The first SAT exam was held in
1) 1899.
2) 1901.
3) 1905.
4) 1961.
The Scholastic Aptitude Test or the SAT is a standardized test used in the United States for college admissions. High school students usually take the SAT at the end of their junior year (11 grade) of High School or at the beginning of their senior year (12 grade). Students are able to re-take the test as many times as they like on any of the test dates, which occur 6-8 times a year. The test is administered all over the world, and most big cities have at least one testing center.
The SAT is developed and run by College Board, an American non-profit organization created to provide teenagers with access to higher education. It was founded in 1899 and was originally called the College Entrance Examination Board (CEEB). Not only does it develop standardized testing, it also develops the Advances Placement (AP) Program. AP classes are offered in most High Schools in the U.S. and provide students with university level classes. These classes allow students to gain college credit and skip some of the basic courses at the university.
Today, the SAT is made up of three main parts: Evidence-Based Reading and Writing, Mathematics and the Essay, but over its long history, the SAT has undergone several changes in format, types of questions and scoring. The first standardized exam was administered by the CEEB in 1901. It consisted of a series of essay questions on topics such as Greek, Latin and Physics, it was completed over the course of 5 days. After the development of the IQ test in 1905, the SAT changed its approach to the test, now testing not specific knowledge, but aptitude for learning. By 1961 the SAT was taken by over 800 thousand students annually.
A lot of changes were made to the SAT between 1994 and 2005: the use of calculators became permitted, the reading passages were chosen to mimic texts students might encounter in college, the scoring system was changed from 1600 to 2400, and an essay section was introduced. Some of these changes were reversed in 2016: the scoring system changed back to 1600 and the essay became optional.
In recent years, the SAT has been criticized for not being a good reflection of students’ academic ability. The test puts a lot of emphasis on speed and time management, prioritizing it over knowledge and reasoning. The reading section contains 52 questions based on 5 reading passages and has a time limit of 65 minutes. Even without the time it takes to read and understand each passage, this gives a student a little over a minute to answer each question, some of which are quite difficult. The other sections are no better. The whole exam takes 4 hours and 5 minutes to complete, and the breaks between its four sections are very short: a 10-minute break between the Reading and Writing sections, 5 minutes between Writing and Math, and only 2 minutes between Math and the essay. Because of these issues, more and more universities are becoming “test-optional”, meaning that they do not require their students to submit standardized test scores.
In the summer of 2018, there was a scandal regarding the August SAT. The test got leaked to the Internet a few days before the exam. Because of this College Board threatened to cancel all the scores. This news resulted in a lot of panicked high school seniors, who would not have time to re-take the test before their college applications were due. A lot of desperate students turned to the ACT (American College Testing), the SAT’s main rival, as an alternative standardized test.
Scholastic Aptitude Test: 20 Important Facts and Practice Questions and Answers
The Scholastic Aptitude Test (SAT) is a test designed to judge the essential skills needed for academic success at the tertiary level.
The current version of the test contains three main sections evaluating basic critical reading, math, and writing skills, as well as an open type not included in the final score.
High school students who require entry into colleges and universities in the United States typically take the SAT.
The SAT has also been approved by other countries such as Israel and Sweden as an entrance exam for admission to higher education institutions.
The SAT is made up of 3 hours and 45 minutes of actual timed sections; however, extra time for timed breaks, administration, and more is given by the administrators of the test.
We are going to look at the 20 important facts about Scholastic Aptitude Test popularly known as SAT.
Gaining knowledge of this test will help you if you are asked to participate in the test as you don’t have to get into what you don’t know.
Here are important facts and tips about the Scholastic Aptitude Test that you need to know to excel in the exam:
- What is SAT?
The full meaning of SAT is “Scholastic Aptitude Test” – a widely recognized college admission test that serves as a requirement to apply for undergraduate programs in most universities across the United States of America.
College Board is a non-profit educational organization that aims to provide each student with equal opportunities to prove what they’ve learned in school.
College Board also conducts SAT – a test that is taken by more than 1.7 million students every year.
- What does SAT assess?
The SAT is designed to assess the student’s knowledge of the English language and mathematics.
With four options to choose the correct one from, the exam pattern uses MCQ (Multiple Choice Questions).
As the SAT has an optional essay writing section, few universities also demand a valid score on the SAT subject test. By taking an SAT exam, you can acquire lots of advantages.
- Who is eligible for the SAT?
The SAT is typically designed for high school juniors and seniors in the United States. The test can also be taken by students from other countries that have completed their 12 years of school education successfully for admission into various streams available in different American colleges.
Students in 11th or 12th class can take the SAT exam, but it is recommended that students take a practice SAT test a year before their intended year of admission.
- What are the criteria for minimum marks on the SAT?
For appearing in the SAT Reasoning Test or SAT Subject Tests, there are no criteria of minimum marks but several colleges require a good SAT score along with a good academic record.
Colleges carry out their own tests in addition to the SAT scores, like Essay Writing which is the Subject Test, Personality Test, and also ask for Curriculum Vitae and recommendations from teachers.
- SAT exam pattern
The SAT consists of two main sections which have 10 sub-testing sections, including Evidence-Based Reading and Writing (EBRW), and Math.
The first section of the exam comprises a 25-minute essay while the last section is a 10-minute multiple-choice writing section.
Twenty-five-minute sections are sections two through 7 while twenty-minute sections are sections 8 and 9.
Candidates close to each other in the same session while taking the test are most likely to get entirely different test books with various content orders.
Wrong answers have no negative marking.
The section known as the SAT subject test is the third section. Only a few universities or programs need their applicants to take part in the SAT subject test.
This test is obtainable in 20 subjects based on five general subject areas such as Math, Science, English, Languages, and History.
- Validity of the SAT score
The SAT scores are valid for a period of five years unless their pattern changes. For this reason, students of the eleventh class can take the test.
If the score is excellent, they can use the same for undergraduate admissions in the United States.
- The method of the SAT score calculation
The highest score you can realize is 1600, which is calculated by adding up the scores of two sections.
The two main sections have the highest score of 800 each.
Raw scores comprise the total number of questions you’ve answered correctly, which is then converted into a scale score ranging from 200 to 800 for each section.
This is done to ensure that the assessment across all test centers throughout the year is equal and fair, and this scaled score is not a relative score.
- SAT score results
SAT score results can be obtained two weeks after the test date. Though the June scores take longer, they are obtainable within 6 weeks of the exam date.
- The dos and don’ts for your SAT exam
Here are some dos and don’ts of the SAT exam that you are about to take, including:
- Bring a watch that is impossible to hear.
- Bring a calculator for SAT math test.
- Bring enough pencils and erasers for the test.
- Bring your admission and identity card.
- Bring some snacks for the two breaks that are provided during the exam.
- Ensure you arrive early at the center, as most exam centers are likely to be open at least 45 minutes before the test.
- Don’t take any electronic devices, as it is strictly disallowed.
- Don’t take color pens, highlighter, compass, etc.
- Don’t take any paper or pamphlets.
- Can you possibly study for the SAT in one day?
Studying for the SAT test in one day is not recommended because, in order to perform better, you need to learn and go through the exam pattern thoroughly.
You can grab most of the exam methods by merely taking the time to understand the pattern of the questions of the SAT test.
- What do you need to do the day before the SAT test?
Don’t stress or over-study before the exam day and catch enough sleep. Also, get ready with exam prerequisites for the SAT test, try to solve SAT practice tests, and don’t spend an extensive amount of time working on SAT.
- SAT exam preparation
The SAT exam can be a little overwhelming. Students are advised to start working on their sample test, mock test, or SAT practice test at least a month before undertaking SAT exam.
You must be prepared with your SAT test-taking strategies as the SAT test date is approaching.
Most times, students who are fully prepared with the SAT course outline do not remember to go through the SAT exam guidelines.
It is quite impressive to learn about SAT before undertaking the test. The benefits of undertaking the test will help you understand the importance of SAT better with learning about the purpose.
SAT exams are divided into three compulsory and one optional category such as SAT Reading, SAT Writing and Language, SAT Math, and SAT Essay (optional).
- The purpose of the SAT examination
The student’s ability to speak English and solve Mathematical equations can be evaluated by the SAT examination.
SAT has an optional test that is based on Essay. As part of your entrance exam requirement listed by your college, you most probably will have to take an SAT examination if you’re a high school senior or junior student who is willing to go after higher education in the United States.
- A regular practice of at least three months is good for the SAT
It’s really necessary that the student gets fully prepared before undertaking the SAT English and Mathematical proficiency tests.
Regular practice of at least 3 months is required for the SAT, which is similar to other entrance exams that suffice a thorough understanding of the test pattern, studies, and time management.
- SAT score verification
To ensure that you have received scores in all sections and nothing has been left out, the SAT Score verification is nothing but a reassessment of your test scores.
So, you may have missed or made a mistake in marking your answers if you feel that the SAT score that you received is different from what you expected.
Another tangible reason for a different SAT score than what you anticipated can be that your Essay is impossible to read or blank when one sees it online.
You have three options, including multiple-choice hand score verification under SAT score verification, essay score verification, or both, as well as multiple-choice and essay scores.
By filling in an SAT score verification form you can put in this request within the next five months after the test day.
It’s recommended to read the instructions given on the form carefully before going further.
You will also need to submit a score verification fee.
This score verification fee will be reduced for students with a fee waiver.
Once you pay the verification fee and submit your form, you will receive a letter with the new and confirmed results within five weeks.
The verification fee will be paid back to support any changes in the SAT scores post verification as a result of an inconsistency in the scoring or scanning process.
- SAT score cancellation
Here are two methods through which you can cancel your SAT scores in case you have any reason to cancel your SAT score:
i. At home
You can cancel your test at home if you find out you got poor performance after you depart the test center. There is however time limit to it.
You can submit your cancellation request by writing to College Board as hurriedly as you can as the deadline for receiving such requests will be 11:59 PM (IST) on a Wednesday after the test date.
ii. At the test center
You can cancel your test right then and there if you have probably skipped a number of questions or feel you are not sure about how the test went.
You can ask the supervisor for a ‘Request to Cancel Test Scores’ form right at that moment, at the test center.
All you need to do is fill in all details along with your signature, and then submit the form to the supervisor.
- SAT cut off
After appearing for their SAT, The College Board does not have any SAT cut-off listed for students desiring to apply for universities abroad.
Candidates are expected to fall within a certain range to be eligible for admission to top schools as there are no strict SAT cut-offs for top colleges/ universities.
However, for unusual cases, exceptions would be made.
- Countries where SAT score is acceptable
Every country has its own criteria for the selection of international students. The SAT Exam is accepted globally in different colleges.
It is most popular for undergraduate courses in the USA and Canada, although it’s also accepted by some universities in the UK and Australia.
- What are the best books recommended for SAT exam?
You would always need a set of the best books to get you prepared for the SAT Exam whether you decide to study on your own or join a coaching class.
This set of books will help you cover the whole syllabus along with a series of sample papers or practice tests.
