Joke Collection Website - Bulletin headlines - Huanggang Golden Ranking Paper, Quiz King, General Review for Primary School Entrance and Graduation, Special Training, Language Accumulation and Application, Reference Answers
Huanggang Golden Ranking Paper, Quiz King, General Review for Primary School Entrance and Graduation, Special Training, Language Accumulation and Application, Reference Answers
The forms of repeated words are: AABB style clean and tidy ABAB style discuss discuss discuss discuss ABAC style powerful swagger AABC style reluctant to leave and come ABB style quiet and soft Modify with the modification symbol Typos in the recipe below.
Cold dishes: Roasted beans, braised buds, bamboo shoots, muddy mule and crab lake
Hot dishes: Stir-fried shrimps, stir-fried holan beans, grapes, stuffed chicken nuggets and pork slices
< p>Snacks: Indian Feiping Babao RiceFruit: Sugar water, pine basket and sweet potato
Classification of ancient poems: By author: For example, Li Bai's poems include "Silent Night Thoughts" and "Looking at Lushan Mountain" Waterfall", "Gift to Wang Lun", etc. Wang Wei's poems include "Deer and Chai", "Send Yuan Er Envoy to Anxi", etc. Du Fu's poems include "Joyful Rain on a Spring Night" and "Walking Alone by the River Looking for Flowers".
According to content: Those who write about spring in the scenery of the four seasons include: "Wind", "Winging Willows", "Spring Dawn", "Spring Night Rain", "Evening Scenery of the Spring River in Huichong", "Spring Day", "It's Not Worth It to Visit the Garden" Pastoral scenes such as "Farewell to the Ancient Grassland" and "Quatrains": "Jiangnan", "Village Living", "Little Pond", "On the Pond", "Children's Fishing", "Pastoral Excitements in Four Seasons", "What I Saw", "Singing the Goose", "Recalling Jiangnan" "Mr. Shu Huyin's Wall" and "April in the Countryside" Wonderful scenery of mountains and rivers: "Looking at Lushan Waterfall", "Looking at Tianmen Mountain", "Looking for Flowers Alone by the River", "Mountain Walk", "Wang Taosha", "Cele Song", "Inscribed on the West Forest Wall" "Deer Chai" "Looking at the Dongting" The beacon fire at the frontier fortress: "Liangzhou Ci" (two poems) "Out of the fortress" "The song under the fortress" Deep nostalgia: "Quiet Night Thoughts" "Night Mooring on Maple Bridge" "Wandering Son's Song" "September" "Reminiscences of Shandong Brothers in Nine Days", "Mooring in Guazhou", "Early Departure from Baidi City", "Qingming Festival" and farewell: "Farewell to Xin Jian at Furong Tower", "Farewell to Yuan Er Envoy to Anxi", "Farewell to Wang Lun", "Farewell to Meng Haoran in Guangling", " Farewell to Dong Da" Life insights: "Le Youyuan", "Climbing the Stork Tower", "River Snow", "Fishermen's Song", "Bamboo and Stone", "Lime Ode", "Summer Quatrains", "Dark Plum", "Bee", "He who seeks hermit will not meet you" 》 Concerned about the country and the people: "Title of Lin'an Mansion", "Compassion for the Farmers" (two poems), "Spring in the South of the Yangtze River", "The Fisherman on the River", "Feelings of Coming Out of the Fence Gate to Welcome the Coolness at Dawn on an Autumn Night", "Miscellaneous Poems of Ji Hai", "Shi'er" "Children are lively, cute and innocent, and often become the writing objects of poets. Many of the ancient poems we have read write about children in ancient times, such as "The Matsushita asked the boy, and the teacher went to collect medicine" ("The one who seeks hermit is not found"), which writes about a young man who lives in seclusion in the mountains with his master. image. Can you still silently write out a few poems describing the lives of children in ancient times? Silence on the line below and write the title of the poem. The moon is beautiful and holy, giving people infinite reverie. Many poets in ancient my country wrote about the moon. Please select a verse with the word "moon" from the ancient poems you have read, and write it silently below.
