How to Choose Easy English Books For Learning

How to Choose Easy English Books For LearningThe question is how to choose easy English books for learning? English is one of the most popular languages spoken in the world. It is used extensively in business, education, entertainment and media.Many people feel that it is very difficult to learn a difficult language such as English. This is true in the sense that learning any language, including English, takes hard work and dedication.However, if you really want to learn English, there are plenty of opportunities available today. A number of websites are available, which provide easy English books for learning. These sites provide a number of choices, which includes sample stories, lesson plans, vocabulary lists, and more. These sites have audio files of native speakers who can help you learn and memorize the vocabulary.There are other ways to learn English which can be done online. This can be done at the comfort of your home. This will allow you to learn at your own pace without th e pressures that may be experienced by using a classroom setting.While you are on the Internet, use a search engine to search for the phrase 'easy English books for learning.' This will give you many sites that you can use. Try using the links provided so that you can read reviews and recommendations for easy English books for learning. This way, you will know which sites will meet your needs and help you learn the language.If you are looking for easy English books for learning, look for a site that offers instructional videos or is accompanied by audio files. This will give you the convenience of learning with someone else who can help you understand the words. The use of visuals and audio will aid your learning process.One of the best places to find easy English books for learning is the community forums. Look for topics related to the language and find out what others have learned. The best part about using forums is that you can learn from others' experiences, you can have conve rsations that will improve your ability to speak and write English.There are so many opportunities available for those who want to learn English. The Internet provides a multitude of choices for learning. You can search through forums and learn from others experience in this particular aspect of language learning.

Tips On Finding The Best Organic Chemistry Tutor

Tips On Finding The Best Organic Chemistry TutorOne of the most challenging aspects in chemistry is how to learn the new skills with a tutor in a satisfying way. If you are looking for an online chemistry tutor then the next two points will help you out in finding the best one to help you learn and apply the lessons. The first point that you should know is that it is not good to try to find a chemistry tutor who is a good conversationalist, this is not a good choice as you are not going to get the quality tutoring. It is better to look for a tutor who is a good communicator and can deliver the lectures in a good manner.A tutor who is a good communicator is very important because this is what makes a good bond formation. If you are a student who is self motivated and like to do the assignments on your own then you will not be able to study the theories properly. The second thing that you should consider is the time frame that you will have to work with. This is very important for find ing the right chemistry tutor to help you learn. The most important thing to remember is that the tutor must be able to give you the lessons in a short time frame to ensure that you are able to tackle the assignments that you are given.The third point that you need to consider before looking for an organic chemistry tutor is that he or she must be well versed in the theory and understanding of the subject. This is the only way that you will be able to learn the lessons effectively. This is because once you find the chemistry lessons difficult to understand then the learning process is lost and the tutor will be able to see this. So this is one of the main reasons why online chemistry tutors are better than those who teach in the regular schools.The fourth thing that you need to know before looking for a chemistry tutor is that you will not be able to find someone who can meet all your needs. The chemistry tutors will not be able to provide the same services that you need. This is be cause the tutors will not have the same skills and knowledge as the other students in the school will. However, it is possible for you to find a tutor who has a good rapport with the students.There are many things that you need to consider before choosing a chemistry tutor. The first thing that you should think about is if he is a good communicator. You will be able to know this from the way he uses the lecture notes. Also, there is a question mark if the tutor will be well versed in organic chemistry. If this is the case then you need to look for a tutor who is an expert in the science of organic chemistry.The fifth and last point that you need to know before choosing an organic chemistry tutor is that he must be willing to attend every day. Some students find it too difficult to maintain a regular schedule to attend the lessons. The reason behind this is that students do not want to spend hours in their lessons just to attend the lesson. This is the reason why the organic chemistr y tutor needs to be available on a daily basis. This is because there is no teacher who is good at drawing the attention of the students.These are the five points that you need to look into before you choose an organic chemistry tutor. These tips will help you in finding the best chemistry tutor that can help you learn better.

