Windows 7 Ultimate Key Practical knowledge of secu

At present, WIN2000 SERVER is additional common server operating systems, in spite of this, for the safe configuration of Microsoft's operating program, is not an easy task. This write-up attempts to win2000 SERVER safety configuration was talked about.

Very first, customise their WIN2000 SERVER:

1. Model of selection: Win2000 many different languages, for us, it is easy to decide on English or Simplified Chinese model, I strongly suggest: The language doesn't turn out to be a barrier, make sure to use the English version. You know, Microsoft's product is identified for Bug & Patch, much far more than the Chinese version of the Bug in English, while the patch will be delayed at least half of the general (ie, generally after Microsoft announced the vulnerability of your machine is also there will be two weeks in the unprotected state)

2. Custom components:

Win2000 installed by default in some typical components, but it really is the default installation is extremely dangerous (Mitre Nico said that he can enter any one installed by default server, although I hesitate to say so, but if your host is the default installation of Win2000 SERVER, I can tell you, you're dead)

you should know exactly what services you need, and only You really need to install the service, according to safety principles, at least the minimum service + permissions = maximum security.

typical WEB servers require a minimum component choice is: only install IIS, Com Files, IIS Snap-In, WWW Server components. If you really need to install further components, please carefully, especially: Indexing Service, FrontPage 2000 Server Extensions, Internet Service Manager (HTML) that several of the risk services.

3. Management application of choice:

choosing a good remote management software is a pretty important thing, not only safety but also of the application needs.

Win2000 the Terminal Service is based to the RDP (Remote Desktop Protocol) remote control software, he's fast, hassle-free to operate, even more suitable for routine operation.

Nonetheless, Terminal Service also has its shortcomings, because it uses the virtual desktop, along with Microsoft's programming isn't strict, when you install the software using Terminal Service or restart the server, etc. interacting with the real Desktop The operation, often there will be enough to create misunderstandings of phenomena, such as: re-using the Terminal Service server from Microsoft's Certification (Compaq, IBM, etc.) might be shut down.

So, for safety reasons, I suggest you go with a remote control software as an aid, and Terminal Service complementarity, as PcAnyWhere is a good option.

Second, properly installed WIN2000 SERVER:

1. The distribution of partition and logical drive, there are some friends in order to save, just the hard drive into a logical drive, all the software installed in the C drive, this is incredibly good, it can be recommended to establish at least two partitions, one program partition, an application partition, this is because there is often a leak of Microsoft's IIS source / overflow vulnerability, if the system and IIS about the same drive, the file will cause the program to leak or even a remote intruder access to ADMIN.

recommended security configuration is to create three logical drives, the initial is greater than 2G, and important to install the program log file, the second put IIS, the third one FTP, IIS, or FTP either way out of the protection holes will not directly affect the program directory and system files.

to know, IIS and FTP is the external services are relatively uncomplicated problems. The separation of the IIS and FTP upload the main system is to prevent intruders to run from IIS. (This could lead to application developers and editors of distress, who cares, anyway you're an administrator)

2. The order of installation options:

Do not think: What is the order important? If installed, how to load you can.

wrong! win2000 installed in a certain order of a few to note:

Very first of all, when the access network: Win2000 there is a flaw in the installation, you enter the Administrator password, the system's built ADMIN $ shared, but did not use the password you just to protect it, this situation until you start again after this period, anyone can enter through the ADMIN $ on your machine; the same time, as long as the installation is complete, the types of service will run automatically, and when the server is covered with loopholes, particularly effortless to enter, therefore, fully installed and configured win2000 SERVER, make sure not to host access network.

Second, the patch installation: the installation of the patch should be installed after all the applications, because patches often have to replace / modify certain system files, if you install the patch before installing the application might cause the patch can not be play the desired effect, such as: IIS's HotFix requires that each change the configuration of IIS to become installed on

Third, protection configuration WIN2000 SERVER:

even if installed properly WIN2000 SERVER, there are still numerous loopholes in the program, but also the need for further detailed configuration.

one. Port:

port is connected towards the computer and the logic of the external network interface, is the 1st barrier the computer, the port is configured properly or not directly affect the protection of the host, in general, only open the ports you will need to make use of safer approach is to configure the network card properties -TCP/IP- Advanced - Options -TCP/IP screening enabled TCP / IP filtering, port filtering, but for win2000, there is a bad feature: only the provisions of What ports to open, can not restrict which ports closed, so that a large variety of ports that require users to open extra painful.