Practicing these questions will give you an insight into the entire feel of the exam paper along with allowing you to figure out how much you have achieved.
- Sample papers and question papers for the SAT exam
Solving SAT Sample papers is one of the most suitable methods of getting ready for the SAT.
Solving SAT Test Papers not only allows the candidate to prepare for the exam day but also self-estimate his performance.
Scholastic Aptitude Test Practice Questions and Answers
Here are practice sample questions and answers to help you in your SAT exam preparation:
Question One
What is the square root of Y if the sum Y of three consecutive even numbers is a perfect square between 200 and 400?
A 15
B 16
C 18
D 19
The answer is C = 18
Explanation:
Let the number be x, x+2, and x+4.
Therefore, Y=x+x+2+x+4 = 3x+6=3(x+2)
This means even number (as the sum of 3 even numbers is even). So, Y should be even and a multiple of 3.
Thus, 256 (16)² and 324 (18)² are the even perfect square number between 200 and 400.
But from the above calculation, Y should be a multiple of 3.
324 is the multiple of 3 instead of 256
So, Y is equal to 324.
And the square root of 324 becomes 18 (answer).
Question Two
The sum of the first T natural numbers is A, for a certain T>1, the sum of their cubes is B, and then log A√B is what?
A. 4
B. 3
C. 2
D. 1
The answer is A = 4
Explanation:
A = sum of n Natural number
=2T (T+1)
B = sum of cubes of N rotation
= (2T (T+1)) 2 log A
B=log2(T(T+1))2
(2T(T+1))21=212log2T(T+1)(2T(T+1)) =4
Question Three
The mean of 16 numbers is 48. What is the new mean if each number is divided by 4 and diminished by 3?
A. 12
B. 48
C. 52
D. 9
The answer is D = 9
Explanation:
Mean of 16 numbers = 48
If each number is divided by 4,
Then mean of 16 numbers = 4
Original mean = 448 =12
Now, 3 is diminished by every number
Mean is also diminished by 3 = 12 − 3 = 9 Ans.
Conclusion
The Scholastic Aptitude Test popularly known as SAT is a globally recognized college admission test that serves as a qualification to apply for undergraduate programs in most of the universities across the United States of America.
The test is a non-profit education organization that is conducted by the “College Board” to provide each student with equal opportunities to prove what they’ve learned in school.
Every year, more than 1.7 million students take the SAT exam.
The aim of this test is to assess the student’s knowledge of the English language and mathematics.
It has MCQ (Multiple-Choice Questions) patterns with four options to choose the right answer, with an optional essay writing section.
This article provided you with the information you need to get yourself ready for the exam if you are asked to sit for the SAT test. Remember that practice is the key to succeeding on the test.
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Scholastic Assessment Test (SAT) — широко распространённый вступительный экзамен в колледжи и университеты США, разработанный частной коммерческой организацией College Board. Тест оценивает готовность старшеклассников к быстрой аналитической работе с разного типа информацией, необходимой для дальнейшего обучения, и позволяет вузам сопоставить уровень претендентов.
Экзамен содержит два обязательных раздела с двумя модулями в каждом, плюс опциональное эссе.
Структура теста SAT:
- Math test: calculator permitted (математика с использованием калькулятора) и Math test: calculator not permitted (математика без калькулятора).
- Reading (аналитическое чтение) и Writing and language test (письмо и языковой тест).
- Essay (сочинение по желанию).
По каждому обязательному разделу можно набрать от 200 до 800 баллов. При суммарном максимуме SAT в 1600 баллов лучшие вузы Америки рассматривают кандидатов с результатом 1400+.
Баллы за эссе учитываются отдельно. Каждый из двух рецензентов оценивает сочинение по трём критериям: чтение, анализ, письмо, начисляя по каждому от 1 до 4 баллов. Итоговая оценка варьируется от 6 до 24 баллов.
Основное тестирование длится 3 часа, эссе — 50 минут.
Экзамен проходит очно в официальных центрах тестирования.
Стоимость SAT составляет $ 52 за основную часть или $ 68 за экзамен с эссе, а также международные сборы: $ 49 для России и других стран Евразии. Кроме того, плату в $ 24 могут взимать местные центры тестирования. Дополнительные затраты стоит учитывать при регистрации по телефону — $ 15 и изменении даты или места тестирования — $ 30.
Math
Математические тесты объединяют решение задач и анализ данных, моделирование и стратегическое использование инструментов. Три раздела математики, на которых сосредоточено внимание, это
- линейные уравнения и системы;
- задачи и анализ данных;
- сложные уравнения.
Дополнительный разделы включают в себя геометрию и тригонометрию.
В целом Math test проясняет, насколько стратегически, гибко и точно вы действуете, быстро ли находите решения, определяя и используя наиболее эффективные подходы.
Math: calculator permitted
38 вопросов, 55 минут
Первая часть Math test разрешает использование калькулятора. В этом модуле можно сосредоточиться на сложном моделировании и рассуждениях, ведь калькулятор экономит время.
Однако встречаются и такие вопросы, для ответа на которые лучше не использовать калькулятор, даже если это разрешено. Тот случай, когда студенты, которые задействуют способность размышлять, могут завершить тест раньше, чем прибегнувшие к калькулятору. Будьте внимательны, призывают разработчики теста, анализируйте. Калькулятор, как и любой другой инструмент, эффективен настолько, насколько умён использующий его человек.
Math test: calculator not permitted
20 вопросов, 25 минут
Этот модуль выявляет, насколько вы владеете математическими понятиями и сильны в вычислениях.
Большинство вопросов в математических тестах предлагают варианты ответа, однако по 22% заданий нужно внести решения в специальные таблицы на листе для ответов.
Reading test
52 вопроса, 65 минут
Тест по чтению фокусируется на знаниях и навыках, лежащих в основе любого процесса обучения и карьеры: как вы воспринимаете, анализируете и используете информацию. Неважно, насколько хорошо вы запоминаете факты и определения. Вопросы в тесте подобными тем, которые звучат в ходе оживленного, вдумчивого и аргументированного обсуждения.
Одни вопросы адресуют к информации, изложенной прямо, другие оценивают способность читать между строк: понимать, что подразумевал автор. Тест выявляет, умеете ли вы использовать контекст; понимаете ли, как выбор слова влияет на тон и стиль повествования; как анализируете научные тексты. Например, вы можете прочитать об эксперименте и получить задание исследовать гипотезы, объяснить данные и проанализировать последствия.
Как правило, тест по чтению содержит:
- отрывок из классического или современного произведения американской или мировой литературы;
- один или два фрагмента из основополагающего документа США или речи общественного или политического деятеля;
- подборку текстов по экономике, психологии, социологии;
- выдержки из научных статей, исследующих основополагающие концепции и достижения в области точных и естественных наук.
Writing and language test
44 вопроса и 35 минут
Тест по письму предлагает редактуру текста: прочитать, выявить ошибки, стилистические или синтаксические недостатки и исправить их. Этот практический навык используется в старшей школе и важен для успешной учёбы в вузе.
Для выполнения некоторых заданий достаточно прочитать одно предложение, другие потребуют изучить объёмный фрагмент текста или инфографику. Вас могут попросить выбрать предложение, которое исправляет неверную трактовку научной таблицы или лучше объясняет важность данных. Возможно и такое задание: обозначить ответ, который обостряет аргументированное утверждение или добавляет соответствующую контексту деталь.
Writing and language test оценивает умение анализировать информацию, формулировать мысли кратко и ёмко, аргументировать заявления, понимать контекст и стилистику.
SAT Essay (по желанию)
50 минут
Некогда обязательный модуль написания сочинения стал опциональным в 2016 году, а к 2021 году из-за пандемии COVID-19 вышел из структуры экзамена для американских школьников. Иностранные абитуриенты смогут выбрать его в последний раз на экзамене SAT в июне. Для некоторых вузов США эссе может стать дополнительным аргументом в пользу вашей кандидатуры.
Во время экзамена вам нужно будет прочитать и проанализировать фрагмент текста: объяснить, как автор выстраивает аргументацию для аудитории, и подтвердить свои доводы примерами из отрывка. Оценочные суждения — склонны вы согласиться с автором или нет — не требуются.
Сочинение оценивается по трём критериям: восприятие текста, анализ и письмо.
SAT Essay демонстрирует, насколько хорошо студент понимает текст и использует его как основу для глубоко продуманного и прекрасно сформулированного высказывания.
Лучшие университеты США предъявляют к абитуриентам высочайшие требования, но мечта оказаться в топовом вузе мира осуществима. Начните подготовку как можно раньше.
Тренируйтесь проходить SAT с помощью специального программного обеспечения, которое используют американские школьники. Узнайте подробности и скачайте демоверсию.
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Мотивационное письмо в зарубежные вузы
Как составить мотивационное письмо, которое впечатлит приёмную комиссию? Скачайте брошюру EDucation Masters, используйте пошаговый план и чек-лист!
В данном задании дается связный текст с семью пропусками. В данной части экзамена это самое сложное задание. Для каждого пропуска предлагаются четыре варианта ответа, из которых только один является правильным. За каждый правильно выбранный ответ дается 1 Балл. За все задание можно получить максимально 7 Баллов.
ЦЕЛЬ ЗАДАНИЯ: Проверить умение использовать лексику в коммуникативном контексте с учетом специфики:
Форм одного слова и слов, близких по написанию и звучанию;
Ф Значений одного слова и его синонимов, антонимов, омонимов;
Ф Норм лексической сочетаемости, принятых в английском языке, и т. д.
СОВЕТЫ ПО ЭФФЕКТИВНОМУ ВЫПОЛНЕНИЮ ЗАДАНИЯ
Заранее ознакомиться с форматом задания и с требованиями по заполнению бланков для данного задания.
Во время первого прочтения
Просмотреть текст с пропусками, постараться понять его содержание.
Во время второго прочтения
1. Читать текст до пропуска. При работе с каждым фрагментом текста с пропуском использовать следующую логику:
♦ читать внимательно весь фрагмент, но особое внимание уделить предложению с пропущенным словом;
♦ внимательно изучить все предложенные варианты ответа, выбрать наиболее подходящий с учетом значения и норм лексической сочетаемости пропущенного слова. ОСОБОЕ ВНИМАНИЕ уделить Синонимам (у них могут Быть разные оттенки значения, они могут иметь Различия в управлении и сочетаемости с другими словами), а также Созвучным словам или словам Со сходным написанием (у них могут быть разные значения).
♦ прочитать предложение с пропуском еще раз, убедиться, что выбранное слово является наиболее корректным для заполнения пропуска. ОБОСНОВАТЬ СВОЙ ВЫБОР, определив, почему другие варианты неверны в данном случае. Если задание выполняется Не на экзамене, проверить правильность сделанного выбора По словарю.
2. Обвести/ записать окончательный вариант ответа в тексте задания.