5 Corporate Team Building Activities Ideas for Introvert Employees - Introvert Whisperer

Introvert Whisperer / 5 Corporate Team Building Activities Ideas for Introvert Employees - Introvert Whisperer 5 Corporate Team Building Activities Ideas for Introvert Employees Want to Bring Out the Best in Your Introverted Employees? Try These 5 Corporate Team Building Activities Ideas With Them in Mind Are you a manager who is always looking for new ways to bring your employees together? Do you see the value in team building but dont always think the exercises work for some of your more shy workers? Do you want to see all of your employees interacting and building bonds with one another? Any great company knows that it takes a diverse workforce to make things happen and that means employees need to learn to collaborate and support one another via fun team bonding ideas. But team building activities for workplace often alienate more introverted employees. If youre ready to include them in a way that will make them feel included and comfortable, read on to get our five top tips for team building event ideas your introverted employees will actually do: Tip #1: Obstacle Course Outdoor obstacle courses are a great interactive corporate team building activities ideas that both build camaraderie and let introverts work as individuals at their own pace. They dont have to talk very much and they can work their way through the obstacle course with their own thoughts and a little help from their teammates. Tip #2: Reflective Activities Having your team work on reflective activities in which they have to read a story or watch a video and then write a response is a nice way to cap a day of team building activities. But why not jumpstart the day with a reflective, mindful activity. This is the sweet spot and the comfort zone for introverts and could help them ease into a day of hyperactivity and talking about team building concepts. When introverts feel comfortable, they open up. So try to incorporate mindfulness and reflection into your team building day. Tip #3: Venture into the Escape Room Escape Room games are a great way to involve the entire team but the key to getting introverts participating is to keep the group small and with colleagues, they feel comfortable with. So this adventure escape games may be a corporate team building activity you introduce later down the line with a close-knit group of employees who know each other rather than an activity you introduce at orientation. In an escape room, there are clues scattered about, and the team must work together to put the clues together and to actually escape the room! Perhaps give some of the more vocal people in the group a talk before going in and ask them to reach out to more introverted members to individually ask them their opinions on the clues while you are all in the escape room. Tip #4: Make Time for Lunch Even lunch can be a team building exercise for your employees and should become a regular part of the day. Assign employees lunch teams and send them to different parts of the city with gift cards. You can do this once a month to give small groups of people the opportunity to share a meal and to learn something new about their fellow workers. This leads to increased productivity and creativity because employees begin to learn from one another and truly believe every person has something to offer the team. Tip #5: Slow Dating The speed dating concept is a frenzied activity designed to get you to meet as many people as possible and learn something about them. But turn this fun activity on its head and you get slow dating for introverts. Create a small group of employees who sit in a circle instead of lines across from one another. Present the first person in the group with a blank booklet and a pen. The first person writes a question on a random page of the blank booklet and then passes it to the next person in the circle, who answers it and writes another random question before passing it along through the circle. At the close of the circle, the last person reads the questions and answers and everyone guesses whose answer it is. Author Bio Paige Ellingson is a creative communication executive and writer, currently based in SE Asia, and writes content for Escape Break. She studied business and communication and proceeded to work in a fast-paced and upscale company in Hong Kong. Her passion for helping people and business in all aspects of content marketing flows through in the job role she is in. Go to top SELF-PROMOTION Let me emphasize that Self-Promotion doesn’t have to be obnoxious to be effective.  But, if you don’t Self-Promote you, who will?  If you ever want to get ahead, you have to learn how to Self-Promote. I want to help you accelerate your career by connecting you with your Free Instant Access to my video that shows you simple, yet effective ways to Self-Promote. Start watching now by clicking here! Brought to you by Dorothy Tannahill-Moran â€" dedicated to unleashing your professional potential. Introvert Whisperer

Online Tutoring - A Great Boon For Struggling Math Students

Online Tutoring - A Great Boon For Struggling Math Students 0SHARESShare Math can trick you to the core if you lack in proper concentration on the subject.  Lacking in attention to classes at school could trigger negative offshoots in the form of failing grades and poor performance. Seeking shelter in online help is the ultimate resort to avoid serious consequences. How does online Math tutoring offer solace and comfort to struggling Math students? It drives away the mental anxiety that shrouds the aptitude of students to provide a jittering attitude towards Math It focuses on strengthening the knowledge of Math concepts in a crystal clear manner without any room for doubt and confusion It renders specific attention to the weak spots of the Math learning skills of the students and suggests ideas for improvement. Suppose the student is weak in the concepts of Trigonometry, he can take recourse to Trigonometry online tutoring to recompense his study gaps with the able guidance of tutors online and get back to the track with efficiency An Algebra student also can do the same when he enters as a freshman into the subject and knows nowhere to go for help. He can resolve Algebra problems with the help of an Algebra solver to settle things smoothly without making room for any pitfalls. It is the individual attention of the Math tutoring online with its tech support that makes student learning process successful and entertaining Tutor Pace. Com has ample tutors who show their best in making Math students competent in the subject with great confidence. [starbox id=admin]

