Thursday, June 13, 2019

ALEGEBRA IDENTITIES

Difference of Squares

a2 - b2 = (a-b)(a+b)
Difference of Cubes
- a3 - b3 = (a - b)(a2+ ab + b2)
- Sum of Cubes
  - a3 + b3 = (a + b)(a2 - ab + b2)
  - Special Algebra Expansions
  - Formula for (a+b)2 and (a-b)2
    - (a + b)2 = a2 + 2ab + b2
    - (a - b)2 = a2 - 2ab +b2
    - Formula for (a+b)3 and (a-b)3
      
      (a + b)3 = a3 + 3a2b + 3ab2 + b3
      
      (a - b)3 = a3 - 3a2b + 3ab2 - b3
      
      Roots of Quadratic Equation
      
      Formula
      
      Consider this quadratic equation:
      
      ax2 + bx + c = 0
      
      Where a, b and c are the leading coefficients.
      
      The roots for this quadratic equation will be:

CIRCLE

Circle

Definition. Circle is a set of all points in the plane which are equidistant from a given point О, called the center of circle.

Properties of a circle

1. Diameter of circle is equal two radiuses.

D = 2r

2. The shortest distance from the center circle to the secant (chord) is always smaller radius.

3. Three points that not placed on a straight line can hold only one circle.

4. Among all closed curves of equal length, circle has the largest area.

5. If two circle touch at one point, this point placed on the line that passes through the centers of the circles

Area and circumference of circle

Length of circumference

1. Formula of the circumference length in terms of the diameter:

C = πD

2. Formula of the circumference length in terms of the radius:

C = 2πr

Formula of the circle area

1. Formula of the circle area in terms of the radius:

A = πr²

2. Formula of the circle area in terms of the diameter:

A = πD²4

Trigonometry (trig) identities

A. Reciprocal identities

a1	sin  A = 1  csc  A	a4	csc  A = 1  sin  A
a2	cos  A = 1  sec  A	a5	sec  A = 1  cos  A
a3	tan  A = 1  cot  A	a6	cot  A = 1  tan  A

B. Ratio identities

b1	tan  A =  sin  A  cos  A
b2	cot  A =  cos  A  sin  A

C. Opposite Angle identities

c1	sin  ( − A ) = −  sin  A
c2	cos  ( − A ) = c o s A (Caution - not like c1, c3)
c3	tan  ( − A ) = −  tan  A

D. Complementary angle identities

e1	sin  A =  cos  π 2 − A
e2	tan  A =  cot  π 2 − A
e3	sec  A =  csc  π 2 − A

Friday, May 3, 2019

A1- How to use ICT Tools

Use of specific ICT tools in education

A Knowledge Map on Information & Communication Technologies in Education

Guiding Questions:

What is known about which ICTs are most useful to benefit education? What do we know about the usefulness, appropriateness, and efficacy of specific ICTs (including radio television, handheld devices, computers, networked computers and the Internet) for educational purposes? What do we know about the use of open source and free software in education?

Note to reader: infoDev – a program of the World Bank – promotes innovation and entrepreneurship in smart agriculture, digital technology, and climate change technology. Through business programs and early stage financing, we help developing countries in the Caribbean, Africa, and Asia go green and develop solutions to local problems.

In the past, infoDev worked with ICT and education. While our programs do support some entrepreneurs and start-ups that develop educational technologies (like Afroes and ListenMi), ICT and education are no longer the focus of our mission.

Current knowledgebase
What we know, what we believe -- and what we don’t

General

The Internet is not widely available in most LDCs; radio and TV are
Broadcast technologies such as radio and television have a much greater penetration than the Internet throughout much of the developing world, and the substantial gap is not expected to be closed soon.

Radio and TV can have high start-up costs, and reinforce existing pedagogical styles
Educational initiatives that utilize radio and television typically have quite high initial start-up/capital costs, but once they are up and running, on-going maintenance and upgrade costs are much lower (making initiatives utilizing radio and TV for distance learning in the education sector particularly appealing for donor support in many cases). One-to-many broadcast technologies like radio and television (as well as satellite distribution of electronic content) are seen as less ‘revolutionary’ ICTs in education, as their usage is seen as reinforcing of traditional instructor-centric learning models, unlike computers, which many see as important tools in fostering more learner-centric instructional models.

Radio instruction has been used widely and is reasonably well studied
Radio instruction in formal education has been well studied, especially the links between the use of radio in combination with school-based educational resources and a variety of pedagogical practices.

TV has been used with success in a few places
Television has been utilized successfully as a mechanism for reaching out-of-school youth in a number of countries, especially in Latin America and China, and the results of such projects have been widely disseminated.

In some cases, where markets have been liberalized, ICTs are used to distribute educational content regionally within a country
Market liberalization has in many countries allowed for the development of locally- (as opposed to centrally-) controlled distribution channels that utilize ICTs (like radio and the Internet, and to a lesser extent television) to create and broadcast educational content more targeted to the needs of specific communities, and as a result have a greater flexibility to employ local languages.