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 1
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A New Family Member
Tracey and her sister had always wanted their own horse. And although neither of them had much spare money, they were about to ∣A22∣Their dream. The tricky part was not getting a horse but actually finding somewhere to keep one. But eventually Mrs Richards aGreed to let the girls ∣A23∣A small field at the far end of the farm. This was going to ∣A24∣Them J500 a year but it would work out at just over J20 per month each which was OK. The horse himself was coming from the Horse Rescue Charity. They would need to make a small donation every year to cover the cost of an animal welfare inspector who would visit twice a year. The ∣A25∣ Expenses after this would be for food and vet bills. But the two girls were
∣A26∣That they could manage and were committed to going ahead. And it was a big commitment. They were getting an eighteen month old skewbald colt named Domino. Horses often live over twenty years and the sisters were taking him on A27∣Life. Actually they had plans to get another horse as a friend for Domino. But first of all Domino would need to settle down. He had been badly treated by his previous owners and was still a bit nervous and difficult to ∣A28∣.
A22 I |
1) realise |
2) consider |
3) have |
4) believe |
A23∣ |
1) borrow |
2) pay |
3) rent |
4) lend |
A24 I |
1) charge |
2) fee |
3) pay |
4) cost |
A25 I |
1) longest |
2) biggest |
3) hugest |
4) tallest |
A26∣ |
1) assured |
2) comfortable |
3) thoughtful |
4) confident |
A27∣ |
1) for |
2) during |
3) at |
4) to |
A28∣ |
1) deal |
2) agree |
3) handle |
4) cope |
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 2
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Unlucky Travellers
Susan sat down, switched on her computer and was just about to read Her overnight emails when the door flew open. “Valerie! What are you doing here? You are A22∣ to be on holiday in Italy!”
Susan was astonished. She and Val worked together as receptionists at the hospital. Because she had expected to be on her own and working twice as hard, she was quite pleased to see Val. On the other hand she knew that Val was really looking ∣A23∣To her holiday. What could possibly have gone wrong? Val walked in but she didn’t say a ∣A24∣ word. It was clear that she was upset and tired. “What is it? What’s happened?” Susan continued. “Is everything OK?” Valerie was silent for some moments but eventually A25__________________________ . “You clearly haven’t
Heard the news. Our travel company went bankrupt on Friday. We didn’t know and so went to the airport on Saturday morning. Actually we have spent the whole weekend at the airport hoping still to get a flight. In the end we gave ∣A26 and came home”. “Oh you poor thing,” Susan gushed. “Let me make you a cup of tea but then you should go home. You still have two weeks holiday to A27[ Is certainly nice enough at the moment.
To Italy still. We had travel insurance and it seems we will get all our money ∣A28[ We’ll try again in the autumn with a different travel company.”
A22 I |
1) proposed |
2) suggested |
3) wanted |
4) supposed |
A23∣ |
1) for |
2) around |
3) forward |
4) after |
A24∣ |
1)separate |
2) single |
3) one |
4) certain |
A25∣ |
1) asked |
2) said |
3) ) spoke |
4) told |
A26 I |
1) up |
2) on |
3) to |
4) at |
A27∣ |
1) make |
2) take |
3) manage |
4) do |
A28∣ |
1) back |
2) still |
3) agreed |
4) together |
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 3
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The Tower of London
‘Her Majesty’s Royal Palace and Fortress’, ‘The Tower’ and ‘The White Tower’ are all names for the building most commonly known as The Tower of London. Construction began in 1078 but work ∣A22∣, on and off, over a period of two hundred years or more.
The Tower was essentially a fortress whose functions eventually extended to that of royal palace, prison, armoury, zoo, Royal Mint and observatory. Since 1303 it has also been used ∣A23∣Storing the Crown Jewels of the United Kingdom. Today, however, The Tower is cared for by an independent charity and receives no funding from the governmEnt or the crown.
The Tower is probably best known for the famous prisoners who were ∣A24∣, and sometimes executed, there. In 1483 the 13-year-old King Edward 5ffi and his 10-year-old brother Richard were murdered there; apparently on the orders of their uncle, the Duke of Gloucester. ∣A25∣The most famous victim of The Tower was Anne Boleyn, the unfortunate second wife of Henry 8th. But Guy Fawkes, Thomas Moore, Sir Walter Raleigh and even the future Queen Elizabeth 1st were all imprisoned behind those fearsome walls.
Most people know the A26∣Legend that if the ravens ever leave The Tower — then the British Monarchy will be doomed. Possibly less people know however that the Tower was also one of the ∣A27∣Zoos. Lions, tigers and large ∣A28∣Of rare and exotic species lived
In the Tower gardens over 800 years ago. |
|||||
∣A22∣ |
1) lengthened |
2) continued |
3) prolonged |
4) increased |
|
A23∣ |
1) as |
2) with |
3) for |
‘∖ |
4) to |
A24∣ |
1) captured |
2) maintained |
3) found |
4) held |
|
A25 I |
1) Thus |
2) Consequently |
3) Probably |
4) Although |
|
A26∣ |
1) ancient |
2) prehistoric |
3) antique |
4) aged |
|
A27 I |
1) newest |
2) youngest |
3) earliest |
4) soonest |
|
A28 I |
1) figures |
2) groups |
3) herds |
4) numbers |
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 4
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Schools for gifted and talented: view of American scholars
Gifted programs often provoke controversy because there is no standard definition of what a gifted student is. There are six ∣A22 of ability often evaluated in order to determine
∣A23∣A child is gifted: general intellectual ability, specific academic aptitude, creative thinking, leadership ability, visual and performing arts, and psychomotor ability. They are ∣A24∣ by combinations of standardized tests, plus peer and teacher evaluations.
On the one hand schools for gifted and talented may ∣A25∣The emotional stress of isolation and peer rejection often experienced by gifted students in a traditional school. On the other hand — social development of a child may be impeded as a result of isolation from the general population.
We can’t deny the fact that gifted programs offer personalized instruction and enriched curriculum suited to the needs of students gifted in this or that area. Such programs allow students to learn at a highly ∣A26 rate according to their ability. School administrators in such schools hire gifted teaching staff and select teachers who can be a source of instructional innovation.
Such schools normally have smaller classes and in general these schools for the gifted are few. Access ∣A27∣ them may be physically difficult because of their location. Besides, they may be not available for families with limited income asthey may be expensive. If such schools are publicly funded, they may be opposed as elitist and money that might go to traditional schools.
A22 I |
1) districts |
2) regions |
3) parts |
4) areas |
A23j |
1) whether |
2) wherever |
3) whenever |
4) whereas |
A24 I |
1) calculated |
2) quantified |
3) determined |
4) measured |
A25∣ |
1) treat |
2) relieve |
3) simplify |
4) improve |
A26∣ |
1) hasty |
2) prompt |
3) accelerated |
4) hurried |
A27∣ |
1) to |
2) for |
3) at |
4) in |
A28∣ |
1) blamed |
2) charged |
3) accused |
4) claimed |
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 5
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From High School to University Students
Some students find transition from secondary school to tertiary education painful. Well- known life is left ∣A22∣ with familiar home and community environment, parents, siblings, friends. Anticipation of unpredictable academic responsibilities and fear of failure, together with fear of disappointing one’s parents and friends ∣A23∣To the stress. They are both ∣A24∣ and afraid of new social responsibilities like dealing with roommates, instructors, male and female student friends. There is fear of not being accepted; fear of loneliness; anxiety and guilt about breaking with the past. They are on the edge of redefining themselves as adults, finding a satisfactory career, abandoning old friends and finding new.
What can be done to ∣A25∣ this stress? Firstly, it’s important to become ∣A26∣ with the university’s scholastic and non-scholastic programs: check the university’s website and request informational brochures. You can also visit the campus and introduce yourself at the Departmental office; talk to students majoring in the Department. If the university can provide the names of roommates, become acquainted in person or by ∣A27∣Prior to classes. Most Universities have orientation programs — first year student assemble on campus for a week before the start of classes. Orientation can be led by Departmental deans, instructors, and majors, introducing new students to academic procedures and standards, enrolling students in their first term classes, assigning ∣A28∣. each new student an upperclassman as mentor to help them adjust to their first year at the university.
I A22∣ |
1) back |
2) behind |
3) apart |
4) aside |
I A23∣ |
1) multiply |
2) raise |
3) rise |
4) add |
I A24∣ |
1) eager |
2) liking |
3) wanting |
4) keen |
I A25 I |
1) shorten |
2) eliminate |
3) refuse |
4) release |
I A26∣ |
1) aware |
2) conscious |
3) acquainted |
4) sensitive |
I A27 I |
1) correspondence |
2) communication |
3) interaction |
4) post |
I A28∣ |
1) to |
2) for |
3) at |
4) — |
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 6
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Education in the UK: Pages of History
Prior to 1944 the British secondary education system was rather haphazard. Schools were created by local governments, private charities, and religious foundations. Schools varied greatly by region. ∣A2¾ Was not available to all, and secondary schools were mainly for the upper and middle classes.
In 1944, secondary education was A23∣ as a right for all children, and universal, free education was introduced. From 1944 to 1976 state-funded secondary education of three types of schools (the Tripartite System): Grammar School, Secondary
Technical School and Secondary Modern School. The basic assumption of the Tripartite System was that all should be entitled to an education appropriate to their nEeds and abilities. It also assumed that students with different abilities should have a different ∣A25∣. Pupils were assigned to one of the three types of school according to their performance in an examination taken at age eleven, the Eleven Plus examination.
Grammar Schools were intended to A26∣A highly academic curriculum. There was a strong focus on intellectual subjects, such as literature, classics and complex mathematics, aimed A27 developing students’ ability to deal with abstract concepts. Secondary Technical Schools were designed to train children with ability in mechanical and scientific subjects. The focus of the schools was on providing scientists, engineers and technicians. Secondary Modern Schools would train pupils in practical skills, equipping them for less skilled jobs and home management.
Due to the expense of building facilities for three types of schools, very few Technical Schools were built, and education in the UK retained its class character: the upper class children attended Grammar School which received the lion’s share of funding, lower class children attended Modern Schools which were largely neglected. Only children who |А28|_ to Grammar Schools had a real chance of getting into a university.
I A22 |
1) Access |
2) Attendance |
3) Entrance |
4) Reception |
I A23 |
1) recognized |
2) recalled |
3) found |
4) realised |
I A24 |
1) inserted |
2) included |
3) contained |
4) consisted |
I A25 |
1) agenda |
2) curriculum |
3) courses |
4) plan |
I A26 |
1) instruct |
2)learn |
3) teach |
4) study |
I A27 |
1) on |
2) at |
3) to |
4) for |
I A28 |
1) attended |
2) admitted |
3) went |
4) graduated |
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 7
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Globalisation
Globalisation is good and bad and inevitable. It is good or at least useful economically because it lowers ∣A22∣To trade and increases the flow of goods, labour and services. It has both ∣A23∣In and encouraged legal migration, and tourism. It has shared the best of the world’s musical culture, sport, TV and films, fashion and dance. It has made the world both familiar and strange. In any main Street from Moscow to Los Angeles or London to Sydney — one can eat Chinese, Indian, Italian or Thai cuisine and it seems perfectly normal. Globalisation has reduced (many argue) the ∣A24∣Of global conflict and it has aided the development of world health policies and humanitarian aid. The charity concert “Live Aid” was watched by 400 million viewers in 60 countries.