Some Times Who You Are Authentically Dictates Your Best Path - Introvert Whisperer

Introvert Whisperer / Some Times Who You Are Authentically Dictates Your Best Path - Introvert Whisperer Some Times Who You Are Authentically Dictates Your Best Path Have you ever noticed that there is never just one way to solve a problem to get to a goal?  Granted, I think there are oftentimes solutions that are considered “standard” but we all know that when you give it more thought, there are alternatives.  It’s easy to fall into the trap of taking a path that most people go simply to save a few brain cells coming up with something different.   The problem with taking the road most other people take is that it may not be the best road for you.   As an introvert, I’ve had to devise alternative strategies to many situations to ensure the kind of outcome I wanted in order to avoid a world of discomfort.  I call them “alternative” because with such things like networking, I had to do it in a way that worked with my personality â€" or said another way â€" “how I function”.  The alternative is due to the fact that the standard approach to things like networking didn’t work for me so a different route was taken.   Your career and each day at work is a series of challenges met by solutions.  When you’re stumped, a good thing to do is to see how other people solve those same issues.  I’d say that’s a pretty good approach. However, you’ll also notice that sometimes a solution for one person is not a solution for you or you try their solution and discover it didn’t work.   When you have poor results or even failure trying something that worked so well for someone else, it hurts your self-esteem.  It can leave you feeling like there is something wrong with you. I get it; I’ve had those reactions. I have found, however, that your career (and your life) is not a “one-size-fits-all” and what works for someone else may not work for you or me.  There is no need to let your self-esteem get damaged.   Find another way.   If you have a challenge in your career you need to know there is a solution.  In fact, there’s more than one solution or path to a satisfying conclusion. Your job is to forge a path that works well for you. Go to top Do you know what your next career step is?  Many people don’t. I want to help you accelerate your career by connecting you with your Free Instant Access to my eBook on how to construct your Career SMART Goals â€" that will help you put together your actions and keep you accountable. Get your copy now and start your action plan today! Brought to you by Dorothy Tannahill-Moran â€" dedicated to unleashing your professional potential. Introvert Whisperer