2. IIS:

IIS is Microsoft's one of the largest component in the vulnerability, an average of two to three months out of a hole should, and Microsoft's IIS is installed by default and can not compliment, so the configuration of IIS is our focus, it truly is now together with me:

Initial, the C disk that what Inetpub directory completely deleted, in the D drive to build a Inetpub (do not worry if you'll be able to use the default directory name, a name change, but they have to remember that) in the IIS Manager home directory will point to D: Inetpub;

secondly, that what the default IIS installation scripts and other virtual directory Yigai delete (source of evil ah, forget a href =

3: Application Configuration:

in the IIS Manager to delete any unwanted outside the map must be, must refer towards the ASP, ASA, and you really need to make use of other types of files , for example, you use stml, etc. (use the server side include), is essentially 90% of the host with the above two maps enough, the rest of the map almost every story has a sad: htw, htr, idq, ida ... ... want to know these stories? to check it before the vulnerability list.

what? can not find where to delete?

in the IIS Manager, right-click the host -> Properties -> WWW Services Edit -> Home Directory Configuration -> application mapping, and then it started to delete one by one (which doesn't decide on all, hehe). Then, in just the bookmarks window application debugging error message within the script to send text ( ASP error unless you want to know your plan when the user / network / database structure) error text writing? whatever you like, own choice. Click OK to exit do not forget to set the virtual site inherit your property.

order to deal with the growing quantity of cgi vulnerability scanners, there is a little trick to refer towards the IIS will HTTP404 Object Not Found error page through the URL to redirect to a custom HTM files, can present, most CGI vulnerability scanner failure. It can be really quite straight forward, most of the time of writing CGI scanner in order to facilitate, through the HTTP code to view the back page to determine whether vulnerabilities exist, for example, are generally well-known vulnerabilities by taking IDQ one. idq to test, if the return HTTP200, to think that there is this vulnerability,Windows 7 Ultimate Key, whereas if the return HTTP404 to think not, if you will HTTP404 error message through the URL redirected to HTTP404.htm files, then scan all vulnerabilities, whether it exists or not will be returned HTTP200, 90% of the CGI vulnerability scanner that what you have, the result will conceal your true vulnerability, so that an intruder at a loss no place to start (instead of martial arts often said that loopholes in the body perfect, can we say is this state?) But from a personal point of view, I think that such a solid occupation safety settings than the far more important tips.

Finally, to become safe, you can use the backup feature of IIS, the setting will be just All backup set down, so that it is easy to always restore IIS protection configuration. Also, if you're afraid of the load is too high causes the server to IIS crash at full capacity, can also open the CPU limitations in performance, for example, the maximum CPU utilization IIS limit 70%.

4. Account Security:

Win2000 account security is another focus, initial of all, Win2000 the default installation allows any user to get the system through the air all the user accounts / share list, this originally for your convenience of LAN users to share files, but a remote user can also get your list of users and crack user password to use violence law. a lot of of my friends know that it is easy to change the registry Local_Machine System CurrentControlSet Control LSA-RestrictAnonymous = one to prohibit 139 null,

fact, the local protection policy win2000 (if that is the domain server, domain server protection and domain protection policy) had this solution RestrictAnonymous (further restrictions for anonymous connections) This option has three values:

0: None. Rely on default permissions (no, depending to the default permissions)

one: Do not allow enumeration of SAM accounts and shares (not enumeration of SAM accounts and shares allowed)

2: No access without explicit anonymous permissions (without explicit anonymous permissions allow access)

0 This value is the default, what restrictions No, the remote user can see all the accounts on your machine, group information, shared directories, network transmission NetServerTransportEnum, etc., within the server for this setup is especially dangerous.

one This value is only allowed to users of non-NULL SAM account information access and share information.

2 in this value is only supported in win2000, to note that if you use this value if your share is estimated on all finished, so I recommend that you set to one or better. Properly, now there is no way an intruder to get a list of our customers, our account safe ... ...