1. Title () Author () 2. Title () Author () 3. Title () Author () After reading the article "Drizzle", can you use the ancient poems you have learned to describe your mood? Our grass, in that slender and weak body, actually contains such powerful vitality! No wonder the ancient poet wrote a poem about chanting grass: "____________________", thousands of years later, it is still exciting to read. Connect the following ancient sayings with proverbs and words with similar meanings. The beetles broke the trees and destroyed the walls. Practice makes perfect. It’s not worth the jade of a foot, but the yin of an inch. If the small hole is not repaired, the big hole will suffer. Play a thousand tunes and then the dawn will sound. Watch a thousand swords and then recognize the weapon. Teacher "One Inch of Time, One Inch of Gold" asks you to choose famous aphorisms or poems to decorate the walls of the classroom. What will you choose: _______________________
For example: ①Idiom expressing "high concentration":
Concentrate, concentrate, concentrate, and keep your eyes focused.
②Famous sayings that illustrate "humility":
Modernity will lead to losses, but humility will benefit. ——"Book. Dayu Mo"
Humility is based on strength, and arrogance is based on incompetence. ——[Germany] Nitz
Modility is the conscience of the body. ——[French] Balzac
The less you talk about your greatness, the more I will think of your greatness. ——[English] Francis Bacon
③Proverbs describing "accumulation":
A thousand small rivers become a big river; a rapid fire is not as slow as a slow sun; dust gathers to form a mountain; swallows carry mud into their nests .
④ Ancient poems describing "spring":
Du Fu's "Walking Alone by the River Looking for Flowers" Ye Shaoweng's "It's Not Worth It to Visit the Garden" He Zhizhang's "Ode to the Willows" Yang Wanli's "Suxin City" Xu Gongdian"
⑤ Ancient poems describing "parting":
Li Bai's "Farewell to Meng Haoran at the Yellow Crane Tower in Guangling" Li Bai's "Farewell to Wang Lun" Gao Shi's "Farewell to Dong Da" 》Wang Changling's "Farewell to Xin Jian in Furong Tower"
2. Guide students to correctly use accumulation.
Teachers purposefully create situations and design some learning activities to awaken students’ accumulation and allow students to use their accumulation correctly. For example:
(1) Hang "ancient poetry plaques" on the flowers, plants and trees in the school.
(2) Design slogans for the following places.
School cafeteria, gymnasium, library and reading room...
(3) Consolidate practice.
1. Carry out comprehensive Chinese learning activities, the content of which can include: idiom solitaire, idiom fill-in-the-blank, ancient poetry recitation, reflections after reading famous quotes, etc.
2. Write as required.
(1) Write idioms starting with the words "one", "hundred", "thousand", "sea", "no", "you", etc.
(2) Write an idiom that expresses "the integrity of revolutionary martyrs".
(3) Write an idiom that means "time flies too fast".
(4) Write two famous quotes about "reading is beneficial".
(5) Write two ancient poems "expressing patriotic enthusiasm".
(6) Write two ancient poems describing "autumn scenery".
(7) Write two ancient poems describing "friendship".
(8) Write two famous quotes about "cherishing time".
(9) Write two "farmer proverbs".
(10) Write two proverbs that reflect "climate".
3. Design slogans for the following places. You can use appropriate famous quotes or create your own.
(1) Music classroom:
(2) Laboratory:
(3) Gym:
Primary school mathematics graduation simulation test paper
1. Fill in the blanks
1. The hundreds of millions is the largest single digit, the tens of millions is 6, the tens of thousands is the smallest composite number, and the thousands is the smallest composite number. is the smallest prime number, and the remaining digits are 0. This number is ( ), rounded to hundreds of millions, it is recorded as ( ) billion.
2. Convert 6:1.8 into the simplest integer ratio ( ), and the ratio is ( ).
3. 3 hours = ( ) points 8.06 cubic meters = ( ) liters
4. A pile of chemical fertilizer has 6 tons. It should be divided among A, B, and A according to 1:3:4. There are three production teams in the country. Team A will be allocated (—) tons of this pile of fertilizer, and team B will be allocated ( ) tons.