Play Thousands of Songs Using these Guitar Chord Progressions

Play Thousands of Songs Using these Guitar Chord Progressions Megan L. Did you know there are a handful of common guitar chord progressions that are repeatedly used throughout hundreds of songs? If youve spent much time on YouTube, you might be familiar with the Axis of Awesome. In their popular video, the Axis of Awesome performs a compilation of around 50 songs in under six minutes, all while using the same guitar chord progression. The video is very entertaining as it creatively reveals a secret that professional musicians have known for decades. Guitar Chord Progressions to Play Thousands of Songs Although most popular songs are based on just a handful of guitar chord progressions, sometimes the chords are modified (adding a 7th or 9th for example). They can also be played in a different order, or using different instruments and grooves. So to the untrained ear it may be hard to detect the same underlying chord structure. Once you understand how the most common guitar chord progressions work, it will open the door for you to play thousands of songs easily. Lets start by learning about some of the most basic guitar chords. 5 Basic Guitar Chords If youre just getting started on the guitar, youll want to learn a few basic chords first. The chord charts below show five of the most common open chords. Open chords are chords where some of the strings are played open, without holding down any of the frets. To read the chord charts, imagine that the top line of the chart is the nut, where the neck of the guitar meets the headstock. Each of the six vertical lines represent a guitar string, with the low E string at the far left and high E at the far right. Each horizontal line represents a different fret on the fretboard. The numbers along the bottom of the chart let you know which finger on your left hand should fret each string. Your left hand fingers are numbered one through four, starting with your index finger. For example, to play the A chord as pictured above, hold down the D string with your middle finger on the second fret, the G string with your ring finger on the second fret, and the B string with your pinkie finger on the second fret. Now, strum from the A string down. The X at the top of the diagram indicates that you should not strum the low E string. Understanding Guitar Chord Progressions A chord progression is a pattern of usually three or four chords that is repeated throughout a song. Some songs use a couple different guitar chord progressions, switching back and forth for the verse and the chorus. You might find other songs that use a single chord progression the whole way through. Many musicians use what is known as the Nashville System to talk about chord progressions. For example, lets look at the common chord progression C-F-G, also known as I-IV-V in C. On the Nashville number system, each note in the scale is given a number one through seven, written as a Roman numeral. The root note of the scale is I. In our example, C is I, the root note. F is the fourth note in the scale, IV, and G is the fifth, V. The Nashville system encourages musicians to focus more on the relationships between notes rather than the notes themselves. This is particularly helpful if you are playing with a singer or another musician and they ask you to change the key you are playing. Rather than scrambling to transpose the song, using your familiarity with the relationships between guitar notes, you can quickly and easily switch keys. I-IV-V Chord Progressions Common guitar chord progressions like G-C-D, A-D-E, and E-A-B are all examples of the I-IV-V chord progression in action. So the next time you are looking at a song and you see one of these sequences, you will know you are looking at a I-IV-V chord progression. The I-IV-V chord progression forms the foundations of countless classic songs and contemporary favorites. According to Ultimate Guitar, the I-IV-V progression, with slight variations, can be used to play the following songs: Imagine by John Lennon or Everybody Talks by Neon Trees (I-IV) The Gambler by Kenny Rogers or Where Everybody Knows Your Name from Cheers (I-V) Basket Case by Green Day or Youre Beautiful by James Blunt (I-IV-V-I) All the Small Things by Blink-182 or Born This Way by Lady Gaga (I-V-IV-I) I-V-vi-IV Chord Progressions Want to learn to play all the songs from the Axis of Awesome video we shared about? Just get familiar with the I-V-vi-IV chord progression and you will have all 50 songs (and many more) in the bag! You can play all the songs from the video using the chord progression C-G-Am-F, plus: Journeys Dont Stop Believing Jason Mrazs Im Yours The Beatles Let It Be ii-V-I Chord Progressions These progressions are commonly seen in jazz standards, though they do creep into pop songs from time to time. Using an ii-V-I progression, such as Dm-G-C, you can play songs ranging from the jazz favorite Autumn Leaves to Justin Biebers Boyfriend. SEE ALSO: Easy Guitar Tabs to Play Now Practicing Guitar Chord Progressions Now that you are familiar with the most common guitar chord progressions, memorizing the chord patterns and practicing will help you get to the point where you can easily learn hundreds of songs. If youre just starting out on the guitar, changing from one chord to another quickly and smoothly might be challenging for you. Choose a chord progression and practice strumming each chord slowly and evenly for four counts. Try to keep your transitions on tempo with the pace you are playing. Once you feel comfortable changing chords, try playing one song in a few different keys. As you play, sing or hum along to hear the difference. Try playing Amazing Grace as pictured above in the key of C and then move it to the key of G. Changing keys helps you to hear the relationships between notes, which makes it easier for you to develop your ear. Write Songs of Your Own Another great way to apply these guitar chord progressions is in writing your own songs. Dont feel like you have to use only these chords. Instead, use them as a starting point to explore your musical vision. If youre just beginning to write your own music, it helps to know which chords will sound good together. Try taking one of the tried and true chord progressions youve just learned and put your own spin on it by adding or subbing a new chord, or playing it with a funky rhythm. For more help with guitar, private lessons with a qualified instructor are the best way to sharpen your skills. The right teacher will give you the personal attention you need to make your dreams a reality. TakeLessons guitar teachers are qualified, pre-screened, and can help you understand more about guitar chord progressions. Search for your perfect guitar teacher today! Interested in Private Lessons? Search thousands of teachers for local and live, online lessons. Sign up for convenient, affordable private lessons today! Search for Your Teacher Photo source  LSkyora