Wait, at least one account password can be run This is the program built-in administrator, how do? I change change change, in Computer Management -> right click administrator user account and then change its name changed to whatever you what, as long as I remember within the line.

not No, I have changed the user name, and how people nonetheless run my administrator's password? Fortunately, my password is long enough, but this is not the answer you? ah, it must be in local or Terminal Service login screen to see , nicely, let's put HKEY_LOCAL_MACHINE SOFTWARE Microsoft WindowsNT CurrentVersion winlogon key in the Don't Display Last User Name string data into a 1, so the program doesn't automatically display the last logon user name.

the server registry HKEY_LOCAL_ MACHINE SOFTWARE Microsoft WindowsNT CurrentVersion Winlogon key in the Don't Display Last User Name string data revised to one to hide the last login console user name.

5. Protection Log:

I encountered such a situation, a host intrusion by others, the system administrator asked me to track down the murderer, I logged into a look: safety log is empty, down, remember: Win2000 the default installation is not open any security audit! then invite you towards the local protection policy -> audit policy, open the appropriate review, the audit recommended that:

account management success or failure

logon events success and failure

object access failure

success or failure

policy changes failed

privilege to make use of the system event success or failure

directory service access failures

account logon events audit project success and failure

small drawback is that there is no record in case you want to see it at all Mozhe; too lots of items will not only review system resources and cause you do not have time to see, so that the significance of losing the audit.

is associated with:

strategy in the account -> Password policy settings:

password complexity requirements enabled

Minimum password length 6

Enforce password history 5

maximum age of 30 days

In the Account Policy -> Account Lockout Policy settings:

account lockout 3 times the error log



locked for 20 minutes 20 minutes
lock count reset
Similarly, Terminal Service protection log isn't open by default, and we can Terminal Service Configration (remote service configuration) - permissions - Advanced to configure security auditing, in general, as long as the record of logon, logoff events on it.

6. directory and file permissions:

to control the user's permissions around the server, but also to prevent a probable invasion and subsequent overflow, we must be rather careful to set the directory and file access permissions, NT access rights are divided into: read, publish, read and perform, modify, list directories, full control. In the default case, the majority of the folder for all users (Everyone in this group) is completely open The (Full Control), you need to apply the required permissions to reset.

making access control, keep in mind the following principles:

1> limit is cumulative: If a user belongs to two groups, he had allowed these two groups of all rights;

2> permission denied permission to allow higher than (denial strategy will be executed) if a Users belong to one is denied access to a resource group, no matter the permissions of other how considerably authority to give him open, he must not access the resources. so please be really careful to use reject, any refusal might have resulted in improper The program can not function properly;

3> file permissions for the folder permissions than the high (need to explain this, right?)

4> use user groups for access control is a mature system administrator one must have good habits;

5> only permissions to the users really need, the principle of least privilege is an important guarantee for that safety;

7: Prevention of DoS:

In the registry HKLM System CurrentControlSet Services Tcpip Parameters, change the following value can help protect you against a certain intensity of DoS attacks

SynAttackProtect REG_DWORD 2

EnablePMTUDiscovery REG_DWORD 0

NoNameReleaseOnDemand REG_DWORD one

EnableDeadGWDetect REG_DWORD 0

KeepAliveTime REG_DWORD 300,000

PerformRouterDiscovery REG_DWORD 0

EnableICMPRedirects REG_DWORD 0

ICMP attacks : ICMP storm attack and fragment attack is also quite daunting NT host attack methods, in fact, fairly simple methods to deal with, win2000 comes with a Routing & Remote Access tool that begun to take shape router (Microsoft really, what should do? I heard recently, to do the firewall) in this tool, we can easily define input and output packet filters, for example, setting the input code 255 ICMP dropped to that drop all ICMP packets alien.