5. A and B are 35 kilometers apart. The length drawn on a map is 7 cm. The scale of this map is ( ).
The least common multiple of 6, 24 and 54 is ( ), and the greatest common divisor is ( ).
7. The sixth grade students carried out a tree planting activity, 80 trees survived, and 5 trees did not survive. The survival rate is the best ( ).
8. The length of a rope is equal to its own length plus meters. The length of the rope is ( ) meters.
9. The total length of the cube's edges is 48 centimeters, its surface area is ( ) square centimeters, and its volume is ( ) cubic centimeters.
10. A can complete a job in 2 days alone. Based on this calculation, the remaining work will take ( ) days to complete.
11. If the height of a cylinder is shortened by 3 cm, the surface area will be reduced by 94.2 square centimeters. The radius of its base is ( ) centimeters, and its volume has been reduced by ( ) cubic centimeters.
2. Judgment
1. There are two symmetrical parallelograms. ( )
2. If x× =y×, then x:y= : ( )
3. Number A can be divisible by number B, and number B must be two The greatest common divisor of numbers. ( )
4. The working hours are fixed, and the time to manufacture each part is proportional to the number of parts. ( )
3. Choice. (Put the number of the correct answer in the brackets) (3 points)
1. 3.496 with two decimal places is approximately ( ).
①3.49 ②4.00 ③3.50
2. To type a manuscript, A takes 5 minutes and B takes 8 minutes. The simplest ratio of the work efficiency of A and B ( )
①5:8 ②8:5
4. Calculation
1. Write the number directly
5.4+8＝
9－2＝
9÷ 3 ×18＝
3.75＋1＝
2 ÷4＝
9.625 -1.375 =
1 ×1.5＝
(1-0.2÷1)÷0.5
2. Solve the equation.
①12-4x＝2
②38:x＝4.75:1
③ x＋x＝1.4
3. Use delivery, etc. formula calculation.
①308×16－14874÷37
②（3 + －2）×1
③3.5÷0.8×2.7+7.3÷1 < /p>
(4)9.8÷[28×(1- )+5]
4. Column calculation.
① Add 2.8 to a number, which equals 12.8. Find this number.
②What is the sum of 12% of 80 plus the quotient of 1.25 divided by ?
5. The following is a statistical chart of the number of boys and girls in the sixth grade of Hongqi Primary School. (1+2+2=5)
6. Application questions
1. A freight train and a passenger train depart from two places 504 kilometers apart at the same time and meet each other in 4.5 hours. The passenger car travels 64 kilometers per hour, how many kilometers per hour does the truck travel?
2. A certain washing machine factory planned to produce 504 washing machines in May. In fact, it completed 5/9 in the first half of the month and 2/3 in the second half of the month. How many washing machines were actually produced this month?
3. A can complete a project in 8 days, while B can complete it in 12 days. Now after A and B work together for 3 days, A will do the rest alone. How many more days will it take to complete?
4. There are 40 more peach trees than apricot trees in the orchard. The number of apricot trees is 80% of that of peach trees. How many peach trees are there?
5. A conical sand pile has a base area of ??3.6 square meters and a height of 1.2 meters.
If this pile of sand is placed in a sandpit that is 2 meters long and 1.5 meters wide, how high can it be filled?
6. The ratio of boys to girls participating in a mathematics competition in a school was 6:5. Later, 5 girls were added. At this time, the number of girls was 8/9 of the number of boys. How many girls actually participated in the math competition?
Chinese
1. Rewrite the sentences as required.
(1) Change the sentence into a rhetorical question.
1. We will never forget the kindness of the party.
2. Human beings need people who have the courage to practice.
3. This story moved me to tears.
4. The cute little girl is my good friend.
5. We will never forget this friendship that is higher than the mountains and deeper than the sea.
6. The slope is so steep that the train cannot climb it.
(2) Change the sentence into a declarative sentence.