Speak Italian by Studying in Italy

Speak Italian by Studying in Italy Learn to Speak Italian through Studying Abroad ChaptersTest your Grammar and Spoken ItalianPrepare for Your Study of the Italian LanguageFinancial Aid for Learning ItalianResources for Italian OnlineWhile studying in a language course can be frustrating, attaining a new language skill is something many university students aim for. If you’ve always dreamed of taking the words and phrases you’ve learned in your language school or in university courses and applying them to real life situations, studying abroad may be the perfect choice for you!If you have been taking an Italian course and want to take your studies a step further, you’re not alone â€" in fact, there are many different ways in which you can learn Italian in Italy.While studying abroad has become an integral part of many a student’s university study, it does take a certain amount of organization. Here are some tips on how to prepare for your study abroad in Italy and towards your journey to speak Italian.Improve your speaking skills with the Italian language co urses here.Let Italy be your language school DanielaItalian Teacher 5.00 (9) £50/h1st lesson free!Discover all our tutors LuciaItalian Teacher 5.00 (4) £17/h1st lesson free!Discover all our tutors MarilùItalian Teacher 5.00 (8) £22/h1st lesson free!Discover all our tutors MarcoItalian Teacher £15/h1st lesson free!Discover all our tutors AntonellaItalian Teacher 5.00 (2) £14/h1st lesson free!Discover all our tutors GiusyItalian Teacher 5.00 (3) £25/h1st lesson free!Discover all our tutors EnricoItalian Teacher 5.00 (2) £20/h1st lesson free!Discover all our tutors FedericaItalian Teacher 5.00 (2) £30/h1st lesson free!Discover all our tutorsTest your Grammar and Spoken ItalianSo you’ve decided to you’d like to speak Italian, and you want to experience language learning in a foreign country? Congratulations! The first step in your journey to speak a new language should involve preparing for the way in which you will learn Italian. In other words, start by testing you r skills in the language.While this may seem like the last step you’d perform before going on a study trip to Italy, many Universities require students to have a level B2 of the language. Beginners and experts alike, if not born in Italy, will have to prove their Italian vocabulary, conversation and grammar skills by an official document.The European Counsel, in fact, publishes reports regularly on what types of language lessons and levels you should have in order to work or study in different countries around Europe.While this may seem unfair for the beginner, keep in mind that while studying abroad, you will have to learn basic Italian verbs and vocabulary in order to communicate with the locals. Taking language lessons isn’t just an important step in appreciating Italian culture and life to the fullest, it also shows respect for the country in which you will live and protect you against being taken advantage of financially, politically and socially.Luckily, there are many tes ts at your disposal that will test your level of Italian grammar, listening comprehension, pronunciation, and basic knowledge of verbs. Here are the tests that are at your disposal:CILS: The Certificazione di Itliano come Lingua Straniera) is recognized throughout Italy. Obtaining a language diploma from the CILS involves exams at four levels, that correspond themselves to the linguistic aptitudes of the speaker: daily situations, specific professional conditions, etc.CELI: The Certificato di Conoscenza della Lingua Italiana is recognized by the Minister of Foreign affairs and is delivered by the University of Perugio. The diploma involves exams at six levels, from level A1 to C2.While there are many ways in which to learn free Italian, taking a language aptitude test and receiving certification do involve a fee. For these two diplomas, not only studying but internships and jobs will be open to you. Generally, the price comes out to around 100 euros, but could go up to even 180 euro s, depending on the level of language the candidate would like to test for.Prepare for Your Study of the Italian LanguageIn order to take advantage of the opportunity to learn Italian culture, and even more Italian words, there is a certain amount of preparation that comes with living abroad. While you should be excited about learning a new language abroad, you should also make sure to complete all the necessary tasks before you leave home.To start, in order to stay in Italy, you will need some form of identity card. Similar to many countries around the world, you will need your passport to enter to all of the local institutions: the bank, the doctor, to rend an apartment, etc.This will be directly linked to getting a codice fiscal. This fiscal identity number is free and will allow you to open a sign up for a phone plan, rent an apartment, find a job, open a bank account. If you’re worried that your Italian lessons didn’t cover enough material for your experience with the Itali an administrative system, don’t worry. You don’t need to be fluent in speaking Italian to attain the codice fiscale.Language lessons can make your daily life in Italy easy!The VisaBefore leaving to study