Fourth, some of the things to note:

In fact, security and application is contradictory in several cases, so you need to find a balance in which, after all, the server is for users to make use of and not to do OPEN HACK , if the system safety policy prevents the application of the principle that the safety isn't a good principle. Network protection is a systematic project, which spans not only space, there is still time span. quite a bit of friends (including some program administrators ) considers an the protection configuration of the host is secure, in fact, of which there is a misunderstanding: we can only say that a host in certain cases some time is safe, with the network structure changes, new vulnerabilities are discovered administrator / user operation, the host of the safety situation is changing at any time, only to protection awareness and safety system throughout the entire process to become truly safe.

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you: highly recommended, worth a visit! Worth collecting! Especially prepared for children in the future!
I admire this man's literary grace so, too determined to, and admiration, respect! I'm sorry he does not turn all!
















































Han Dynasty

southern South
can Picking, Lin Ye Hetian fields.
Fish play lotus East, the fish show lotus West,
Fish play South lotus, fish, lotus Opera North.

Geese
LUO
goose, goose, geese, crooked to the Tiange,
white hair floating green water, Anthurium call ha.

Willow
He Zhizhang
jasper makeup into a tree height, million green silk sash hanging down.
I do not know who cut out Egeria? February spring like scissors.

Deng Guanquelou
Wang Zhihuan
sun mountains, the Yellow River into the sea.
For a grander sight, a higher level.





Liangzhou words
Wang Han
Remanbar wines, want to drink immediately pipa reminder. Jun Mo
Zuiwo battlefield laugh a few people since ancient times fought back?



Changling Changling
Hanyu gradually
into the night with Wu Jiang, Ping Ming Chu Shangu see a visitor.
relatives such as phase Q Luoyang, a Bing Yu Hu.

Chile Northern Caribbean folk songs

Chile Chuan, Yinshan,
blue canopy, covers a vast area.
green and wild vast,
wind-swept pastures of cows and sheep. Li Qiao


wind down three Akiba
solution, able to flower in February.
thousand feet across the river waves, into the bamboo pole skew million.


Wang Zhihuan
Liangzhou word on the white clouds far from the Yellow River, an isolated city Maninsan. Why should we complain willow
bamboo flute, spring is not the degree Pass.




Chunxiao
Haoran
春眠不觉晓, Everywhere Birds Are Singing.
night comes wind and rain, Whispering Colour?



Frontier

Qin Shiming Wang Changling Han Guan month, the Long March who did not return.
but makes Dragon fly in, do not teach Hu Yin Ma degrees. Wei Lu Zhai



empty mountains but not people, but the famous person language sound.
Deep in the woods back to King, according to the moss on the complex.

send Yuan Er
Weicheng Zhao Yu Wang
dampening the dust, guest houses green Green is the Willow.
advise you to do one more glass of wine, West of Yang Guan no reason people.

September 9 Brothers in Shandong Wei

stranger alone in a foreign land, their loved ones during the festive season.
know brothers climb away, Biancha cornel but one person.

Jingyesi
Bai
Moonlight, the suspect is frost on the floor.
raise my eyes to the moon, looking down and think of home.





Old Lang month line

did not know Li Bai
hour month,herve leger for sale, calls for white plate.
they suspect Yaotai mirror,Herve Leger Dresses, flying in the Pik-side.

望庐山瀑布
incense Health Zi Yan Bai
sunshine, very thick waterfall hanging Maekawa.
waterfalls three thousand feet, the suspect is charged Galaxy nine days. To Wang Lun


Li Bai Li Bai
boat will want to line, when I suddenly stepped ashore singing.
Peach Blossom Pool thousand feet deep, not as Wang Lun love for me.

Yellow Crane Tower Crane Tower
sent Bai
Haoran old friend West by the Yellow Crane Tower, the fireworks in March in Yangzhou.
Gu Fan Yuan shadow blue sky to make, only see the flow of the Yangtze River skyline.

Baidicheng
premature resignation of Li Bai Bai Di
North Korea Choi, Trinidad Jiangling 一日 also.
monkeys are two sides could not cry, my boat these ten thousand mountains.