But Globalisation is also dark. The process began through “discovery” and colonization. It demanded integration ∣A25∣The expense of local independence, colour and “difference”. It grew out of monstrous transnational corporations that became so powerful that neither trade unions nor governments had the power to hinder. It came with the opportunity to produce goods on an unprecedented scale at previously unimagined prices. Globalization ∣A26∣ to the independent manufacturers of the world — “grow with us, or die”.
And Globalization is inevitable. Elements of the late 20th century phenomenon can be seen throughout history in the rise and fall of every empire: where dress, cuisine, culture and even language were ∣A27∣ across continents. Many believe that it is now US culture that has displaced traditional diversity, local uniqueness and identity. Personally I am unable to argue for or against globalisation. It is truly ∣A28∣And utterly terrible and completely inevitable.
I A22∣ |
1) obstructions |
2) blockades |
3) difficulties |
4) barriers |
I A23∣ |
1) caused |
2) affected |
3)founded |
4) resulted |
I |
||||
I A24 I |
1) opportunity |
2) occasion |
3) likelihood |
4) reason |
I A25 I |
1) at |
2) for |
3) on |
4) by |
I A26 I |
1)spoke |
2) told |
3) said |
4) talked |
I A27∣ |
1) exposed |
2) imposed |
3) imported |
4) obliged |
I A28∣ |
1) well |
2) good |
3) nice |
4) superior |
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 8
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Quarrelling Neighbours
England and France are neighbours and have a famous 1000 year old, love-hate ∣A22∣. An early milestone was 1066, when William of Normandy conquered England. As any English football fan will ∣A23∣You “It’s their fault, they started it!” and ever since there has been conflict; both “teams” selecting their own highlights! The English generally choose the Battle of Agincourt (1415) and of course the ∣A24∣ of Napoleon (conveniently forgetting that several other nations were actually involved). A more recent low occurred wHen Churchill ordered the sinking of the French Fleet after France surrendered to Germany. ∣A25∣ many claim the UK’s role in the liberation of France rather made up for this!
English-French rivalry continues to the present time — in sport, language and culture. In any big sporting tournament (especially football or rugby) the French become “Frogs” — a nickname derived ∣A26∣The (inexplicable to English taste) French inclusion of frogs, snails and other unmentionables in their cuisine.
In the last decades the French have even battled against the invasion of the English language — “Le weekend”, “Le sandwich” and so forth. But it seems that the English language is a ∣A27∣Opponent. The rivalry recently flared up again most recently when London narrowly beat Paris in the bid to A28∣ the 2012 Olympics. But in fairness, since William “kicked-off” in 1066 there have been plenty of French victories as well, and in reality the nations are the best of friends as much as “best” enemies and their rivalry is often quite witty and entertaining.
A22j |
1) relationship |
2) rapport |
3) acquaintance |
4) connection |
A23 I |
1) talk |
2) speak |
3) say |
4) tell |
A24 I |
1) loss ; |
2) defeat |
3) failure |
4) collapse |
A25 I |
1) Thus |
2) Although |
3) Therefore |
4) Nevertheless |
A26∣ |
1) of |
2) for |
3) from |
4) off |
A27∣ |
1) tough |
2) solid |
3) heavy |
4) hard |
A28∣ |
1) accommodate |
2) host |
3) settle |
4) contain |
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 9
Прочитайте текст с пропусками, обозначенными номерами А22—А28. Эти номера соответствуют заданиям А22-А28, в которых представлены возможные варианты ответов. Обведите номер выбранного вами варианта ответа.
A Night at the Museum
Friday 6th March 2010, was special for Laura, and me — our sleep over at the American Museum of Natural History (AMNH). I am guessing you’ve seen the movie? A22∣ in 2006 and called “A Night at the Museum” with Ben Stiller starring. It’s a kicking comedy about a night guard who ∣A23∣An ancient curse that makes the animals on display come to life every night and trash the place. ___
I am not sure if the night Laura and I spent at the museum was ∣A24∣By the film, but it was way cool. Fact, fact, fact! AMNH is one of the largest Museums in the world. There are 25 buildings and 46 ∣A25∣Exhibition halls set in fab grounds near Central Park, New York. There is a famous library, research labs and a totally awesome 32 million specimens. The night costs $129 per person. Grandma paid for us as early birthday presents.
It began at 5.45pm and ∣A26∣All the way to 9.00am on the 7th. It was real creepy as the doors swung closed and locked and the lights dimmed away. We switched on torches — and so our first mission began: Looking for fossil facts. I can ∣A27∣Describe to you walking through those dark halls, our torches cutting beams through the inky black. There was a way scary moment when a huge buffalo head lit up and made me jump like a wuss.
After some bites and coolin’ we settled down to sleep — directly ‘neath a 94 foot blue whale and next to a mighty fine Brown Bear. Luckily no animals came to ∣A28∣And we slept like babies. Wicked!
A22 |
1) Made |
2) Done |
3) Issued |
4) Screened |
A23 |
1)learns |
2) opens |
3) discovers |
4) investigates |
A24 |
1) aroused |
2) encouraged |
3) pushed |
4) inspired |
A25 |
1) constant |
2) permanent |
3) stable |
4) steady |
A26 |
1) ended |
2) lasted |
3) went |
4) carried |
A27 |
1) hardly |
2) obviously |
3) fairly |
4) apparently |
A28 |
1) alive |
2) reality |
3) real |
4) life |
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 10
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Blue Whale Watching
For years I have had the same dream about a blue whale. I see the sea darken as the gigantic mammal comes to the surface. Then I see the monster ∣A22∣At me through the clear green water.
But finally I am about to see my dream come true. Several months of planning had brought me to the warm waters off the southern tip of Sri Lanka. Less than an hour after leaving the harbour we A23∣At the location whales had been seen the day before.
Blue Whales are the largest creatures that have ever lived. Compared to the big“Blue” — elephants, hippos and the biggest great white sharks are tiny. My fellOw tOurists ∣A24∣The deck — all of us breathless with anticipation. Each of us A25 first to see the darkening of the sea.
I heard a shout behind me and suddenly the boat engines roared noisily as the my life’s ∣A28∣, to the realization of beautiful sight I have ever seen.
A22 I |
1) watch |
2) stare |
3) see |
4) observe |
A23∣ |
1) arrived |
2) reached |
3) entered |
4) achieved |
A24 I |
1) among |
2) between |
3) besides |
4) along |
A25 I |
1) persuaded |
2) convinced |
3) determined |
4) assured |
A26∣ |
1) directed |
2) set |
3) pulled |
4) parked |
A27 I |
1) after |
2) to |
3) forward |
4) off |
A28∣ |
1) trip |
2)journey |
3) travel |
4) destination |
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 11
Прочитайте текст с пропусками, обозначенными номерами А22-А28. Эти номера соответствуют заданиям А22-А28, в которых представлены возможные варианты ответов. Обведите номер выбранного вами варианта ответа.
The Best Breakfast in the World?
The “Greasy Spoon” cafe on Arundel Road offers the best full English breakfast on the planet. Of course people ∣A22∣ about what “full English” should consist of but I think there is a small clue in the word “full”. This is a breakfast that knows no modesty. This is not a breakfast for those on a diet. It is the breakfast of Kings; it should be enjoyed ∣A23∣ leisure and last for the day.
That the “full English” (FE) contains both bacon and eggs is A24_____________ dispute. After this
There are different schools of thought. Sausage, mushrooms, beans, black pudding, fried tomatoes and toast are often ∣A25[ in different line ups and combinations competing for the best, all time classic FE. These are ∣A26∣ in different portions and styles and a decent breakfast is the almost guaranteed outcome. But an FE on Arundel Road beats all contenders for the best FE in the world because it includes ALL of these ingredients in ∣A27∣Quantities! They also serve hot toast on traditional toast racks with real butter. But best of all, each customer is served their own pot of traditional English tea (with tea cosy) which may be drunk with milk or cream. And all of this is offered for just J5 per person — and with a newspaper included! The Greasy Spoon is popular with working people and students alike. It opens early during the week for the lorry drivers and on Sunday mornings ∣A28∣ families come in and spend half the day there.
I A22 I |
1) discuss |
2) debate |
3) quarrel |
4) argue |
I A23 I |
1) for |
2) at |
3) on |
4) in |
I A24 I |
1) beyond |
2) behind |
3) besides |
4) below |
J |
||||
I A25 I |
1) contained |
2) included |
3) held |
4) enclosed |
I A26∣ |
1) suggested |
2) advised |
3) offered |
4) intended |
∣A27∣ |
1) generous |
2) rich |
3) luxurious |
4) multiple |
I A28∣ |
1) full |
2) complete |
3) total |
4) whole |
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 12
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A night at the Museum
Anna and Ira are best friends. They are both Russian but ∣A22⅛ the Southbank International School as their parents both work in London. They are fifteen now and are studying hard for their International Baccalaureate.
Every Saturday they love to visit museums and galleries in London and so now they have visited A23∣All of them. But, above all, their absolute favourite is The Natural History Museum in South Kensington.
They filled in an online A24∣Form and became “members”. This means they get free magazines called “Evolve” and “Second Nature”, get fast track entry to special exhibitions and they get invited to previews, workshops, talks and special A25____________________________________________________ . They even get to use the
Special member’s room where there are free refreshments, magazines and internet access. It ∣A26∣Them J56 For the year but they felt it was really good value for money.
Last weekend they took part in “Dino snores” — an event A27∣By the film “A Night at the Museum”. They were given a talk about bugs by TV nature presenter Nick Baker, explored the Dinosaur gallery in the dark on a torch-lit tour, watched films and played games, and then slept in sleeping bags under the shadow of the huge Diplodocus in the Museum’s iconic Central Hall. It was a night they’ll never forget. Although Ira and Anna are both interested in Dinosaurs — they are more interested in present day wildlife and most interested of all in ≡— Russian wildlife. When they go back to Moscow both want to study and eventually
Become wildlife research scientists.
A22 |
1) attend |
2) visit |
3) go |
4) enroll |
A23 |
1) about |
2) almost |
3) already |
4) approximately |
A24 |
1) application |
2) admission |
3) entrance |
4) request |
A25 |
1) dealings |
2) actions |
3) procedures |
4) events |
A26 |
1) cost |
2) charged |
3) priced |
4) spent |
A27 |
1) inspired |
2) motivated |
3) stimulated |
4) encouraged |
A28 |
1) struggling |
2) preserving |
3) securing |
4) supporting |
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 13
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Day schools VS Boarding schools
The majority of modern public schools in the UK and state schools in the USA — schools that offer free education— are со-educational day schools. Children that attend these schools remain in family settings with family support and nurture that helps to reduce the stress of ∣A22∣Any school for a child. They are able to retain contacts with friends and neighbours.