in Italy, you will most likely need to obtain a visa, depending on your citizenship status. A tourism visa or a student visa are both are determined by the motivation of entry into the country. If you are planning to stay more than 90 days in Italian territory, a student visa will be necessary. In any other case, a tourist visa should suffice.The student visa can only be issued by the Italian consulate (or by the consulate section of the Italian embassy), depending on the territory of the country of residence that you are applying to the visa from. It will be helpful at this point if you have started to learn to speak some Italian phrases, as you will most likely encounter only Italian speakers throughout this process.Whether you are applying to a student or tourist visa, it is important that each candidate acquire these documents:A valid passport of at least 3 monthsA round-trip plane ticket (or other method of transport) that is attesting to the start and end date of your journeyProof of sufficient financial means for your stay in ItalyConfirmation of a hotel or other lodgingsHealth insuranceAll of these documents should validate your study visa, as well as the document attesting to your acceptance into a particular study program. Learn to understand administrative phrases, as they will go a long way in your communication with the Italian consulates during every step of the application process.LodgingFinding accommodation in Italy should not be too painstaking of a process, as there are a lot of different options depending on each person’s lifestyle.If you are studying abroad, you will have a very important option at your disposal, which is: student housing. Talk to your advisors at your home school and your future, Italian university in order to revie w the options for student housing. While every university normally has a limited space for foreign students, you shouldn’t have a problem attaining one if you allow plenty of time for the application process.If you would like to live outside of a student residence, one solution is to find an apartment or a flat share. In Italy, landlords and roommates often require a month of rent as commission, and between 1 and 3 months rent worth of security deposit. You should make sure to include this into your monthly budget. For example, a studio in a big city like Rome can cost you between 400 and 600 euros a month.InsuranceThe first step you should take for finding health insurance in Italy is to look into the European insurance card â€" which is free and valid for one year. This will allow you, while you are a European student, to benefit from some free treatments.The next step is to sign up for the Azienda Sanitaria Locale. Functioning similar to a national security service, becoming pa rt of this will allow you to benefit from treatments like locals.Financial Aid for Learning ItalianConcerning finances in general, it is worth noting that while Italy tends to be cheaper than the UK, the cost of living is about the same. Tuition fees, normally between 1000 and 1300 euros on average, should be taken into account in conjunction with about 1000 euros worth of monthly expenses.While this may sound like a lot of money, learning how to speak foreign language doesn’t have to be pricey. If you are worried that your quest in taking Italian courses will not be financially possible for you, there are some scholarship programs that exist for international students.These include programs such as the Erasmus scholarship. There are many students who are empowered to study because of this scholarship, which aims to facilitate the cost burdens of studying abroad and taking language courses. The Minister of Foreign Affairs also has some scholarships geared towards students studying abroad and is worth checking out.These types of scholarships, awarded by the Italian government, can reach up to 700 euros a month. The scholarship is, at its core, a research scholarship, destined towards foreign students who study specific disciplines.Take advantage of conversational practice in Italian to improveResources for Italian OnlineBefore departing for Italy, it might be helpful for both the new and experienced language learner to understand that fluency in a language will depend on the level of immersion within the language and culture. There are many online classes that are at your disposal to practice your conversational Italian speaking skills before you start your journey.If you’re worried about what life will be like as a local, there are also many sites online that aim to give advice and information for people who are moving to Italy. Whether you’re looking for professional opportunities or more information on your study abroad, be sure to check out:The websit e for the UK’s foreign affairsThe site for European Health InsuranceCultural institutes of Italy in the UKWhile completing all of these tasks may seem discouraging in the face of what you thought you would be doing on your stay in Italy, namely all the adventures and foods you’d be having, understanding what kinds of administrative tasks you will need to complete will help you later on. Ultimately, completing all of these tasks beforehand will help you profit from la dolce vita once you’re there!

