Mathematical formula and definition of grade one to grade six in primary school (PEP)

Mathematical formula and definition of grade one to grade six in primary school (PEP)

The basic formula of mathematics formula of grade one to grade six of primary school is: 1. Number of each piece × number of copies = total number of copies

PEP 1 ~ 6 grade Chinese review materials, 1 ~ 6 grade mathematics concept, 3 ~ 6 grade English four words sentence, 3 ~ 6 grade science concept Thank you

Mathematics: 1. Number of copies × number of copies = total number
Total number △ number of copies = number of copies
Total number of copies = number of copies
21 times × multiple = several times
Several times △ 1 times = Multiple
Several times △ times = 1 times
3 speed x time = distance
Distance △ speed = time
Distance △ time = speed
4 unit price × quantity = total price
Total price / unit price = quantity
Total price / quantity = unit price
5 work efficiency x working time = total work
Total work △ work efficiency = working time
Total work × working time = work efficiency
6 addend + addend = and
Sum - one addend = another
7 minuend minus = difference
Minus minus = minus
Difference + subtraction = minuend
8 factor × factor = product
Product △ one factor = another
9 divisor △ divisor = quotient
Divisor △ quotient = divisor
Quotient × divisor = divisor
Primary school mathematics figure calculation formula
1 square
C perimeter s area a side length
Perimeter = side length × 4
C=4a
Area = side length × side length
S=a×a
Cube 2
5: Volume a: edge length
Surface area = edge length × edge length × 6
S table = a × a × 6
Volume = edge length × edge length × edge length
V=a×a×a
3 rectangle
C perimeter s area a side length
Perimeter = (length + width) × 2
C=2(a+b)
Area = length × width
S=ab
4 cuboid
5: Volume s: Area A: length B: width H: height
(1) Surface area (L × W + L × H + W × h) × 2
S=2(ab+ah+bh)
(2) Volume = length × width × height
V=abh
5 triangle
S area a bottom h height
Area = bottom × height △ 2
s=ah÷2
Triangle height = area × 2 △ bottom
Triangle base = area × 2 △ height
6 parallelogram
S area a bottom h height
Area = bottom × height
s=ah
7 trapezoid
S area a upper bottom B bottom h height
Area = (bottom + bottom) × height △ 2
s=(a+b)× h÷2
8 round
S area C circumference Π d = diameter r = radius
(1) Circumference = diameter ×Π = 2 ×Π × radius
C=∏d=2∏r
(2) Area = radius x radius x Π
9 cylinder
v: Volume H: height s; bottom area R: bottom radius C: bottom perimeter
(1) Side area = perimeter of bottom surface × height
(2) Surface area = side area + bottom area × 2
(3) Volume = bottom area × height
(4) Volume = side area △ 2 × radius
Cone 10
v: Volume H: height s; bottom area R: bottom radius
Volume = bottom area × height △ 3 total number △ total number = average number
The formula of sum difference problem
(sum + difference) △ 2 = large number
(sum difference) 2 = decimal
The problem of sum times
And △ (multiple-1) = decimal
Decimal × multiple = large number
(or sum decimal = large number)
Differential multiple problem
Difference × (multiple-1) = decimal
Decimal × multiple = large number
(or decimal + difference = big tree planting problem
1. Tree planting on non closed lines can be divided into the following three situations:
(1) if trees are to be planted at both ends of an unclosed line, then:
Number of plants = number of segments + 1 = total length △ plant spacing-1
Total length = plant spacing × (number of plants - 1)
Spacing = 1
(2) if trees are to be planted at one end of an unclosed line and not at the other end, then:
Number of plants = number of segments = total length × plant spacing
Total length = spacing × number of trees
Plant spacing = total length △ number of trees
(3) if trees are not planted at both ends of the unclosed line, then:
Number of plants = number of segments-1 = total length × plant spacing-1
Total length = plant spacing × (number of plants + 1)
Plant spacing = total length × (number of plants + 1)
2. The quantitative relationship of tree planting on closed lines is as follows
Number of plants = number of segments = total length × plant spacing
Total length = spacing × number of trees