CAI is not highly regarded by experts and in OECD countries, but still, receives much interest in LDCs
The usefulness of computer-aided instruction (CAI), in which computers are seen as simple replacements for teachers, has been largely discredited, although there appears to still be great interest in CAI in many LDCs where computers are being introduced.

It is unclear where to place computers to make sure they are used most efficiently
There is very little research on the most appropriate placement of computers in schools, or in the community, used to achieve various learning objectives.

Multi-channel learning is a useful concept
The emerging practice of ‘multi-channel learning’, which focuses on enriching the educational experience by engaging all resources that are available to help effect incremental change by coordinating the various ways to connect learners with information, knowledge, and stimulation, and to mediate those interactions, provides valuable insight into how blended learning approaches can be delivered and tailored in areas of great resource scarcity.

Satellite is much hyped but under-studied
While satellite broadcasting of electronic educational resources is thought to hold much promise, there are few case studies of successful implementation of satellite broadcasting to small LDCs.

New Internet technologies hold promise but are not yet operational
Emerging Internet technologies, especially recent and emerging wireless protocols (including 802.11, and shortly WiMax), are thought to hold much promise for providing connectivity to remote areas, but projects utilizing such technologies are for the most part in pilot or planning stages, and face many regulatory hurdles.

Mobile Internet centers (vans, etc.) are being deployed as a way to reach rural areas
A number of educational initiatives utilizing mobile Internet centers have been piloted in the past decade, but little cost and impact data has emerged from such projects.

Community telecentres are a hot topic, but successful, replicable models have not yet emerged
Community telecentres (sometimes based in schools) have be touted as important tools to provide access to learners (including teachers engaged in personal enrichment and professional development opportunities) to ICTs outside of formal school settings.

The use of handheld devices is just now receiving serious widespread attention
Little research has been done on uses of handheld devices (including personal digital assistants and mobile phones) in education.

‘Free software’ holds promise, but costs and impact are still not well documented
The uses of ‘free’ software is widely touted as a cost-effective alternative to the uses of proprietary software (especially Microsoft products), but research in this area is largely advocatory in nature.

Comments

General comments

We know that technology changes – rapidly – and newer, more cost-effective and more powerful technologies will continue to emerge of potential use in education. At the same time, evidence shows that, once installed in schools, ICTs continue to be used for the life of the functioning life of the technology, whether or not newer, more cost-effective and powerful technologies emerge (especially as upgrade paths are seldom part of initial planning).

Much of the publicly available information about the effectiveness of particular ICT tools is generated by the companies who market such products and related services.

Applicability to LDC/EFA context

While it is clear that it is the application of various ICTs that are the most important determinants of the effectiveness of such tools in education, the choices of tools are quite varied and each has its own advantages and disadvantages. Policymakers and donor staff are often bombarded by information and studies from vendors on the suitability of their products or services, and there is a need for further, independent research on the appropriateness on specific tools with potential to help meet education-related MDGs.

Some areas for further investigation and research

What models exist for the effective utilization of ICTs to support on-going professional development for educators? What are the best practices for mainstreaming pilot projects involving interactive radio instruction (IRI) at the Ministry of Education, and how are such projects managed and maintained over time? Where should computers reside if they are to have the greatest learning impact in education? Is the use of ICTs as in-class presentation mechanisms a cost-effective use of technology? How have/can handheld devices (including SMS-enabled mobile phones) be used to support education (especially related to the professional development of teachers and school administration), and what are the emerging best practices? How can existing community and interactive radio networks outside the education sector be used to benefit education? What successful models exist for opening ICT facilities in schools to the wider community? Does the use of so-called "open source software" offer compelling benefits in education? What models exist on effective public-private-community partnerships in education for ICT equipment provision and maintenance?

Some Recommended Resources
to learn more ….

African Tertiary Institutions Connectivity Study (Draft Report) [Steiner 2004]

Applying New Technologies and Cost-Effective Delivery Systems in Basic Education. World Education Forum Education For All 2000 Assessment [Perraton 2001]

Free Open Source Software - A General Introduction [Wong 2004]

Interactive Radio Instruction: Twenty-three Years of Improving Educational Quality [Bosch 1997]

Integrating ICTs into Education: Lessons Learned [UNESCO-Bangkok 2004]

Learning With Handhelds: Findings From Classroom Research [Vahey 2003]

Open Source as Appropriate Technology for Global Education [Carmichael 2004]

Schoolnet Toolkit [UNESCO-Bangkok 2004]

The Use of Information and Communications Technology (ICT) in Learning and Distance Education [Intelecon Research 2000]

Excerpted from infoDev's Knowledge Maps: ICTs in Education -- What do we know about the effective uses of information and communication technologies in education in developing countries?

Suggested citation:
Trucano, Michael. 2005. Knowledge Maps: ICTs in Education. Washington, DC: infoDev / World Bank.