Graduation Rates Of Athletes

Graduation Rates Of Athletes Practice, class, practice, class, practice, homework, class, clubs/organizations, homework, game, practice, class, homework, projects, practice game and then maybe laundry goes the schedule of collegiate athletes. Compare that to a typical full-time students schedule of class, homework, clubs/organizations and of course maybe laundrymaybe. A student athletes schedule is more demanding than a typical students. However, N.C.A.A. student athletes are now graduating at record rates, higher rates than other students, according to the N.C.A.A.s annual release on graduations figures, cited by an article in The New York Times. The N.C.A.A.s release stated that 79 percent of Division I student athletes beginning their freshmen years in between the 2000/2001 and 2003/2004 school years acquired a degree within six years. The latest entering class beginning in 2003/2004 school year reached the 79 percent mark, matching the record high of the two previous years. The federal graduation statistics were different, however. These statistics showed this years student athletes only graduate at a 64 percent mark, which was higher than the overall student bodys numbers at 63 percent. The N.C.A.A. uses its own statistics, separate from federal numbers. The New York Times stated that student athletes typically graduate higher than the overall student body. Division I football and basketball student athletes still have the lowest graduation figures of all athletes. However, they are performing better in the classroom and graduating at now higher percentages. Scholarships could be the factor that is helping student athletes graduate at higher percentages than the overall student body. Many students drop out of college or fail to complete their degrees because of financial constraints. Most but not all student athletes receive full scholarships as long as they meet specific grade requirements. These full scholarships create stronger incentives and more opportunities for athletes to stay in college. Also, the N.C.A.A. has demonstrated a strong commitment to increasing its student athletes graduation figures.