Plant spacing = total length △ number of trees
Profit and loss
(profit + loss) × the difference between the two distributions = the number of shares participating in the distribution
(large profit small profit) × the difference between the two distributions = the number of shares participating in the distribution
(large deficit small deficit) × the difference between the two distributions = the number of shares participating in the distribution
Encounter problem
Encounter distance = speed and X encounter time
Encounter time = encounter distance △ speed sum
Speed sum = encounter distance △ encounter time
Follow up on Problems
Chase distance = speed difference × pursuit time
Catching time = chasing distance △ speed difference
Speed difference = pursuit distance ×pursuit time
Flow problems
Downstream velocity = still water velocity + current velocity
Countercurrent velocity = still water velocity current velocity
Still water velocity = (downstream velocity + countercurrent velocity) × 2
Flow velocity = (downstream velocity - countercurrent velocity) × 2
Concentration problem
Weight of solute + weight of solvent = weight of solution
Weight of solute × weight of solution × 100% = concentration
Weight of solution × concentration = weight of solute
Weight of solute △ concentration = weight of solution
Profit and discount
Profit = selling price - cost
Profit rate = profit ＋ cost × 100% = (selling price ＋ cost-1) × 100%
Up / down amount = principal × up / down percentage
Discount = actual price × original price × 100% (discount < 1)
Interest = principal × interest rate × time
After tax interest = principal × interest rate × time × (1-20%)
Ancient Chinese Poetry:
Jiangnan
Yuefu in Han Dynasty
Jiangnan can pick lotus, lotus leaf He Tian Tian
Fish playing with lotus leaves East, fish playing with lotus leaves West,
Fish play lotus leaf south, fish play lotus leaf north
Geese
lo bingwang
Goose, goose, goose, song Xiang Tian song,
White hair floating green water, red palm dial clear wave
Chanting willows
he zhizhang
Jasper make up a tree height, 10000 hanging green silk ribbon
I don't know who cut the thin leaves? The spring breeze in February is like scissors
Climbing stork tower
wang zhihuan
The sun beyond the mountains glows; the Yellow Riverseawards flows.
You can enjoy a grander sight by climbing to a greater height.
Liangzhou Ci
Wang Han
Grape wine luminous cup, to drink Pipa immediately urge
Don't laugh when you are drunk on the battlefield. How many people have been fighting since ancient times?
Seeing Xin Jian off at Lotus tower
wang changling
Cold rain lianjiang night into Wu, pingming send off guests Chu mountain alone
Luoyang relatives and friends such as asked, a piece of ice in the jade pot
Chile song
Folk songs of Northern Dynasties
Chilechuan, under the Yinshan Mountain,
The sky is like a vault, covering all fields
The sky is blue and the wild is vast,
Cattle and sheep can be seen in the wind and grass
wind
Li Qiao
Fall off three autumn leaves, can bloom in February
A thousand feet of waves cross the river, into the bamboo ten thousand rod slant
Liangzhou Ci
wang zhihuan
The Yellow River is far up among the white clouds, a lonely city of ten thousand Ren mountain
Why should the Qiang flute blame the willows? The spring breeze does not pass the Yumen pass
spring morning
meng haoran
Spring sleep not aware of dawn, everywhere heard the birds
The sound of wind and rain at night, how many flowers fall?
Out of the way
wang changling
Qin Ming moon Han Guan, the long march has not been returned
But make the Dragon City Flying general in, don't teach Hu Ma Du Yin Mountain
Luchai
Wang Wei
No one is seen in the empty mountains, but the sound of their voices is heard
Back into the deep forest, the moss again
Send yuan Er to Anxi
Wang Wei
Weicheng morning rain light dust, guest house green willow color new
Advise you to make a glass of wine, West out of Yangguan no old friend
Memory of Shandong brothers on September 9
Wang Wei
I am a stranger in a foreign land, and I miss my relatives every holiday
Distant know brother ascends the high place, insert dogwood all over, less one person
In the Quiet Night