1. Comrade Li Dazhao is full of confidence in the revolutionary cause, so how can he be afraid of reactionary warlords?
2. Him! You are an old man, why are you still ordering these things?
3. How can one hundred thousand arrows be made in three days?
4. You asked for it yourself, how can I help you?
5. Isn’t that a happy song played by the waves?
6. How can we forget the teacher’s teachings?
7. As long as Marie Curie signed the patent, wouldn’t all the difficulties be solved?
(3) Expand the sentences.
Example: Brand-new machines are manufacturing parts day and night.
1. The good news reached the school.
2. The train passes through the valley.
3. The spring breeze blows all over the earth.
4. People wave flowers.
5. My father is a worker.
6. I make a study plan.
7. Willow branches stirred the water.
(4) Abbreviate sentences.
1. Zhan Tianyou is an outstanding patriotic engineer in our country.
2. The loud bells echoed in the sky for a long time.
3. The beloved Premier Zhou cared for the young soldiers meticulously.
4. Zhou Yu, the governor of Wu State, was very jealous of the talented Zhuge Liang.
5. The silver snow shines on the endless prairie.
6. In summer, old people like to go fishing under the shade of the trees by the river.
7. The gift given to us by Father Time is precious.
(5) Change direct quotations into indirect quotations.
1. King Zhao told Lin Xiangru: "You have to take Baoyu to Qin."
2. Liu Ping told the teacher: "I will be in charge of this squadron. "
3. Wu Song said: "This is strange! Why don't you sell me wine?"
4. Lin Xiangru said: "I am not afraid of King Qin. Are you afraid of General Lian?"
5. She said deeply: "I was always shy when I was little."
(6) Change the sentence to "ba". words.
1. Wu Song quickly threw the whistle stick aside.
2. Every day, the classroom is cleaned cleanly by the students.
3. Xiaohua took away the math textbook.
4. Lin Xiangru defeated the King of Qin.
5. Lin Xiangru’s words and deeds of putting national interests first moved Lian Po.
(7) Change the sentence into a "bei" sentence.
1. Lin Xiangru defeated the King of Qin.
2. Lin Xiangru’s words and deeds of putting national interests first moved Lian Po
2. Zhuge Liang borrowed one hundred thousand arrows.
3. Wu Song finally killed the ferocious insect.
4. He quickly ate all the food taken from the broken ship.
5. Liu Hulan’s touching deeds deeply moved us.
(8) Comprehensive exercises.
1. The thick rosin glows golden in the sun. (Abbreviation)
2. Students answer the questions.
(Extended sentence)
3. Lin Xiangru said to King Zhao: "I am willing to take He's Bi to Qin." (Change to indirect speech)
4. Horse's A flying swallow is stepping on its hind hooves. (Replace with the word "quiet")
5. Grandpa said to Xiaoying: "I tell you, this is the most famous flower in China." (Indirect quotation)
6 , At that time, the Qing government was corrupt and incompetent. As soon as it proposed the construction plan of the "Beijing-Zhangjiakou" railway, the imperialists came out to obstruct and threaten it. (Replaced in terms of "causal relationship")
7. The sun rises. (Extended sentence)
8. I think the King of Qin is not sincere, so I have to send the Heshi Bi back to the State of Zhao. (Change to rhetorical question)
9. Isn’t that a happy song played by the waves? (Change to rhetorical question)
10. These three grams of radium embody the great personality of a scientist. (Change to exclamation, rhetorical question, double negative)
11. What is the use of money on an isolated island?
2. How to use dashes.
① Explanation; ② Indicates a change of meaning; ③ Indicates the prolongation of the sound.
(1) This is the last day of the year - New Year's Eve. ( )
(2) There was a smell of roasted moths floating in the street, because it was New Year's Eve - she couldn't forget this. ( )
(3) Those were a pair of big slippers - so big, they were always worn by her mother. ( )
(4) On the eve of the 50th anniversary of its founding, the United Nations received a precious birthday gift - a giant bronze vessel - the "Century Tripod" presented by 1.2 billion Chinese people. ( )
(5) Although there are not many children - only two. ( )
3. Usage of ellipses.
3. Text perception and understanding.
(1)
Bu Suanzi
Yong Mei
Mao Zedong
, . There are already hundreds of feet of ice on the cliff, but there are still beautiful flowers and branches.