Being less expensive, these schools offer a wider ∣A23∣Of courses and activities. On the other hand, these schools have larger classes and lower academic standards as compared to more selective schools.
Pupils there have a greater ∣A24∣ of encountering bad social trends: drug culture, gangs, anti-intellectualism. Of course, much depends on the regional location and the administrative policy of each school.
Boarding or recreational schools have smaller classes with more individualized iNstruCtion; can often (though not always) boast higher academic standards that are focused ∣A25 making students more independent thinkers; encourage them to make many decisions on their own. Graduates of such schools may have an advantage when applying at more popular universities.
Students of such schools ∣A26∣Lifetime friendships and the so-called ‘old school tie’ — the system of after school, lifelong support and lobbying former schoolmates — can be truly applied in this case.
But there is the ∣A27[ Side of the medal: missed opportunities for parents to educate their children on values; disruption of family: homesick kids, parents missing their children; narrower and less-diverse ∣A28∣Contacts; expensive tuition.
A22 |
1) entering |
2) starting |
3) going |
4) getting |
A23 |
1) group |
2) collection |
3) mixture |
4) selection |
A24 |
1) ability |
2) opportunity |
3) chance |
4) prospect |
A25 |
1) on |
2) at |
3) for |
4) to |
A26 |
1) assemble |
2) build |
3) construct |
4) design |
A27 |
1) another |
2) other |
3) different |
4) optional |
A28 |
1) social |
2) sociable |
3) society |
4) civil |
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 14
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Times are Changing
I grew up in tiny village in East Anglia — population 210 people. Everybody knew each other and seemed to know everyone else’s business. What strikes me now — looking back ∣A22∣ 40 years ago — is that the village contained several social groups and there were clear distinctions and unspoken (and certainly unwritten) rules of engagement.
We had two ∣A23∣Class families living in the village: The Brandings, who lived in the manor house, and the very honourable Archer family. The Brandings were well ∣A24∣But certainly not rich. They were extremely posh and so were the Archers who — on the contrary — were fabulously wealthy. But socially — the Brandings and Archers were ∣A25∣. They could socialise with the vicar and my family (because my Dad was an RAF Officer) but their contact with the other villagers was ∣A26∣To friendly but polite greetings. Then we had 8 or 10 middle class families; teachers, a scientist, a factory director and so on. In so small a village we knew each other well and socialised a lot.
The ∣A27∣ comprised of the true working class. They worked in shops, or on the farms. We had also had quite a few elderly couples who in their young days had been “in service”. We didn’t socialise but relations were friendly and we greeted on first name terms.
It’s all changed now of course. Our village is a small town — far too large to be anything like the community of my youth. I may be wrong, but it seems like society has contracted into featureless ∣A28∣And that nowadays people often don’t even know their neighbours’ names.
A22 I |
1) above |
2) over |
3) beyond |
4) behind |
A23∣ |
1) upper |
2) aristocratic |
3) high |
4) noble |
A24∣ |
1) allied |
2) associated |
3) linked |
4) connected |
A25 I |
1) commoners |
2) equivalents |
3) equals |
4) parallels |
A26∣ |
1) restricted |
2) framed |
3) enclosed |
4) narrowed |
A27∣ |
1) remnants |
2) reminders |
3) remain |
4) remainder |
A28∣ |
1) likelihood |
2) sameness |
3) neutrality |
4) equality |
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 15
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Education in the UK: Modern schools
The 1976 Education Act abolished the Tripartite System in favour of a system of free Comprehensive Schools that were ∣A22∣ to provide Grammar School education for all. In the UK today, schools reflect elements of both the Tripartite and the Comprehensive models.
The UK system of state schools is complex and ∣A23∣ the following types: Primary Schools (ages 4-11), Secondary Schools (ages 11-16), Sixth Form Colleges (non-compulsory, ages 16-18), Special Schools for children with physical, emotional and behavioral learning needs, City Technology Colleges (CTCs) and City Colleges for the Technology of the Arts (CCTAs) (ages 11-18). These schools provide a broad secondary education with special emphasis on science and technology and offer a ≡— _ range of vocational qualifications.
Grammar Schools remain and continue to select almost all of their pupils ∣A25∣ reference to high academic ability. Independent Schools are private schools that obtain most of their finances from ∣A26 paid by parents and income from investments. Some of them are
Selective but many are not. Some of the larger independent schools are ∣A27∣ as Public Schools. Most Independent Schools are Church Schools.
Most state schools (primary and secondary) are со-educational day schools, but some secondary schools accept boarders. Independent Schools include day and boarding schools and are mostly single-sex, although an increasing number of junior and some senior schools are coeducational. There has been a sharp increase in the number of children ∣A28∣Independent Schools, owing to the increasing dissatisfaction with academic standards at State Comprehensive Schools.
I A22 I |
1) intended |
2) aimed |
3) offered |
4) proposed |
I A23 I |
1) fits |
2) includes |
3) engages |
4) composes |
I A24 I |
1) high |
2) intensive |
3) extensive |
4) wide |
I A25 I |
1) by |
2) at |
3) for |
4) about |
I A26 I |
1) costs |
2) bills |
3) fees |
4) taxes |
I A27∣ |
1) famous |
2) known |
3) notorious |
4) familiar |
I A28∣ |
1) accepting |
2) entering |
3) going |
4) attending |
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 16
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Mining in Australia
Australia is the “mainland” of the world’s smallest continent. It is mostly very flat and much of it is inhospitable desert. ∣A22∣Of the population lives in the South East and South West where there is a ∣A23∣Climate. But the weather played only a relatively minor part in establishing population centres. Many argue that the real story was about mining.
The early colonies in South Australia had a terrible struggle economically. But after significant silver, lead and copper ∣A24j were discovered in Southern Australia, the local
Populations began to grow. In 1841 silver and lead were discovered at Glen Osmond — now a suburb of Adelaide: Then came the discovery of copper at Kapunda in 1845.
But the big story was gold! The first “strike” was at Ophir, New South Wales in 1851. ∣A25∣Weeks more gold was found in the colony of Victoria. The Australian gold rushes had a major impact ∣A26∣, Victoria and Australia as a whole. They coloured every aspect of Australian society and elements of it are still clearly visible today. Victoria became the richest colony and Melbourne Australia’s largest city.
The population of Australia changed dramatically ∣A27∣Of the discovery of gold. In 1851 the population was just 437,655. 10 years later it was 1,151,947. The rapid growth came from “new chums” — recent immigrants from the UK and British Commonwealth. As a lot of Australians will be quick to tell you, much of the new wealth was “stolen” back to England. But enough wealth remained to fund substantial development in industry and infrastructure and to ∣A28∣The foundations for building modern Australia.
A22 I |
1) Most |
2) Many |
3) Mainly |
4) Main |
I A23 I |
1) temperature |
2) temperate |
3) tempered |
4) temporal |
L⅛24J |
1) riches |
2) stores |
3) deposits |
4) treasures |
A25 I |
1) Throughout |
2) During |
3) While |
4) Within |
[A2βJ |
1) at |
2) on |
3) for |
4) in |
I A27∣ |
1) because |
2) due |
3) as |
4)thanks |
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 17
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The storybook wolf
Josii Luis Rodriguez of Spain is the overall winner of The Wildlife Photographer of the — a wolf jumping over a gate! He visualized his photo many years ago, when Iberian wolves first returned to Bvila in the Castilla у Leyn region of northern Spain, and cattle
Ranchers ∣A23∣ war on them. His idea was a picture that would symbolize the ancient conflict ∣A24∣ humans and wolves, while showing the beauty and strength of this fabled
Animal. But it took a long time to find the ideal ∣A25∣, let alone a wolf that would jump a gate. His chance came when he found a landowner who was happy to have both the wolves and Josfi Luis on his property, and also had the ideal setting: a copse and an ancient, disused cattle corral.
Josfi Luis started by placing meat in the corral. Once he knew a male wolf was visiting regularly, jumping the gate, he began to introduce the bits of equipment needed to up a camera trap. At first, the wolf didn’t like the flash triggered by the trip beam, but after a few weeks he ∣A27 no notice of the light or the clicks of the hidden digital camera. Now that the wolf was happy and the camera ∣A28∣ was right, it was time to take the final picture with a medium-format camera. When the first transparencies arrived back from the lab, Josfi Luis was overjoyed to find he finally had the picture he had dreamt of.
A22 |
1) tournament |
2) competition |
3) test |
4) race |
A23 |
1) pronounced |
2) revealed |
3) broadcasted |
4) declared |
A24 |
1) between |
2) among |
3) within |
4) amongst |
A2δ |
1) situation |
2) sight |
3) location |
4) destination |
A26 |
1) put |
2) place |
3) set |
4) build |
A27 |
1)took |
2) received |
3) gave |
4) paid |
A28 |
1) posture |
2) positioning |
3) posing |
4) pose |
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 18
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Christmas
As a small child I loved almost everything about Christmas. The excitement of Christmas Eve was almost unbearable. We’d go from house to house singing Christmas carols and be given hot mince pies and other ∣A22∣.
Before bed our parents would read us stories and eventualLy puT us to bed with warnings that Santa Claus would not come if we stayed awake. Before ∣A23∣Into bed we would leave out a mince pie for Santa and something for his reindeers as a “thank you”: For me Santa was the great hero and I never ∣A24∣That he would come down our chimney to deliver my presents.
I loved, as I mentioned before, “almost everything”. Immediately after ChristMas I was told by my parents that I had to write “thank you letters”. As a six your old, writing ∣A25∣One letter was a task, but several made a mountain — pressing down on my small world. “Why” I argued to my Mum “should I write to grandparents, aunts and uncles? Santa brought me all my presents”. ___
And my mother would lie to her son. ∣A26Lies of how Santa helped Granddad choose my toy car and with the help of elves and reindeer delivered it for Granddad — but that still I should thank Granddad for the small part he played in it. The following year her lies were even more devious as she tried to ∣A27∣Me convinced. As I eventually solved this annual mystery, I of course lost all A28∣For not writing the “Thank you letters” as the realisation dawned that Granddad had managed everything by himself.
I A22 I |
1) surprises |
2) treats |
3) presents |
4) souvenirs |
|
I A23 I |
1) getting |
2) going |
3) putting |
4) lying |
|
I A24 I |
1) hesitated |
2) suspected |
3) mistrusted |
4) doubted |
|
I A25∣ |
1) only |
2) yet |
3) even |
4) still |
|
I A26 I |
1) Vague |
2) Elaborate |
3) Complete |
4) Formless |
|
• |
A27 I |
1) hold |
2) stay |
3) keep |
4) remain |
A28∣ |
1) reasons |
2) defenses |
3) motives |
4) excuses |
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 19
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The Magnificent Six
This is a real life story. When I was about eight, I [A22∣An organization called the “Cub Scouts”. We met once a week and learned basic first aid and were trained ∣A23∣ various techniques related to camping and the outdoor life. For each skill learned, there would be a test — which if passed would result in earning a badge. These badges were cArefulLy sewn on our uniforms; green caps with yellow piping, green shirts with a type of scarf ∣A24j a
Neckerchief and short trousers. Our leader was called Akela — after the wolf pack____________ leader in
Rudyard Kipling’s “The Jungle Book” and we were formed in units of six boys — called a “Six” and led by a “Sixer”.