Li Bai
The moon in front of the bed is the frost on the ground
Raising my head, I see the moon so bright; withdrawing my eyes, my nostalgia comes around.
Gulang's monthly trip
Li Bai
Hours do not know the moon, called white jade plate
Also suspected Yao Tai mirror, flying in the blue cloud end
Wanglushan waterfall
Li Bai
In front of Zichuan, there is a waterfall
Flying down three thousand feet, it is suspected that the Milky way is falling nine days
To Wang Lun
Li Bai
Li Bai was about to go on a boat when he heard the sound of singing on the bank
Taohuatan deep thousands of feet, not as good as Wang Lun send me love
The Yellow Crane Tower sends Meng Haoran to Guangling
Li Bai
The old man West Yellow Crane Tower, fireworks in March Yangzhou
Lonely sail far shadow blue sky, only see the Yangtze river skyline flow
Early departure of Baidi City
Li Bai
The White Emperor's farewell to the imperial palace is still a thousand miles away
The boat passed thousands of mountains with apes shouting without endless.
Looking at Tianmen Mountain
Li Bai
The gate of heaven is interrupted by the Chu River, and the clear water flows eastward to the north
The green hills on both sides of the Strait are opposite, and a single sail is coming from the sun
Another Dong Da
Gao Shi
Thousands of miles of yellow clouds daytwilight, north wind blowing geese snow one after another
Don't worry about the road ahead without a confidant. Who in the world doesn't know you?
Quatrains
Du Fu
Two orioles sing green willows, a row of egrets on the blue sky
Window with Xiling Qianqiu snow, door Park East Wu Wan Li ship
Spring night rain
Du Fu
Good rain knows the season, when spring is happening
Sneak into the night with the wind, moisten things silently
Wild path cloud all black, river boat fire alone bright
When it is dawn, the damp soil will be covered with red petals, and there will be countless colorful flowers in the streets and alleys.
Quatrains
Du Fu
In the late days, the rivers and mountains are beautiful, and the spring breeze and flowers are fragrant
Swallows flying in the mud, mandarin ducks sleeping in the sand
Looking for flowers by the river
Du Fu
Huangshi Pagoda in front of the river east, lazy spring sleepy lean breeze
Peach blossom a cluster of ownerless, lovely crimson love light red
To Moor at Night at the Maple Bridge
Zhang Ji
The moon is falling and the sky is full of frost, and the river Maple fishing fire is sleeping in sorrow
Hanshan Temple outside the city of Gusu, the bell rings to the passenger ship in the middle of the night
Wandering chant
Mengjiao
Mother's hand thread, wandering body jacket
I'm afraid I'll come back late
Who said inch grass heart, reported the three Chunhui
River Snow
Liu Zongyuan
Thousands of mountains of birds fly away, thousands of paths of people disappear
A lone boat with a coir hat and an old man fishing alone for snow in the cold river
Fisherman's song
Zhang Zhihe
In front of the Xisai mountain egrets fly, peach blossom water, mandarin fish fat
Green reed hat, green coir raincoat, no need to return
LuLun
The wild geese fly high on the moon and flee alone at night
I will ride with a sword
Wang Dongting
Liu Yuxi
Lake light Autumn Moon two phase and, pool surface no wind mirror not grinding
Looking at the green landscape of Dongting, there is a green snail in the silver plate
The waves wash the sand
Liu Yuxi
Jiuqu Yellow River thousands of miles of sand, waves and winds from the end of the world
Now straight to the Milky way, with the Altair Zhinv home
Send off the ancient grass
Bai Juyi
From the lush grass on the plains in one year, withers and thrives once each year.
The wildfire can't burn out, and the spring wind blows again
Far Fang invades the ancient road, the green meets the desolate city
He sent Wang and sun, and Qiqi was full of farewell
Ikegami
Bai Juyi
The little baby supports the small boat, stealthily picks the white lotus to return
Do not understand the hidden traces, duckweed open together
Recalling Jiangnan
Bai Juyi
The south of the Yangtze River is good, and the scenery is old
At sunrise, the flowers are as red as fire, and in spring the water is as green as blue