Wang Li Bai
days Tianmenshan
Chujiang open the door interrupts, clear water flows east to the North.
relatively out of both sides of Castle Peak, one at the side of a boat to.

not large
Gao Dong Huang day twilight
miles north wind and snow geese have. Mo anterior
no confidant, who Bushi Jun world?

quatrains
Cui Liu Ming Fu
two Oriole, egrets on the sky line. Xiling Snow Chiaki with
window, door parking Wu Wanli ship. Rain in Spring Night Fu



good rain knows the time, when the spring is happening.
sneaked into the night wind, moisten things silently.
both wild black cloud diameter, Jiang boat on.
look red and damp at dawn and spent re-Jin Guan city.

quatrains
Jiangshan Li Du
later date, spring flowers and incense.
mud financial swallows son, sand warm sleeping ducks.



River only solution to find flowers
Huang Shih-Fu
before the river east tower, leaning difficulties lazy spring breeze.
a cluster of open bona peach, sweet love dark red light red.

Midnight Bells
Zhang
moonset Wuti frost sky, Jiang Feng and boat lights, I sleepless lie.
Outside Suzhou Han Shan Temple, the midnight bell to the ship. Jiao zi yin



the hands of a loving mother line, wandering clothing.
departure sew, For fear.
Who made the inch of grass, reported in the apartments.

Jiangxue
Liu
Qianshan bird must, million tracks were off track.
boat PC World Weng, fishing alone, trees and snow.

Yuge Zhang and
sub
the coming of egrets fly, peach water mandarin fish fertilizer.
Green Ruoli, green hygrophila and Inclined rain do not need to go.



plug on the next song
Lulun
high black wild geese, Chanyu night seeing them.
by wishing scooters, heavy snow over the bow knife.

Wang Yuxi

Dongting lake and two-phase Moon, lake surface did not wear no goggles. Looking Dongting
landscape Tsui, Lo Hitodo silver tray.

Yellow Gold and Sand
Yuxi
nine miles of sand, wind waves toss from Amoy End of the World.
now straight to the Galaxy, to the cows with the Weaver family.

grass Fu De Gu Yuan Bai
Lili farewell
on the original grass, a dry-year-old wing.
wild fire, in spring.
Yuanfang invasion Road,Herve Leger Sale, then Huang Cheng Ching Tsui.
and give Sun-go, full of lush do not love.

Ikegami
Bai
Xiaowa support boats, stealing lotus back.
understand hidden traces of duckweed an opening.




Bai Yi Jiangnan Jiangnan
good old landscape had come to know.
Sunrise River bonuses and signs such as blue green river spring.
can not Yi Jiangnan? Fishing


Woo children can learn
uncover his head down Lun little children, sitting side grass mapping units berry body.
waving passers-by ask away, scared the fish should not surprise people.

Benjamin Li Shen
agricultural
hoe Wo day when afternoon, sweat Wo Soil. Who knows
chopping block 粒粒皆辛苦.

not met
find hermit asked the boy Jia Dao
Panasonic, teacher is collecting herbs.
in the mountains somewhere in the clouds Department.

mountains far on the line
Mu Han Shan Shi Jing
ramp, Bai Yunsheng at someone in the family. Fenglin late parking
love to sit, Red Leaves in Flowers.



Ching Ming Tomb Sweeping Festival
Mu
rain have, pedestrians Deep Sorrow. I ask a restaurant where there
? Shepherd Yao Zhi Heng Fa Chuen. Jason Jiang



miles Dalian Green Ying Mu, water, wind Jiuqi Murayama Guo;
Temple Southern four hundred and eighty, the number of towers in the misty rain.

Yueyou Yuan yin

evening among the Italian discomfort, Gordon drove the ancient original.
sunset is magnificent, it is almost dusk.

bee
both plain and jian Luo Yin
, unlimited scenery to make the occupied.
picked flowers into honey, the sweet for whom for whom hard work.

river fishing on the river who
Zhongyan
between people, but love bass beauty. Jun
see leaf boat, haunted Storm.



motohi
Wang
firecrackers year-old addition to the spring breeze warm carcass into the Soviet Union,
one thousand million, the total of the new replace the old character.

berthing guazhou
Wang
Jingkou melon water, the Zhongshan separated by only a few mountains.
spring south bank of Green River, when the moon as I have.

book
Lake Yinxian Sheng Wang Mao eaves wall
long sweep no moss, flowers and trees into a stretch of hand suicides.
protection of water around the green fields, the two rows door of an inner room to send Green Mountain to.