I can ∣A25∣ remember our Six. We were nicknamed “the dwarves” after the fairy tale “Snow White and the Seven Dwarves”. This was nothing to do with our height (and we were of course six rather than seven) but rather it was to do with our ∣A26∣. We were “Sneezy” (real name Richard), “Bashful” (OLiver), “Grumpy” (Jim), “Doc” (Henry), “Sleepy” (Rupert) and I was “Happy”. Only “Dopey” was ∣A27∣From the original seven! And really that was what we were like. Richard always seemed to have a cold, Oliver was shy, Jim always in a bad mood and so forth. But we all, without fail, had enormous fun — especially on our annual camping ∣A28∣ to the Lake District. Every day was filled with adventure and discovery and the reality was — we werd all truly happy.
I A22∣ |
1) entered |
2) enrolled |
3)joined |
4) registered |
I A23∣ |
1) in |
2) on |
3) at |
4) for |
I A24 I |
1) pronounced |
2) named |
3) entitled |
4) called |
I A25 I |
1) always |
2) forever |
3) ever |
4) still |
I A26∣ |
1) characters |
2) features |
3) dispositions |
4) persons |
I A27 I |
1) away |
2) missing |
3) gone |
4) absent |
I A28∣ |
1) excursion |
2) trip |
3) travel |
4)journey |
ТРЕНИРОВОЧНОЕ ЗАДАНИЕ № 20
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David Bowie
British Singer David Bowie was always famous for changing his appearance and his musical styles throughout his career. At the beginning, in the late 1960’s — he was compared ∣A22∣ fifties singers like Tommy Steele and Anthony Newley. Then he grew his hair and became “Major Tom” — a weird, futuristic space traveller — for his number one album called “Space Oddity”: His appearance made more remarkable for having one eye blue and one brown (the result of a childhood A23∣).
As the years passed he continued to change his appearance — often with fabulous and dramatic costumes that A24∣Each new stage character. After the “space phase” he created the character “Ziggy Stardust”. At this stage Bowie was the most important artist in the early 70’s glam rock era: His costumes sparkling in silvers, reds and golds and his bright orange hair feathered out like a flaming ∣A25∣. Then he became “Aladdin Sane” with a bizarre lightening flash motif painted on his face. Soon after this his hair was again short but wavy, he wore ∣A26Size suits and became an “American” soul singer before transforming again into
Yet another character — a central European “Thin White Duke”.
Probably of all British pop stars — he has become the one most A27[ with change and transformation. Even now after 40 years in the business, he continues to ∣A28∣Strange and original music for his countless fans worldwide. Some believe his 1972 hit song “Changes” predicted all this. It is a song about change and time and the inevitable conflict between one generation and the next.
A22 |
1) to |
2) for |
3) on |
4) at |
A23 |
1) incident |
2) event |
3) thing |
4) accident |
A24 |
1) described |
2) named |
3) defined |
4) recognized |
A25 |
1) lamp |
2) torch |
3)lantern |
4) light |
A26 |
1) above |
2) over |
3) extreme |
4) upper |
A27 |
1) related |
2) fixed |
3) combined |
4) associated |
A28 |
1) shape |
2) form |
3) make |
4) do |
Ключи
Первое задание (В4-В10).
Образование грамматических форм
Тренировочное задание № 1 |
Тренировочное задание № 2 |
Тренировочное задание № 3 |
|
В4 |
Stood |
Islocated |
Took |
В5 |
Sheep |
Larger |
Eldest / oldest |
BG |
Strongest |
Cooking |
Mostimpressiυe |
В7 |
Was swimming |
Doesn’t/does not need |
Standing |
В8 |
Those |
Cutting |
Found |
В9 |
Hasrealized |
Nearer |
Women |
BlO |
One |
Best |
Impersonating |
Тренировочное задание № 4 |
Тренировочное задание № 5 |
Тренировочное задание № 6 |
|
B4 |
Broke |
Others |
Took |
B5 |
Wasmurdered |
Begins |
Hadto |
B6 |
Their |
Walking |
Waswearing |
B7 |
Wasrecording |
Me |
Her |
B8 |
Wereplayed |
Biggest |
Started |
B9 |
Lasting |
Closer |
Advertising |
BlO |
Bigger |
Trapped |
Was |
Тренировочное задание № 7 |
Тренировочное задание № 8 |
Тренировочное задание № 9 |
|
B4 |
Hasbeeneducating |
Its |
Societies |
B5 |
Our |
Arelooking |
Worse |
B6 |
Receives |
Ar elocated |
Fastest |
B7 |
Toknow |
Including |
My |
B8 |
Willhave∕have |
Offers |
Won, tget/Willnotget |
Тренировочное задание № 7 |
Тренировочное задание № 8 |
Тренировочное задание № 9 |
|
B9 |
Tnorecheerful |
Оиг |
Hascoτne/сате |
BlO |
Arenot/aren’ Hncluded |
Getting |
Has joined |
Тренировочное задание № 10 |
Тренировочное задание № 11 |
Тренировочное задание № 12 |
|
B4 |
Diaries |
First |
Beexperienced |
B5 |
Most |
Wasacknowledged |
Windest |
B6 |
Believed |
Fell |
Less |
B7 |
Their |
Bears |
Discussing |
B8 |
Biggest |
Sailed |
Willbe |
B9 |
Falls |
His |
Knows |
BlO |
Arepresented |
Didn’t Zdidnotrealized |
Appearing |
Тренировочное задание № 13 |
Тренировочное задание № 14 |
Тренировочное задание № 15 |
|
B4 |
Friend’s |
Including |
Involves |
B5 |
Was covered |
Hascontinued |
These |
B6 |
Fell |
Isknown |
Arelearning |
B7 |
Used |
Wereworn |
Me |
B8 |
Caught |
Women |
Eating |
B9 |
Us |
Enemies |
Wasorganised |
BlO |
WascryingZhadbeencrying |
Greater |
Is |
Тренировочное задание № 16 |
Тренировочное задание № 17 |
Тренировочное задание № 18 |
|
B4 |
Mostfamous |
Made |
Working |
B5 |
Our |
Him |
Their |
B6 |
Stepped |
First |
Their |
B7 |
Heroes |
Wastrying |
Divided |
B8 |
Beheld |
Hadseen |
Hasdeveloped |
B9 |
Doesn’t / doesnotdeserve |
Ran |
Followed |
BlO |
Voting |
Mostfamous |
Greater |
Тренировочное задание № 19 |
Тренировочное задание № 20 |
|
B4 |
Wascalled |
Living |
B5 |
Leading |
Iscalled |
B6 |
Fittest |
Hidden |
B7 |
Lives |
Nightclubs |
B8 |
Better |
Togo |
B9 |
Became |
Couldnot/couldn’t |
BlO |
Third |
Hasn’t/hasnottroubled |
Второе задание (В11-В16).
Словообразование
Тренировочное задание № 1 |
Тренировочное задание № 2 |
Тренировочное задание № 3 |
|
Bll |
Unpopular |
Environmental |
Fruitless |
В12 |
Commercial |
Preservation |
Adventurous |
В13 |
Mainly |
Development |
Significant |
В14 |
Addition |
Responsible |
Generally |
В15 |
Anxious |
Politicians |
Managerial |
В16 |
Reality |
Economic |
Reality |
Тренировочное задание № 4 |
Тренировочное задание № 5 |
Тренировочное задание № 6 |
|
Bll |
Unpopular |
Environmental |
Tricky |
B12 |
Commercial |
Imagination |
Impossible |
B13 |
Daily |
Responsible |
Unpredictable |
B14 |
Addition |
Establishment |
Resourceful |
B15 |
Anxious |
Visitors |
Expensive |
B16 |
Difference |
Lives |
Disagree |
Тренировочное задание № 7 |
Тренировочное задание № 8 |
Тренировочное задание № 9 |
|
Bll |
Necessarily |
Educators |
Feelings |
B12 |
Activity |
Independently |
Hardship |
B13 |
Highly |
Inappropriate |
Formation |
B14 |
Routinely |
Necessity |
Unattractive |
B15 |
Independence |
Membership |
Personality |
B16 |
Academic |
Easily |
Impression |
Тренировочное задание № 10 |
Тренировочное задание № 11 |
Тренировочное задание № 12 |
|
Bll |
French |
Artist |
Believable |
B12 |
Psychological |
Notable |
Connection |
B13 |
Discouraged |
Smoky |
Indicators |
B14 |
Ambitious |
Violent |
Remarkably |
B15 |
European |
Sadly |
Investigations |
B16 |
Tension |
Surroundings |
Distinctive |
Тренировочное задание № 13 |
Тренировочное задание № 14 |
Тренировочное задание № 15 |
|
Bll |
Greatness |
Originally |
Scientist |
B12 |
Adventurous |
Honestly |
Achievements |
B13 |
Important |
Visitors |
Scientific |
B14 |
Generally |
Certainly |
Additional |
B15 |
Industrial |
Occasionally |
Equipment |
B16 |
Reality |
Disagree |
Subscriptions / subscription |
Тренировочное задание № 16 |
Тренировочное задание № 17 |
Тренировочное задание № 18 |
|
Bll |
Impossible |
Certainly |
Dramatically |
B12 |
Indistinguishable |
Invisible |
Additional |
B13 |
Buildings |
Kingdom |
Dangerous |
B14 |
Realistically |
Wonderful |
Passionate |
B15 |
Cultural |
Expensive |
Government |
B16 |
Impressive |
Disagree |
Helpful |
Тренировочное задание № 19 |
Тренировочное задание № 20 |
|
Bll |
Residential |
Physicist |
B12 |
Permission |
Achievements |
B13 |
Responsibility |
Unreasonable |
B14 |
Accountability |
Enthusiastic |
B15 |
Healthy |
Indignation |
B16 |
Relaxation / relaxing |
National |
Третье (A22-A28).
