these five tests. Formula: _ _ _ _ _ _ _ _ _ _ _ _ _ _ 2. Li Hong and Wang Gang have just bought five and three identical exercise books. It is understood that Li Hong paid 7.20 yuan more than Wang Gang. What is the unit price of this exercise book? 3. Two athletes, A and B, practice running. A runs 7 meters per second and B runs 6.5 meters per second.

If B is allowed to run out of 10 meter first, and A starts again, how many seconds will it take for A to catch up with B? Car A travels 50 kilometers per hour, and car B travels 56 kilometers per hour. Two cars travel back and forth from two places 20 kilometers apart. A few hours later, the distance between the two cars was 274.4 kilometers. A swimming pool is 50m long, 30m wide and 3m deep. Spread square bricks with the length of 1 decimeter on the four walls and bottom of the swimming pool. How many square bricks do you need? If this swimming pool is filled with water, how many cubic meters can it release? 6. There are 730 peach trees in the orchard, which is 20 fewer than 1.25 times that of pear trees. How many pear and peach trees are there in the orchard? 7. The engineering team wants to build a 7.4-kilometer expressway, which has been built for 12 days, with an average of 0.35 kilometers per day. The remaining 8 days to complete, how many kilometers per day on average? The fifth grade, the second volume, the final examination paper of mathematics 1. Fill in the blanks.

1 and 24 have () divisors, and the minimum multiple of 24 is (). 2. In the natural number 1-20, there are both even numbers and prime numbers (); There is a strange and complicated ().

3. The greatest common divisor of A and B is 1, and the least common multiple is (). 4. When the side length of a cube is expanded by 3 times, its volume will be expanded by () times and its surface area will be expanded by () times.

5, 3 liters 60 ml = () liters = () ml. 6. A number = 2*3*5*7 B number = 2*5* 1 1, then the greatest common divisor of two numbers is (), the smallest common multiple is () 7, and the prime factor of decomposition 96 is ().

8. Divide the 4-meter-long wooden stick into 7 segments on average, each segment is () meters long, and each segment accounts for () of the total length. 9, = () ÷15 =15 ÷ () =10, the maximum true score is (), the minimum false score is (), and the minimum band is ()1and 6544.

The decimal unit of 2 is (), and the decimal unit of 20 is (). 12. Li Ming is one year old and Sean is a+b years old; Five years later, the age of the two.