June 27 Lake-House Sushi
drunk book
not cover the ink turned dark mountains, white rain chaos jump into the ship Pearl.
volume to the wind suddenly blew away, hope the lake water, such as day downstairs.

drink after the rain on the lake early Qing Shi
Shuiguang
glittering sunny side is good, the rain kept empty mountains are strange.
For the West than the West, wiping thick makeup total affordable.



Hui Chong Su Chun Jiang Xiaojing
Peach thirty-two
bamboo outside, Spring plumbing ducks. Montreal reed shoots Artemisia
short, it is like when the puffer.

title
West Wall
Wang Shi as many different angles, near and far different level.
do not know the truth, just because in this mountain.

quatrains
Qingzhao
summer students as odds, death is also a male ghost.
still thinking Xiang Yu refused to have River.

said Lu
children die per
know everything empty,Herve Leger Outlet, but the sad but not Nine. scheduled for the North
Wang Shi Zhongyuan date not been forgotten.

autumn night will dawn a cool felt
Lu Ying Li Men
three miles east of the river into the sea, five thousand yards on the Ferris Yue. Tears do Huchen
Dynasty,Discount Herve Leger Dresses, the South Wang Wang Shi after year.



pm Garden Miscellaneous Fan Chengda
diurnal Hing
Ma Ji Yun Tian night, the masters of the village children.
Tong Sun unsolved for farming organizations, also near the school Jhonggua Yin Sang. Koike


Xi Yang Wanli
spring silent trickle, according to the water love sunny soft shade. Lotus Just Showing
sharp angle, stand on top of already dragonfly.


out Jingci Xiao Yang Wanli

send the woods side of West Lake in June, after all, the scenery and the seasons are not the same. Bi
then endless days of lotus leaves, lotus flowers reflect the sunshine day.

spring
Fang Zhu
Surabaya seeking victory at Sea, boundless new temporary condition.
Truthfulness east side, always colorful spring.

title
Lin Lin Sheng Di
outside the Castle Hill Restaurant Filled, Lake Dance Stop?
heater Xunde visitors drunk, straight to Hangzhou for Bian state.



garden worth
Weng
should pity clog the Compilation of teeth marks changtae, eventually becoming a small button Chaifei open.
Spring garden extra duty, an affair to. Weng, April


Village Green over the mountain of the original volume
White Man River, cuckoo sound in the rain to smoke.
small village idlers in April, before the sericulture and insert fields. Plum Blossoms
Wang Mian


wash my Yanchi head tree, blossoming flowers light ink marks. Do not boast color
good people, leaving only the clear air over heaven and earth. Yu Qian Yin


lime hammer million
carved thousands of mountains, the fire burning if lightly,
pieces muddy not afraid to stay plainer in the world. Bamboo and Rock ZHENG Xie


insist Castle
not relaxed, rooted in the broken rock.
thousands of grinding million hit Kennedy also strong, Seoul, the East and West wind. Yuan Mei


see
boy riding cattle, singing Zhen-Lin Yue.
desire to catch Maemi, suddenly closed set.

Murai
high tripod
Orioles February day long grass, brush embankment Yang Liu drunk smoke.
children returned from school early and busy place to take advantage of wind kite




1 = total number of shares each
few × ÷ total number of copies of each number = ÷ total number of shares

2 1 = number of times each × multiplier = number of times the number of times
multiple = multiple
÷ 1 ÷ factor = 1 times the number of times
3 speed × time = distance ÷ speed = time

walk distance ÷ time = speed
4 total unit price × quantity = Price = total number of

÷ ÷ total number of efficiency = unit
5 × working hours = total work
work efficiency = total ÷ total work hours
÷ the efficiency of working time = addend + addend =
6 and
and - another one addend = addend
7 minuend - subtrahend = difference
minuend - SD =
subtrahend subtrahend = difference + minuend
8 factor × factor ÷ volume = plot
Another factor is a factor = dividend ÷ divisor
9 = business = Business
dividend ÷ divisor
provider × divisor = dividend