Лексическое задание на множественный выбор
А22 |
А23 |
А24 |
А25 |
А26 |
А27 |
А28 |
|
Тренировочное задание № 1 |
1 |
3 |
4 |
2 |
4 |
1 |
3 |
Тренировочное задание № 2 |
4 |
3 |
2 |
3 |
1 |
2 |
1 |
Тренировочное задание № 3 |
2 |
3 |
4 |
3 |
1 |
3 |
4 |
Тренировочное задание № 4 |
4 |
1 |
4 |
2 |
3 |
1 |
3 |
Тренировочное задание № 5 |
2 |
4 |
1 |
2 |
3 |
1 |
4 |
Тренировочное задание № 6 |
1 |
1 |
4 |
2 |
3 |
2 |
3 |
Тренировочное задание № 7 |
4 |
4 |
3 |
1 |
3 |
2 |
2 |
Тренировочное задание № 8 |
1 |
4 |
2 |
4 |
3 |
1 |
2 |
Тренировочное задание № 9 |
1 |
3 |
4 |
2 |
2 |
1 |
4 |
Тренировочное задание № 10 |
2 |
1 |
4 |
3 |
1 |
4 |
2 |
А22 |
А23 |
А24 |
А25 |
А26 |
А27 |
А28 |
|
Тренировочное задание № 11 |
4 |
2 |
1 |
2 |
3 |
1 |
4 |
Тренировочное задание № 12 |
1 |
2 |
1 |
4 |
1 |
1 |
2 |
Тренировочное задание № 13 |
2 |
4 |
3 |
1 |
2 |
2 |
1 |
Тренировочное задание № 14 |
K 2 |
1 |
4 |
3 |
1 |
4 |
2 |
Тренировочное задание № 15 |
1 |
2 |
4 |
1 |
3 |
2 |
4 |
Тренировочное задание № 16 |
1 |
2 |
3 |
4 |
2 |
1 |
3 |
Тренировочное задание № 17 |
2 |
4 |
1 |
3 |
3 |
1 |
2 |
Тренировочное задание № 18 |
2 |
1 |
4 |
3 |
2 |
3 |
4 |
Тренировочное задание № 19 |
3 |
1 |
4 |
4 |
1 |
2 |
2 |
Тренировочное задание № 20 |
1 |
4 |
3 |
2 |
2 |
4 |
3 |
Справочное издание
Соловова Елена Николаевна
John Parsons
ЕГЭ
АНГЛИЙСКИЙ ЯЗЫК
[1] Общеевропейские компетенции владения языком: Изучение, преподавание, оценка. МГЛУ, 2003.
[2] Поскольку весь возможный спектр уровней владения иностранным языком представлен в документе Совета Европы лишь шестью уровнями, очевидно, что внутри каждого из них можно выделять определенные подуровни. Обозначение базового уровня ЕГЭ как А2+ означает, что из описания уровня А2 для подготовки заданий базового уровня разработчики ориентируются на дескрипторы, лежащие ближе к уровню Bl, а не к Al.
Normal Random Variables
Sheldon M. Ross, in Introductory Statistics (Third Edition), 2010
Example 6.1
Test scores on the Scholastic Aptitude Test (SAT) verbal portion are normally distributed with a mean score of 504. If the standard deviation of a score is 84, then we can conclude that approximately 68 percent of all scores are between 504 – 84 and 504 + 84. That is, approximately 68 percent of the scores are between 420 and 588. Also, approximately 95 percent of them are between 504 – 168 = 336 and 504 + 168 = 672; and approximately 99.7 percent are between 252 and 756.
The approximation rule is the theoretical basis of the empirical rule of Sec. 3.6. The connection between these rules will become apparent in Chap. 8, when we show how a sample mean and sample standard deviation can be used to estimate the quantities μ and σ.
By using the symmetry of the normal curve about the value μ, we can obtain other facts from the approximation rule. For instance, since the area between μ and μ + σ is the same as that between μ – σ and μ, it follows from this rule that a normal random variable will be between μ and μ + σ with approximate probability 0.68/2 = 0.34.
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Metric Predicted Variable with Multiple Metric Predictors
John K. Kruschke, in Doing Bayesian Data Analysis (Second Edition), 2015
18.1.3 The posterior distribution
Figure 18.5 shows the posterior distribution from the SAT data in Figure 18.3 and model in Figure 18.4. You can see that the slope on spending (Spend) is credibly above zero, even taking into account a modest ROPE and MCMC instability. The slope on spending has a mode of about 13, which suggests that SAT scores rise by about 13 points for every extra $1000 spent per pupil. The slope on percentage taking the exam (PrcntTake) is also credibly non-zero, with a mode around −2.8, which suggests that SAT scores fall by about 2.8 points for every additional 1% of students who take the test.
Figure 18.5. Posterior distribution for data in Figure 18.3 and model in Figure 18.4. Scatter plots reveal correlations among credible parameter values; in particular, the coefficient on Spending (“Spend”) trades off with the coefficient on Percentage taking the exam (“PrcntTake”), because those predictors are correlated in the data.
The scatter plots in the bottom of Figure 18.5 show correlations among the credible parameter values in the posterior distribution. (These are pairwise scatter plots of credible parameter values from the MCMC chain; these are not scatter plots of data.) In particular, the coefficient for spending (Spend) trades off with the coefficient on percentage taking the exam (PrcntTake). The correlation means that if we believe that the influence of spending is smaller, then we must believe that the influence of percentage taking is larger. This makes sense because those two predictors are correlated in the data.
Figure 18.5 shows that the normality parameter for these data is fairly large, suggesting that there are not many outliers for this particular selection of predictors. It is worth noting that values of y are not inherently outliers or nonoutliers; they are only outliers relative to a spread of predicted values for a particular model. A value of y that seems spurious according to one set of predictors might be nicely linearly predicted by other predictors.
Finally, Figure 18.5 also shows a posterior distribution for a statistic labeled R2, which is called the proportion of variance accounted for in traditional least-squares multiple regression. In least-squares regression, the overall variance in y is algebraically decomposed into the variance of the linearly predicted values and the residual variance: ∑i(yi−y¯)2=∑i(yi−y^i)2+∑i(y^i−y¯)2, where y^i is the linearly predicted value of yi. The proportion of variance accounted for is R2=∑i(y^i−y¯)2/∑i(yi−y¯)2 when y^i is the linear prediction using coefficients that minimize ∑i(yi−y^i)2. If that makes no sense to you because you have no previous experience with least-squares regression, do not worry, because in Bayesian analysis no such decomposition of variance occurs. But for people familiar with least-squares notions who crave a statistic analogous to R2, we can compute a surrogate. At each step in the MCMC chain, a credible value of R2 is computed as R2=∑jζjry,xj, where ζj is the standardized regression coefficient for the jth predictor at that step in the MCMC chain, and ry,xj is the correlation of the predicted values, y, with the jth predictor values, xj. These correlations are constants, fixed by the data. The equation for expressing R2 in terms of the regression coefficients is used merely by analogy to least-squares regression, in which the equation is exactly true (e.g., Hays, 1994, Equation 15.14.2, p. 697). The mean value in the distribution of R2, when using vague priors, is essentially the least-squares estimate and the maximum-likelihood estimate when using a normal likelihood function. The posterior distribution reveals the entire distribution of credible R2 values. The posterior distribution of R2, defined this way, can exceed 1.0 or fall below 0.0, because R2 here is a linear combination of credible regression coefficients, not the singular value that minimizes the squared deviations between predictions and data.
Sometimes we are interested in using the linear model to predict y values for x values of interest. It is straight forward to generate a large sample of credible y values for specified x values. At each step in the MCMC chain, the combination of credible parameter values is inserted into the model and random y values are generated. From the distribution of y values, we can compute the mean and highest density interval (HDI) to summarize the centrally predicted y value and the uncertainty of the prediction. As was the case for simple linear regression, illustrated back in Figure 17.3 (p. 481), the uncertainty in predicted y is greater for x values outside the bulk of the data. In other words, extrapolation is more uncertain than interpolation.
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Noncognitive Measures for Higher Education Admissions
W.E. Sedlacek, in International Encyclopedia of Education (Third Edition), 2010
Keeping Up with Change
The world is much different than it was when the SAT and other tests were developed in the last century. International students, women, people of color, gays, lesbians, and bisexuals, among others, are participating in higher education in more extensive and varied ways (Knapp et al., 2002). Commonly employed tests have not kept up with these changes (Sedlacek, 2004).
We need a fresh approach. It is not good enough to feel constrained by the limitations of our current ways of conceiving of tests. Instead of asking, “How can we make the SAT and other such tests better?” we need to ask, “What kinds of measures will meet our needs now and in the future?” The purpose of this article is to present the underlying logic and research supporting a method that yields such measures. We do not need to ignore our current tests, we need to add some new measures that expand the potential we can derive from assessment.
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Distributions of Sampling Statistics
Sheldon M. Ross, in Introductory Statistics (Fourth Edition), 2017
Review Problems
- 1.
-
The sample mean and sample standard deviation of all student scores on the last Scholastic Aptitude Test (SAT) examination were, respectively, 517 and 120. Find the approximate probability that a random sample of 144 students would have an average score exceeding
- (a)
-
507
- (b)
-
517
- (c)
-
537
- (d)
-
550
- 2.
-
Let X‾ denote the sample mean of a sample of size 10 from a population whose probability distribution is given by
P{X=i}={0.1if i=10.2if i=20.3if i=30.4if i=4
Compute
- (a)
-
The population mean μ
- (b)
-
The population standard deviation σ
- (c)
-
E[X‾]
- (d)
-
Var(X‾)
- (e)
-
SD(X‾)
- 3.
-
In Prob. 2, suppose the sample size was 2. Find the probability distribution of X‾, and use it to compute E[X‾] and SD(X‾). Check your answers by using the values of μ and σ.
- 4.
-
The mean and standard deviation of the lifetime of a type of battery used in electric cars are, respectively, 225 and 24 minutes. Approximate the probability that a set of 10 batteries, used one after the other, will last for more than
- (a)
-
2200 minutes
- (b)
-
2350 minutes
- (c)
-
2500 minutes
- (d)
-
What is the probability they will last between 2200 and 2350 minutes?
- 5.
-
Suppose that 12 percent of the members of a population are left-handed. In a random sample of 100 individuals from this population,
- (a)
-
Find the mean and standard deviation of the number of left-handed people.
- (b)
-
Find the probability that this number is between 10 and 14 inclusive.
- 6.
-
The weight of a randomly chosen person riding a ferry has expected value 155 and standard deviation 28 pounds. The ferry’s capacity is 100 riders. Find the probability that, at capacity, the total passenger load exceeds 16,000 pounds.
- 7.
-
The monthly telephone bill of a student residing in a dormitory has an expected value of $15 with a standard deviation of $7. Let X denote the sum of the monthly telephone bills of a sample of 20 such students.
- (a)
-
What is E[X]?
- (b)
-
What is SD(X)?
- (c)
-
Approximate the probability that X exceeds $300.
- 8.
-
A recent newspaper article claimed that the average salary of newly graduated seniors majoring in chemical engineering is $54,000, with a standard deviation of $5000. Suppose a random sample of 12 such graduates revealed an average salary of $45,000. How likely is it that an average salary as low as or lower than $45,000 would have been observed from this sample if the newspaper article were correct?
- 9.
-
An advertising agency ran a campaign to introduce a product. At the end of its campaign, it claimed that at least 25 percent of all consumers were now familiar with the product. To verify this claim, the producer randomly sampled 1000 consumers and found that 232 knew of the product. If 25 percent of all consumers actually knew of the product, what is the probability that as few as 232 (that is, 232 or less) in a random sample of 1000 consumers were familiar?
- 10.