, . When the mountain flowers were in full bloom, she smiled among the bushes.
(1) Complete the words according to the words.
(2) "Yong Mei" is a poem. Among them, the sub-word brand name is , and the title is . This poem was written by Mao Zedong after reading the poem "Plum Blossoms" written by Mao Zedong.
(3) Talk about it; list the sentences that describe the characteristics of plum blossoms and praise the character of plum blossoms.
1. The cliff is already covered with hundreds of feet of ice, but there are still beautiful flowers and branches.
2. When the mountain flowers were in full bloom, she smiled in the bush.
(2)
(1) "A hundred rivers flow eastward to the sea, . If a young man does not work hard, ." These lines are selected from " ", which is a Yuefu poem written by the author It is used as a metaphor for the rapid passage of time, and I encourage people to use it. From it, you realize
.
(2) "The buds are there, the beans are there. The original is here, why be too hasty?" The poem is selected from Cao Zhi's " of( ) .
(3)
Going out of the fortress
Wang Changling
The bright moon in the Qin Dynasty led to a long march of thousands of miles.
But the flying generals of Dragon City are here, and they don’t teach Hu Ma.
Must memorize the definition theorem and formula
(3) Ancient Chinese
1. Fill in the blanks and explain the words filled in.
(1) The Chu people ( ) used shields and spears, ( ) said: ( ) The shield is so strong that nothing can defeat it ( ).
(2) If the Zheng people have and place ( ), they should first sit on their feet ( ), and then forget ( ) when they reach ( ).
2. Connect the meanings of the following classical Chinese texts in modern texts with lines.
There are people who can’t help it
Maybe it’s a sub-market
Then what’s wrong with me
I’ll tell you how the market is
>3. Read it. Write the meaning of the sentence.
(1) My shield is so strong that nothing can trap it.
(2) The sharpness of my spear can trap everything.
(3) How about using Zi’s spear and trapping Zi’s shield?
(4) When you get to the market, you forget to deal with it.
(5) Why not give it a try?
(6) What is the reason why Zi Zhizi wins?
(7) Yes, keep it and don’t lose it.
Volume and surface area
The area of ??a triangle = base × height ÷ 2. Formula S= a×h÷2
The area of ??a square = side length × side length Formula S= a2
The area of ??a rectangle = length × width Formula S= a×b
p>The area of ??the parallelogram = base × height formula S = a × h
The area of ??the trapezoid = (upper base + lower base) × height ÷ 2 formula S = (a + b) h ÷2
Sum of interior angles: The sum of interior angles of a triangle = 180 degrees.
The surface area of ??the cuboid = (length × width + length × height + width × height) × 2 Formula: S = (a × b + a × c + b × c) × 2
< p>Surface area of ??the cube = Edge length × Edge length × 6 Formula: S = 6a2Volume of the cuboid = Length × Width × Height Formula: V = abh
Cuboid (or cube ) = base area × height formula: V = abh
Volume of the cube = edge length × edge length × edge length formula: V = a3
Perimeter of the circle = diameter ×π formula: L＝πd＝2πr
The area of ??a circle = radius × radius × π formula: S＝πr2
The surface (side) area of ??the cylinder: the surface (side) area of ??the cylinder ) area is equal to the perimeter of the base multiplied by the height. Formula: S=ch=πdh=2πrh
Surface area of ??a cylinder: The surface area of ??a cylinder is equal to the circumference of the base multiplied by the height plus the area of ??the circles at both ends. Formula: S=ch+2s=ch+2πr2
The volume of a cylinder: The volume of a cylinder is equal to the base area times the height. Formula: V=Sh
The volume of the cone = 1/3 base × area height. Formula: V=1/3Sh
Arithmetic
1. Commutative law of addition: When two numbers are added, the positions of the addends are exchanged, and the sum remains unchanged.