Primary Mathematics graphics

formula
1 S square
C perimeter area of ​​a side
perimeter = side length × 4
C = 4a
area = side length × side length
S = a × a
2 cube
V: volume of a: edge length
edge length × surface area = length × 6
S edge of the table = a × a × 6
size = length × edge × edge long edge long
V = a × a × a
3 rectangular
C perimeter area of ​​a side length S
perimeter = (length + width) × 2
C = 2 (a + b)
area = length × width
S = ab
4 rectangular
V: Volume s: size a: Long b: W h: High
(1) surface area (length × width × height + length + width × height) × 2
S = 2 (ab + ah + bh)
(2) Volume = length × width × height
V = abh
5 area of ​​a triangle
s h high-end area = base × height
÷ 2
s = ah ÷ 2
triangle = area × 2 ÷ high end of the triangle
end = area × 2 ÷ high
6 area of ​​a parallelogram
s h high-end area = base × height

s = ah
7
s area of ​​a trapezoid on the bottom b
area under the high end of h = (bottom + down on the bottom) × high ÷ 2
s = (a + b) × h ÷ 2
8 round
S area of ​​the circumference of Π d C = diameter r = radius
(1) circumference = diameter × Π = 2 × Π × radius
C = Πd = 2Πr
(2) area = radius × radius × Π
9 cylinder
v: volume h: high-s; bottom area of ​​r: the radius of the bottom c: bottom perimeter
(1) side of the area = circumference × height bottom
(2) area = side area + base area × 2
(3) Volume = base area × height
(4) Volume = side area ÷ 2 × radius
10 cone
v: volume h: high-s; bottom area of ​​r : bottom radius
volume = base area × height ÷ 3


÷ total number of shares

= average
and differential equation problems
(and + poor) ÷ 2 = large numbers
(and - worse) ÷ 2 = decimal
and times of problems
and ÷ (factor -1) = decimal fraction × multiplier =
large numbers
(or with - decimal = large numbers)
bad times worse problem
÷ (multiples - 1) = decimal fraction × multiplier =
large numbers
(or decimal + SD = large numbers)


planting questions
1 tree planting on non-closed circuit problems can be divided into the following three cases:
⑴ closed if the non-tree planting both ends of the line, then:
NUMBER = number of segments + 1 = length ÷ length = -1
spacing and plant spacing × (number of plant -1)
spacing = length ÷ (number of plant -1)
⑵ If the non-closed end of the line to tree planting, Do not plant trees the other end, then:
number of trees = number of segments = length = length ÷
spacing spacing spacing = length × number of trees

⑶ ÷ number of trees in non-closure of the line if both ends do not tree planting, then:
number of trees = number of segments -1 = full length = -1
÷ spacing and plant spacing × (NUMBER +1)
spacing = length ÷ (NUMBER +1)
2 closed line relationship between the number of tree-planting problems are
number of trees = number of segments = length = length ÷
spacing spacing spacing = length × number of trees
÷ number of trees
profit and loss issues
(profit + loss) ÷ difference = twice the amount allocated to participate in the distribution of copies
(large surplus - a small profit) ÷ = ​​twice the difference between the amount allocated to participate in the distribution of copies
(burned - a small loss) ÷ volume of the two distribution participate in distribution of the difference between the number of copies =



encounter problems
meet distance = speed × time
encounter encounter encounter time = distance ÷ speed and
speed = distance ÷ meet meet time
catch the problem
distance = speed chase and chase and the time difference ×
chase and chase and time = distance ÷ speed difference
velocity difference = distance ÷ chase and chase and time
water problems downstream speed = hydrostatic speed
+ speed = flow velocity
upstream hydrostatic speed - the speed
hydrostatic flow velocity = (speed + upstream downstream speed) ÷ 2
flow rate = (downstream speed - upstream speed) ÷ 2
concentration the weight of the problem
solute + solvent = solution of the weight of the weight of the weight of the solute ÷
the weight of the solution concentration
× 100% = weight × concentration of solution = weight of solute ÷ weight of the solute concentration
= weight of the solution and discounts

profit profit = selling price - cost margin = Profit ÷
cost × 100% = (selling price ÷ cost -1) × 100%
the amount of ups and downs Percentage Change = principal × the actual selling price = ÷
the original discount price × 100% (off