GMAT Quant Strategies Summing an Arithmetic Sequence

GMAT Quant Strategies Summing an Arithmetic Sequence GMAT MBA Admissions Blog One of the more difficult GMAT problem types deals with summing an arithmetic sequence. Problem 157 in the 12th edition Official Guide is an example: 157. For any positive integer n, the sum of the first n positive integers equals (n(n + 1))/2. What is the sum of all the even integers between 99 and 301? (A) 10,100 (B) 20,200 (C) 22,650 (D) 40,200 (E) 45,150 In this problem the GMAT provides us with an equation, and we can use that equation along with a bit of algebra to solve the problem. However, this might not always be the case, and no doubt in the future the test writers will introduce problems without helpful hints - indeed there are a couple in the 12th and 13th editions of the OG. Consequently, students should know how to do this type of problem in general. First a definition: Arithmetic sequencesare ordered lists of numbers (on the GMAT these numbers are most likely integers) where the difference between adjacent numbers is constant. The most common example on the GMAT are lists of consecutive integers. For example: {1, 2, 3, 4, 5, 6}, or, in general, any list of the form {x, x + 1, x + 2, x + 3...} Arithmetic sequences are similar, but the difference between the terms can be anything. For example: {3, 7, 10, 13, 16}, {1/2, 5/2, 9/2, 13/2}, {2, 4, 6, 8, 10, 12, 14}, or, in general {x, x+ d, x + 2d, x+ 3d...} Everything we need to know about an arithmetic sequence can be summed up in three pieces of information: 1. The first (or last) term 2. The difference between the terms 3. The number of terms For the most part, the first two pieces of information are explicitly or implicitly stated. If we are summing even integers, the difference is two and the first and last terms must both be even regardless of the range stated in the problem. The third piece of information is something we generally have to derive for ourselves. I'm going to use a simple example to explain how to do this. How many integers are there between 7 and 15, inclusive? Intuitively, it seems like we should find the difference between the two numbers, 15 - 7 = 8, and that will be the number of terms. If we take the brute force approach of actually listing the integers we find that the intuitive approach is off by 1: {7, 8, 9, 10, 11, 12, 13, 14, 15}. If you count the integers, you'll find that there are nine of them in the list. It might seem like we should just take the brute force approach every time we need to solve this sort of problem, but for larger sets this would be impractical. So, why is the intuitive approach incorrect? It pretty simple - by subtracting the 7, we don't include it in the set, and the count is off by one. To compensate for this, we add one to the difference. If x is less than y, the number of integers between xand y, inclusiveis y- x + 1 We have to modify this formula if we want to use it count an arithmetic sequence where the difference between terms is greater than 1. If d is the difference between the terms in the sequence, and xis less than y, then the number of terms in the sequence is (y- x)/d + 1 We have to be a bit careful applying this formula. If we're asked to find the number of multiples of 3 between 2 and 34, our first term is not 2, it's 3, and our last term isn't 34, it's 33 - this is because we're only counting multiples of 3. So, now that we know how to count the number of terms we can move on to finding the sum of the terms. First we need a couple of definitions 1. The averageor arithmetic meanof a set of numbers is The sum of the terms/The number of terms For example, the average of the first 5 positive even integers (2, 4, 6, 8, and 10) is (2 + 4 + 6 + 8 + 10)/5 = 30/5 = 6 2. The medianof a set of ordered numbers is the middle term of the set or the average of the two middle terms. That is, if an ordered set has 5 numbers, the 3rd term will be the median; if an ordered set has 6 numbers, the average of the 3rd and 4th terms will be the median. Two examples: To find the median of the set {8, 17, 7, 13, 4}, we order the terms of the set from least to greatest (or vice versa) and find the middle term. The middle term of the set {4, 7, 8, 13, 17} is 8. So the median of the set is 8. To find the median of the set {8, 17, 7, 13, 4, 31} we follow the same procedure, but now we take the average of the two middle terms. The average of the two middle terms of the set {4, 7, 8, 13, 17, 31} are 8 and 13. So the median of the set is (8 + 13)/2 = 10.5 Arithmetic sequences of numbers have the nifty property that the median and mean of the set are the same number. Mean of an arithmetic sequence = Median of an arithmetic sequence Furthermore the mean of an arithmetic sequence is just the average of the first and last term, and since the median is equal to the mean, the median is also the average of the first and last term. If this seems mysterious, remember that there is a geometric interpretation of the mean. The mean of two numbers on the number line is the midpoint, e.g. the mean of 1 and 7 is 4, because the distance from 1 to 4 is equal to the distance betwen 4 and 7. In an arithmetic sequence the midpoint between the first and last term is exactly the median. Now let's derive the formula for the sum of an arithmetic sequence. Recall that Mean = Sum of terms/Number of terms Therefore (Mean)(Number of terms) = Sum of terms So, if xis the first term of an arithmetic sequence,yis the last term, and d is the difference, the sum of the sequence is [(x+ y)/2][((y - x/)d) + 1] = Sum of terms Now let's return to problem 157 from the 12th OG: 157. For any positive integer n, the sum of the first n positive integers equals (n(n + 1))/2. What is the sum of all the even integers between 99 and 301? (A) 10,100 (B) 20,200 (C) 22,650 (D) 40,200 (E) 45,150 Because we are only concerned with the even integers, the first term of the sequence is 100 and the last term of the sequence is 300. The mean of the sequence is (100 + 300)/2 = 400/2 = 200 The number of terms in the sequence is ((300 - 100)/2) + 1 = (200/2) + 1 = 100 + 1 = 101 Thus, the sum of the sequence is (101)(200) = 20,200 The explanation is the OG is much more convoluted, with unnecessarily obscure notation. The method presented here is clean and quick. Try it for yourself. 1. Find the sum of the first 100 positive integers 2. Find the sum of all the multiples of 3 between 1 and 100 3. Find the sum of the multiples of 7 between 47 and 624 4. The sum of a set of 50 consecutive positive odd numbers is 172. Find the fist and last term of the sequence I hope you enjoyed this post. I will post answers to the questions with explanations in a subsequent post. Please visit our GMAT Tutoring page to learn more about MyGuru's approach to test prep. About the Author John E. is a Senior MyGuru GMAT tutor in Chicago. He also tutors the GRE, SAT, ACT, and almost anything math related. He holds a B.S. in Mathematics and English from Indiana University, and a M.S. in Mathematics from UIC. He's scored in the 99th percentile on all of the above standardized tests, and has worked for MyGuru and other companies to develop proprietary test prep questions and explanations of difficult quantitative concepts to help students improve their GMAT scores. He's currently working with MyGuru to develop proprietary test prep material focused on the most difficult GMAT question types. Are you interested in more GMAT explanations and practice problems that are similiar to the above? hbspt.cta._relativeUrls=true;hbspt.cta.load(215486, 'c962711f-eb4d-4fa9-9c75-db61122354d0', {});