2. Associative law of addition: a + b = b + a
3. Commutative law of multiplication: a × b = b × a
4. Multiplication Associative law: a × b × c = a × (b × c)
5. Distributive law of multiplication: a × b + a × c = a × b + c
6 , Properties of division: a ÷ b ÷ c = a ÷ (b × c)
7. Properties of division: In division, the dividend and divisor expand (or shrink) by the same multiple at the same time, and the quotient is not Change. O divided by any number that is not O is O. Simple multiplication: For multiplications with O at the end of the multiplicand and multiplier, you can multiply the ones before the O first. Zeros do not participate in the operation. Several zeros are dropped and added to the end of the product.
8. Division with remainder: dividend = quotient × divisor + remainder
Equations, algebra and equality
Equation: the value on the left side of the equal sign and An equation in which the values ??on the right side of the equal sign are equal is called an equation. Basic properties of equations: If both sides of the equation are multiplied (or divided) by the same number at the same time, the equation still holds.
Equation: An equation containing unknown numbers is called an equation.
Linear equation of one variable: An equation that contains an unknown number and the degree of the unknown is linear is called a linear equation of one variable. Learn the examples and calculations of linear equations of one variable. That is, give an example of the formula with χ and calculate it.
Algebra: Algebra is the use of letters instead of numbers.
Algebraic expression: An expression represented by letters is called an algebraic expression. For example: 3x =ab+c
Fraction
Fraction: Divide the unit "1" evenly into several parts, and the number that represents such a part or several points is called a fraction.
Comparison of fractions: Compared with fractions with the same denominator, the one with the larger numerator is larger and the one with the smaller numerator is smaller. When comparing fractions with different denominators, first make the common denominator and then compare; if the numerators are the same, the one with the larger denominator will be smaller.
The rules for adding and subtracting fractions: When adding and subtracting fractions with the same denominator, only add and subtract the numerators, leaving the denominator unchanged. To add and subtract fractions with different denominators, first add and subtract the common denominators.
When multiplying a fraction by an integer, use the product of the numerator of the fraction and the integer as the numerator, and the denominator remains unchanged.
To multiply a fraction by a fraction, use the product of the numerators as the numerator, and the product of the denominators as the denominator.
The rules for adding and subtracting fractions: When adding and subtracting fractions with the same denominator, only add and subtract the numerators, leaving the denominator unchanged. To add and subtract fractions with different denominators, first add and subtract the common denominators.
The concept of reciprocal: 1. If the product of two numbers is 1, we say one is the reciprocal of the other. These two numbers are reciprocals of each other. The reciprocal of 1 is 1, and there is no reciprocal of 0.
Dividing a fraction by an integer (other than 0) is equal to multiplying the fraction by the reciprocal of the integer.
The basic properties of fractions: the numerator and denominator of a fraction are multiplied or divided by the same number (except 0) at the same time, the size of the fraction
The division method of fractions: divide by a number (except 0), which is equal to multiplying the reciprocal of this number.
Proper fraction: The fraction whose numerator is smaller than the denominator is called a proper fraction.
Improper fractions: A fraction whose numerator is greater than the denominator or whose numerator and denominator are equal is called an improper fraction. An improper fraction is greater than or equal to 1.
Mixed numbers: Writing improper fractions in the form of integers and proper fractions is called mixed numbers.
Basic properties of fractions: If the numerator and denominator of a fraction are multiplied or divided by the same number (except 0) at the same time, the size of the fraction remains unchanged.