Can you not remember Jiangnan?
Children's fishing
Hu lingneng
Pengtou children learn to hang Lun, sit on the side of the strawberry table grass reflecting the body
Passers-by beckons at the distance, afraid of fish should not be startled
Be merciful to agriculture
Li Shen
When weeding, sweat drips under the soil
Who knows that the dishes are hard
Seeking out Hermit without success
Jiadao
beneath the pine I asked the boy, he said master's out collecting herbs.
just somewhere in this mountain here, but deep clouds set me wondering where.
mountaintrip
Du Mu
Far up the cold mountain, the stone path is inclined, and there are people living in Baiyun
Park and sit in the maple forest late, frost leaves are red than February flowers
Qingming
Du Mu
A drizzling rain falls like tears on the Mourning Day; The mourner's heart is going to break on his way.
Where can a wineshop be found to drown his sad hours? A cowherd points to a cot mid apricot flowers.
Jiang nanchun
Du Mu
Thousands of miles Yingying green Yinghong, water village shanguo wine flag wind;
Four hundred and eighty temples in the Southern Dynasty, how many towers in the misty rain
Leyouyuan
Li Shangyin
Feeling uncomfortable in the evening, I drove to Guyuan
The setting sun is infinitely good, but near dusk
bee
Luo Yin
Regardless of the plain and the peak, the infinite scenery is occupied
After gathering flowers into honey, for whom hard work, for whom sweet
Fishermen on the river
Fan Zhongyan
The river people, but love bass beauty
You see a leaf boat, haunting in the storm
Wang Anshi
In the sound of firecrackers, the spring breeze brings warmth to Tu su,
Thousands of households in the sun, always the new peach for the old symbol
Berthing at Guazhou
Wang Anshi
Between the waters of Guazhou in Jingkou, Zhongshan is only separated by several heavy mountains
Spring breeze and green river south bank, the moon when I return
Shuhuyin Mr. wall
Wang Anshi
Grass eaves long sweep without moss, flowers and trees into a bed, hand cut
A water field protection will be around the green, two mountains to send green
June 27, Wanghu tower drunk book
Su Shi
Black clouds turn ink not cover the mountains, white rain jump into the boat
The wind of the rolling ground blows suddenly, and the water in the lake tower is like the sky
Drink on the lake, after the first clear rain
Su Shi
The water is bright and sunny, and the mountains are clear and rainy
If you want to compare the West Lake with the West Lake, it's always appropriate to make up light and heavy
Spring River in huichong
Su Shi
Bamboo peach blossom three or two branches, spring river warm duck prophet
Artemisia, reed bud is short, puffer fish is ready to go
On the wall of Xilin
Su Shi
As a peak on the side of the ridge, the distance is different
I don't know the true face of Lushan Mountain, but I live in it
Summer quatrains
Li Qingzhao
Life is a hero and death is a ghost
Up to now, he has been thinking of Xiang Yu and refused to cross Jiangdong
Sheer
Lu You
Death yuan know everything empty, but sad with Kyushu
Wang Shi North Central Plains day, family sacrifice without forgetting to sue naiweng
Autumn night will dawn out of the fence door to welcome the cool
Lu You
Thirty thousand li River East into the sea, five thousand Ren mountain skyscrapers
The adherents shed tears and looked at Wang Shi for another year
The countryside flourished in the four seasons
Fan Chengda
Day out of the field, night Jima, village children each head
Children and grandchildren did not understand for farming and weaving, but also learn to grow melons by mulberry shade
Small pool
Yang Wanli
Spring silent, cherish the stream, tree shade light water, love sunny soft
Small lotus just show sharp horn, dragonfly stands on the head
Seeing Lin Zifang off at Jingci Temple
Yang Wanli
After all, the scenery of the West Lake in June is different from that of the four seasons
Next to the sky, the lotus leaves are boundless blue, and the lotus flowers are different in color
Spring day
Zhu Xi
SHENGRI to find Fangsi waterfront, boundless scenery is new
When you know the east wind, you will always be in spring
On Lin'an residence
Lin Sheng