More resources

Use of specific ICT tools in education(URL)

A2- How to browse the internet

Browsing the Internet: An introduction

What do l need to know?

A browser is a program on your computer that enables you to search ("surf") and retrieve information on the WorldWideWeb (WWW), which is part of the Internet. The Web is simply a large number of computers linked together in a global network, that can be accessed using an address (URL, Uniform Resource Locator, e.g. http://www.veths.no for the Oslo Veterinary School), in the same way that you can phone anyone in the world given their telephone number.
URLs are often long and therefore easy to type incorrectly. They all begin with http://, and many (but not all) begin withhttp://www. In many cases the first part (http://, or even http://www.) can be omitted, and you will still be able to access the page. Try this with http://www.cnn.com.
URLs are constructed in a standard fashion. This may be of use to you. Take, for example, the address of this page:

http://oslovet.veths.no/teaching/internet/basics.html

The ".no" indicates that the server is in Norway. The page you have accessed is called basics.html, and it resides in a folder on the server called "internet", which is in the folder called "teaching". If the URL that you type does not work, and you have typed it correctly (no mistakes are allowed!), the reason may be that the host has renamed the web page, or moved it to another folder on the server, or you are not allowed access to that level.
Try removing the text of the URL stepwise from the right-hand end in this example, until you reach the main page:

http://www.bbc.co.uk/info/purpose/public_purposes/index.shtml.

It is possible, in many cases, to find your way back down through the hierarchy to the page you were interested in.

You don't need to know how the telephone network functions to be able to make a phone call. However, you ought to know how to use your telephone apparatus and the finesses (software) it contains. Your computer is the equivalent of the telephone, and a browser is the equivalent of the software that modern telephones contain. (A browser can also be used to handle electronic mail, create and edit information on the Internet, as l have done here, and to contact discussion groups. This presentation is limited to the use of browsers to surf the WorldWideWeb).

Searching the Web

If you don't know the telephone number of the person you wish to ring to, you need a telephone directory.   The Web provides two methods of searching for pages providing information:
    • sites presenting web pages sorted by category and subcategories, e.g. Yahoo (several sites, including http://www.yahoo.com and http://www.yahoo.no)
    • sites offering search engines that return lists of web pages containing text that matches a search word or string, e.g. Google (http://www.google.com), AltaVista (http://www.altavista.com) and FAST Search (http://www.alltheweb.com).

Many web sites offer both, or a combination of, these alternatives.

Before you conduct a search, it is important to consider, among others, the following points:

1. Is your choice of search term is adequate, too restrictive or too general?
2. Is the search you have planned to undertake most suited for a search engine that categorizes web sites, so that you can browse through appropriate subcategories when the first results are returned?
3. Are you more interested in using a search engine that merely returns all the web pages it has found containing the search term?
4. Have you read the Search Help pages that most search pages offer? These will tell you how the search engine conducts the search, and therefore how you ought to plan your search.
5. Bear in mind the fact that engines differ in their coverage of the Internet, their speed and whether they are largely compiled manually by people or automatically by 'robots' that scan the Internet.

A search strategy must include knowledge of how the search engine you have planned to use handles Boolean Logic and other similar search terms, e.g.

• transgenic AND mice will find all pages covering transgenic mice, but not pages that only mention transgenic rats
• transgenic NOT mice will return pages on all species other than mice.
• "transgenic mice" will find pages that contain the phrase "transgenic mice", i.e. where the words are adjacent in the text, but will not return a page containing the text "transgenic rodents, including mice", for which transgenic NEAR mice would be necessary
• transgen* will return occurences of trangenesis, transgenic and transgenic (thereby increasing your chances of finding pages you are interested in), but will also return pages featuring the word 'transgender', which is probably not what you were looking for!

N.B. Not all search engines support all these options, some support many more, and all of them have a "default" function (e.g. AND or OR) which you must check before you start.

To illustrate the enormous implications that this may have for your search results, try out the following search strings in the AltaVista or Google search engines and note the number of web pages returned for each alternative:

• Karina Smith
• "Karina Smith"
• Karina and Smith
• KARINA and SMITH
• Karin* Smith
• Karin*Smith

Excellent reviews of these processes have been written by information specialist Krys Bottrill. These cover:

• Basic principles when searching the Web
• Choice of search terms and strategies
• Comparison of Search engines on the Web

Some websites about the Internet in general and animals in particular

These include:

• NetVet
• The Electronic Zoo

The author of these two sites, veterinarian Ken Boschert, has published a book containing summaries of the most important links on these pages: "Mosby's Guide to the Internet".

An introduction to the Internet written in Norwegian.

While you are on the Internet, you can donate free food to the starving:http://www.thehungersite.com

Jenifer Peter

Thursday, June 13, 2019

ALEGEBRA IDENTITIES

Algebra Identities

Difference of Squares

Difference of Cubes

Sum of Cubes

Special Algebra Expansions

Formula for (a+b)2 and (a-b)2

Formula for (a+b)3 and (a-b)3

Roots of Quadratic Equation

Formula