Quantity relationship calculation formula
Unit price × quantity = total price 2. Unit output × quantity = total output
Speed ??× time = distance 4. Work efficiency × time = total amount of work
Addend + addend = sum one addend = sum + another addend
Minuend - Minuend = Difference Minuend = Minuend - Difference minuend = subtrahend + difference
Factor × factor = product one factor = product ÷ another factor
Divisor ÷ divisor = quotient divisor = dividend ÷ quotient dividend = quotient × Divisor
Unit of length:
1 kilometer = 1 kilometer 1 kilometer = 1000 meters
1 meter = 10 decimeters 1 decimeter = 10 centimeters 1 Centimeter = 10 millimeters
Area unit:
1 square kilometer = 100 hectares 1 hectare = 10,000 square meters
1 square meter = 100 square decimeters 1 Square decimeter = 100 square centimeters 1 square centimeter = 100 square millimeters
1 mu = 666.666 square meters.
Unit of volume
1 cubic meter = 1000 cubic decimeters 1 cubic decimeter = 1000 cubic centimeters
1 cubic centimeter = 1000 cubic millimeters
1 liter = 1 cubic decimeter = 1000 ml 1 ml = 1 cubic centimeter
Unit of weight
1 ton = 1000 kilograms 1 kilogram = 1000 grams = 1 kilogram = 1 Shijin
ratio
What is ratio: The division of two numbers is called the ratio of the two numbers. For example: 2÷5 or 3:6 or 1/3. The first and last terms of the ratio are multiplied or divided by the same number (except 0) at the same time, and the ratio remains unchanged.
What is proportion: The formula that expresses the equality of two ratios is called proportion. For example, 3:6=9:18
The basic property of proportion: In proportion, the product of two external terms is equal to the product of two internal terms.
Solving the proportion: Finding the unknown items in the proportion is called solving the proportion. For example, 3:χ=9:18
Positive proportion: two related quantities, one quantity changes, and the other quantity also changes. If the corresponding ratio of the two quantities ( That is to say, if the quotient k) is certain, these two quantities are called directly proportional quantities, and their relationship is called a directly proportional relationship. For example: y/x=k (k is certain) or kx=y
Inverse proportion: two related quantities, if one quantity changes, the other quantity will also change. If these two quantities The product of two corresponding numbers in is constant, these two quantities are called inversely proportional quantities, and their relationship is called an inversely proportional relationship.
For example: x×y = k (k is certain) or k / x = y
Percent
Percent: A number that expresses what percentage of another number a number is, called percentage. Percentage is also called percentage or percentage.
To convert a decimal into a percentage, just move the decimal point two places to the right and add a percent sign at the end. In fact, to convert a decimal into a percentage, just multiply the decimal by 100%. To convert a percentage to a decimal, just remove the percent sign and move the decimal point two places to the left.
To convert a fraction into a percentage, usually first convert the fraction into a decimal (when division cannot be completed, usually three decimal places are retained), and then convert the decimal into a percentage. In fact, to convert a fraction into a percentage, you first need to convert the fraction into a decimal and then multiply it by 100%.
To convert a percentage into a fraction, first rewrite the percentage into a fraction, and then reduce the ratio that can be reduced to the simplest fraction.
You must learn to convert decimals into fractions and fractions into decimals.
Multiples and Divisors
Greatest common divisor: The common divisor of several numbers is called the common divisor of these numbers. There are a finite number of common factors. The largest one is called the greatest common divisor of these numbers.
Least common multiple: The common multiple of several numbers is called the common multiple of these numbers. There are an infinite number of common multiples. The smallest one is called the least common multiple of these numbers.
Co-prime numbers: Two numbers whose common divisor is only 1 are called co-prime numbers. Two adjacent numbers must be mutually prime. Two consecutive odd numbers must be relatively prime. 1 is relatively prime to any number.
Common fraction: converting fractions with different denominators into fractions with the same denominator that are equal to the original fraction is called a common fraction. (Use the least common multiple for common fractions)
Reduction: Divide the numerator and denominator of a fraction by a common factor at the same time. The fraction value remains unchanged. This process is called reduction.
Simplest fraction: A fraction whose numerator and denominator are coprime numbers is called the simplest fraction. At the end of the fraction calculation, the number must be converted into the simplest fraction.
Prime number (prime number): If a number has only two divisors, 1 and itself, such a number is called a prime number (or prime number).
Composite number: If a number has other divisors besides 1 and itself, such a number is called a composite number. 1 is neither a prime number nor a composite number.