The determinant of linear algebra is proved by mathematical induction cosα 1 1 2cosα 1 1 2cosα 1 Dn=| ...|=cosnα ... ... 1 2cosα 1 1 2cosα

Obviously, when n = 1, the determinant is cosa, and when n = 2, the determinant is equal to cosa * 2cosa - 1 = cos2a
We start with the last line of this determinant, obviously
For the last 2cosa, the corresponding cofactor = D (n-1)
For the 1 in the last row, if the corresponding cofactor is s (n-1), then
D(n) = 2cosa D(n-1) - S(n-1)
S(n-1) = 2cosaD(n-1) - D(n)
S(n) = 2cosa D(n) -D(n+1)
If the proposition holds for all N, then
S(n) = 2cosa cos(k)a -cos(k+1)a
Obviously, when n = 2, the matrix corresponding to s (2) is
cosa 0
11
S(2)= cosa
And 2cosa cos2a - cos (2 + 1) a = 2cosa cos2a - cos2a cosa + sin2asina = cos2acosa + sin2asina = cosa
So s (n) = 2cosa cos (k) a - cos (K + 1) a holds when n = 2
We assume that for n

The following determinants are proved by mathematical induction

If n = 1, let (AIJ) = a, (bij) = B, and the determinant on the left side of the equation is g (n). Suppose n-1 holds, that is, G (n-1) = a (n-1) times b (n-1). Then, when n, expand according to the first row, G (n) = all a1i multiply its algebraic cofactors in G (n) and sum, and the algebraic cofactors of each a1i in G (n) are equal to a

Find the real number a so that the following equation holds for all positive integers, and prove your conclusion 1 / (1 × 2 × 3) + 1 / (2 × 3 × 4) +. + 1 / (n × n + 1 × n + 2) = (N2 + an) / (4 × n + 1 × n + 2) It's all written down... Big guy... 100 more after that

Add the sum by adding
1/n(n+1)(n+2)
=1/2[2/n(n+1)(n+2)]
=1/2[(n+2)-n]/n(n+1)(n+2)]
=(1/2)[(n+2)/n(n+1)(n+2)-n/n(n+1)(n+2)]
=(1/2)[1/n(n+1)-1/(n+1)(n+2)]
So sum = (1 / 2) [1 / 1 * 2-1 / 2 * 3 + 1 / 2 * 3-1 / 3 * 4 + +1/n(n+1)-1/(n+1)(n+2)]
=(1/2)[1/1*2-1/(n+1)(n+2)]
=n(n+3)/[4(n+1)(n+2)]
Proof of mathematical induction, I don't think you'll have a problem yourself

1. Write the conditions for the following equation （1）√x(x-1)=√x*√x-1. "√" means root sign

X (x-1) ≥ 0, and X ≥ 0, and X-1 ≥ 0, X ≥ 1

The following equation must hold A. The third power of the root a × the third power of the root - B = - AB the root AB B. the square of the root a / the cubic power of the root - B = the square of a / b × the root - ab

A is certain, B is not. Because the sign of the square root of a number is the same as that of the original number, but the square root is not

0

2^6-1=63

Math problem 23-7 = 1 move a number to make the equation true

The third power of 2 - 7 = 1

Move a match to make the equation true 12 times 9 times 9 = 288 129-6 times 8 = 9 times 8 The multiplier signs are matchsticks, and the crossed numbers are spelled with matchsticks. For example, the appearance of 8 is equivalent to the Chinese character "day"

12 * 3 * 8 = 288 or 12 * 8 * 3 = 288 move a match from one of the two 9s to the other 9 to make them 3 and 8, respectively
120-6 * 8 = 9 * 8 change 9 of 129 to 0