Prime factors: If a prime number is a factor of a certain number, then the prime number is the prime factor of the number.
Decomposing prime factors: Expressing a composite number in terms of prime factors is called decomposing prime factors.
Characteristics of multiples:
Characteristics of multiples of 2: Each bit is 0, 2, 4, 6, 8.
Characteristics of multiples of 3 (or 9): The sum of the numbers in each digit is a multiple of 3 (or 9).
Characteristics of multiples of 5: Each bit is 0, 5.
Characteristics of multiples of 4 (or 25): the last two digits are multiples of 4 (or 25).
Characteristics of multiples of 8 (or 125): the last three digits are multiples of 8 (or 125).
Characteristics of multiples of 7 (11 or 13): The difference (big-small) between the last three digits and the remaining digits is a multiple of 7 (11 or 13).
Characteristics of multiples of 17 (or 59): The difference (big-small) between the last 3 digits and 3 times the remaining digits is a multiple of 17 (or 59).
Characteristics of multiples of 19 (or 53): The difference (big-small) between the last 3 digits and 7 times the remaining digits is a multiple of 19 (or 53).
Characteristics of multiples of 23 (or 29): The difference (big-small) between the last 4 digits and 5 times the remaining digits is a multiple of 23 (or 29).
For two numbers in a multiple relationship, the greatest common divisor is the smaller number, and the least common multiple is the larger number.
For two numbers that are mutually prime, their greatest common divisor is 1 and their least common multiple is their product.
When two numbers are divided by their greatest common divisor, the resulting quotients are relatively prime.
The product of two numbers and their least common multiple is equal to the product of the two numbers.
The common divisor of two numbers must be the divisor of the greatest common divisor of the two numbers.
1 is neither a prime number nor a composite number.
Use 6 to divide prime numbers greater than 3, and the result must be 1 or 5.
Odd and even numbers
Even numbers: Numbers whose ones digit is 0, 2, 4, 6, or 8.
Odd numbers: numbers whose units digit is not 0, 2, 4, 6, or 8.
Even number ± even number = even number Odd number ± odd number = odd number Odd number ± even number = odd number
The sum of an even number of even numbers is an even number, and the sum of an odd number of odd numbers is an odd number.
Even number × even number = even number Odd number × odd number = odd number Odd number × even number = even number
The sum of two adjacent natural numbers is an odd number, and the product of adjacent natural numbers is an even number.
If one of the numbers in the multiplication is an even number, then the product must be an even number.
Odd number ≠ even number
Divisible
If c|a, c|b, then c|(a±b)
If , then b|a, c|a
If b|a, c|a, and (b, c)=1, then bc|a
If c|b, b|a, then c|a
Decimals
Natural numbers: Integers used to represent the number of objects are called natural numbers. 0 is also a natural number.
Pure decimal: a decimal whose ones digit is 0.
With decimals: decimals with each digit greater than 0.
Recurring decimal: A decimal, starting from a certain digit of the decimal part, one number or several numbers appear repeatedly in sequence. Such a decimal is called a recurring decimal. Such as 3. 141414
Non-recurring decimal: A decimal, starting from the decimal part, does not have a number or several digits that repeatedly appear in sequence. Such a decimal is called a non-recurring decimal. Such as 3. 141592654
Infinitely recurring decimal: A decimal, from the decimal part to an infinite number of digits, one number or several numbers appear repeatedly in sequence. Such a decimal is called an infinitely recurring decimal. Such as 3. 141414...
Infinite non-recurring decimals: A decimal, starting from the decimal part to an infinite number of digits, without one number or several numbers repeating in sequence, such a decimal is called infinite non-recurring decimal. Such as 3. 141592654...
Profit
Interest = principal × interest rate × time (time is generally in years or months, which should correspond to the unit of interest rate)
Interest rate: The ratio of interest to principal is called interest rate. The ratio of one year's interest to the principal is called the annual interest rate. The ratio of one month's interest to the principal is called the monthly interest rate.
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