-
A club basketball team will play a 60-game season. Of these games 32 are against class A teams and 28 are against class B teams. The outcomes of all the games are independent. The team will win each game against a class A opponent with probability 0.5, and it will win each game against a class B opponent with probability 0.7. Let X denote the total number of victories in the season.
- (a)
-
Is X a binomial random variable?
- (b)
-
Let XA and XB denote, respectively, the number of victories against class A and class B teams. What are the distributions of XA and XB?
- (c)
-
What is the relationship among XA,XB, and X?
- (d)
-
Approximate the probability that the team wins 40 or more games. (Hint: Recall that the sum of independent normal random variables is also a normal random variable.)
- 11.
-
If X is binomial with parameters n=80 and p=0.4, approximate the following probabilities.
- (a)
-
P{X>34}
- (b)
-
P{X≤42}
- (c)
-
P{25≤X≤39}
- 12.
-
Consider the following simple model for daily changes in price of a stock. Suppose that on each day the price either goes up 1 with probability 0.52 or goes down 1 with probability 0.48. Suppose the price at the beginning of day 1 is 200. Let X denote the price at the end of day 100.
- (a)
-
Define random variables X1,X2,…,X100 such that
X=200+∑i=1100Xi
- (b)
-
Determine E[Xi]
- (c)
-
Determine Var(Xi)
- (d)
-
Use the central limit theorem to approximate P{X≥210}
- 13.
-
The following are the percentages of U.S. residents, classified by age, who were not covered by health insurance in 2002.
Age Percentage not covered under 18 11.6 18 to 24 29.6 25 to 34 24.9 35 to 44 17.7 45 to 64 13.5 65 and over 0.8 Suppose random samples of 1000 people in each age category are selected. Approximate the probability that
- (a)
-
At least 100 of those under 18 are not covered.
- (b)
-
Fewer than 260 of those 25 to 34 years old are uncovered.
- (c)
-
At most 5 of those 65 and over and at most 120 of those 45 to 64 years old are uncovered.
- (d)
-
More of those who are 18 to 24 years old than of those who are 25 to 34 years old are uncovered.
- 14.
-
A university administrator wants a quick estimate of the average number of students enrolled per class. Because he does not want the faculty to be aware of his interest, he has decided to enlist the aid of students. He has decided to randomly choose 100 names from the roster of students and have them determine and then report to him the number of students in each of their classes. His estimate of the average number of students per class will be the average number reported per class.
- (a)
-
Will this method achieve the desired goal?
- (b)
-
If the answer to part (a) is yes, explain why. If it is no, give a method that will work.
- 15.
-
Teams 1, 2, 3, 4 are all scheduled to play each of the other teams 10 times. Whenever team i plays team j, team i is the winner with probability Pi,j. If
P1,2=.6,P1,3=.7,P1,4=.75P2,1=.4,P2,3=.6,P2,4=.70
- (a)
-
approximate the probability that team 1 wins at least 20 games. Suppose we want to approximate the probability that team 2 wins at least as many games as does team 1. To do so, let X be the number of games that team 2 wins against team 1, let Y be the total number of games that team 2 wins against teams 3 and 4, and let Z be the total number of games that team 1 wins against teams 3 and 4.
- (b)
-
Are X,Y,Z independent.
- (c)
-
Express the event that team 2 wins at least as many games as does team 1 in terms of the random variables X, Y, Z.
- (d)
-
Approximate the probability that team 2 wins at least as many games as team 1.
Hint: Approximate the distribution of any binomial random variable by a normal with the same mean and variance.
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Cognitive Psychology and Educational Statistics
H.S. Kim, S. Embretson, in International Encyclopedia of Education (Third Edition), 2010
Multicomponent Latent Trait Model
Many ability and achievement tests have sources of multidimensionality in the item domain. For example, the Scholastic Aptitude Test (SAT) algebra items require multiple skills or stages to arrive at a correct response, such as prerequisite skills for symbols and conventions, algebraic manipulations, linear functions, and simultaneous equations (Gierl et al., 2007). To better explain why an examinee answers a specific item incorrectly, statistical models that can assess the sources of multidimensionality are needed.
One important aspect of multidimensionality is that the skills or processing stages in the items are often sequentially dependent. Thus, cognitive models for tasks typically postulate a flow of information from one stage to another. Four possible forms of hierarchical structures of processing stages in task performance are presented in Figure 1 (Gierl et al., 2007). In all the structures, there is a prerequisite skill (stage 1) and orderings among all or some processing stages except in Figure 1(d), which is an unstructured hierarchy.
Figure 1. Four different hierarchical structures. Reproduced from Gierl, M. J., Leighton, J. P., and Hunka, S. M. (2007). Using the attribute hierarchy method to make diagnostic inferences about examinees’ cognitive skills. In Leighton, J. P. and Gierl, M. J. (eds.) Cognitive Diagnostic Assessment for Education, pp 242–274. New York: Cambridge University Press.
The multidimensional latent trait model (MLTM; Whitely, 1980) was designed to properly reflect the sequentially dependent stages (called components in this model) based on a product of processing outcome probabilities as follows:
[10]P(Xis=1)=∏kP(Xisk)=∏kexpθsk−βik1+expθsk−βik,
where P(Xis = 1) is the probability of success for person s on item i and ∏k P(Xisk) is the product of success on each processing component k, given the correct outcome of the preceding component. The right side of the equation contains terms from the Rasch models for the probability of success on each component, where θsk is the trait level of person s on component k and βik is the difficulty of item i on component k.
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An Overview of Statistics in Education
S. Sinharay, in International Encyclopedia of Education (Third Edition), 2010
Analysis of Variance, Analysis of Covariance, and Multivariate Analysis of Variance
Analysis of variance (ANOVA) is the statistical procedure of comparing the means of a variable across several groups of individuals. For example, ANOVA may be used to compare the average SAT critical reading scores of several schools. The name of the technique arises from the fact that the first step in an ANOVA is to partition the variance present in the observations into several components. The ANOVA method was the second most frequently used data-analysis procedure in a survey of articles published between 1971 and 1998 in three reputed educational-research journals (Hsu, 2005). Generalizability theory (Cronbach et al., 1963), which is a competitor to the classical theory of reliability of tests, usually applies ANOVA procedures to test scores.
Analysis of covariance (ANCOVA) is used when, like in ANOVA, the interest is in comparing several means, but the investigator also has the values of an additional variable that influences the variable of interest. For example, ANCOVA may be used to compare the average SAT critical reading scores of several schools where the preliminary scholastic aptitude test/national merit scholarship qualifying test (PSAT/NMSQT) critical reading score of each examinee is available in addition to the SAT critical reading score. (The PSAT/NMSQT is supposed to provide firsthand practice for the SAT.)
Multivariate analysis of variance (MANOVA) is used to compare means of several variables simultaneously across several groups of individuals. For example, one could apply MANOVA to simultaneously compare the average scores on several subjects across several schools. Longford (1990) provides such an example.
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Overview of the Generalized Linear Model
John K. Kruschke, in Doing Bayesian Data Analysis (Second Edition), 2015
15.1.1 Predictor and predicted variables
Suppose we want to predict someone’s weight from their height. In this case, weight is the predicted variable and height is the predictor. Or, suppose we want to predict high school grade point average (GPA) from Scholastic Aptitude Test (SAT) score and family income. In this case, GPA is the predicted variable, while SAT score and income are predictor variables. Or, suppose we want to predict the blood pressure of patients who either take drug A, or take drug B, or take a placebo, or merely wait. In this case, the predicted variable is blood pressure, and treatment category is the predictor.
The key mathematical difference between predictor and predicted variables is that the likelihood function expresses the probability of values of the predicted variable as a function of values of the predictor variable. The likelihood function does not describe the probabilities of values of the predictor variable. The value of the predictor variable comes from outside the system being modeled, whereas the value of the predicted variable depends on the value of the predictor variable.
Because the predicted variable depends on the predictor variable, at least mathematically in the likelihood function if not causally in the real world, the predicted variable can also be called the “dependent” variable. The predictor variables are sometimes called “independent” variables. The key conceptual difference between independent and dependent variables is that the value of the dependent variable depends on the value of the independent variable. The term “independent” can be confusing because it can be used strictly or loosely. In experimental settings, the variables that are actually manipulated and set by the experimenter are the independent variables. In this context of experimental manipulation, the values of the independent variables truly are (in principle, at least) independent of the values of other variables, because the experimenter has intervened to arbitrarily set the values of the independent variables. But sometimes a non-manipulated variable is also referred to as “independent,” merely as a way to indicate that it is being used as a predictor variable.
Among non-manipulated variables, the roles of predicted and predictor are arbitrary, determined only by the interpretation of the analysis. Consider, for example, people’s weights and heights. We could be interested in predicting a person’s weight from his or her height, or we could be interested in predicting a person’s height from his or her weight. Prediction is merely a mathematical dependency, not necessarily a description of underlying causal relationship. Although height and weight tend to co-vary across people, the two variables are not directly causally related. When a person slouches, thereby getting shorter, she does not lose weight. And when a person drinks a glass of water, thereby weighing more, she does not get taller.
Just as “prediction” does not imply causation, “prediction” also does not imply any temporal relation between the variables. For example, we may want to predict a person s sex, male or female, from his or her height. Because males tend to be taller than females, this prediction can be made with better-than-chance accuracy. But a person s sex is not caused by his or her height, nor does a person s sex occur only after their height is measured. Thus, we can “predict” a person s sex from his or her height, but this does not mean that the person s sex occurred later in time than his or her height.
In summary, all manipulated independent variables are predictor variables, not predicted. Some dependent variables can take on the role of predictor variables, if desired. All predicted variables are dependent variables. The likelihood function specifies the probability of values of the predicted variables as a function of the values of the predictor variables.
Why we care: We care about these distinctions between predicted and predictor variables because the likelihood function is a mathematical description of the dependency of the predicted variable on the predictor variable. The first thing we have to do in statistical inference is identify what variables we are interested in predicting, on the basis of what predictors. As you should recall from Section 2.3, p. 25, the first step of Bayesian data analysis is to identify the data relevant to the analysis, and which variables are predictors and which variable is predicted.
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Psychometrics of Intelligence
Peter H. Schonemann, in Encyclopedia of Social Measurement, 2005
Predictive Validities of College Admission Tests
Over the decades, these tests have been refined by infusing ever more sophisticated theoretical and computational advances. However, this did not help improve them in terms of traditional measures of test efficiency. For example, it has been well-known virtually since its inception that the SAT has validities for First Year College GPA (GPA1) that hover around 0.4, approximately 10 correlation points below those of High School Rank (HSR). A tabulation published by the College Board shows that over the time span from 1964 through 1982, the HSR validities varied little (between 0.46 and 0.54, thus explaining approximately 25% of the criterion variance). For the SAT, they range between 0.37 and 0.46 (17%). To make matters worse, Humphreys showed in 1968 that the ACT validities drop into the 0.20s (4%) once the prediction interval is extended to the eighth semester GPA (GPA8). Similarly, it has repeatedly been shown (e.g., by Horn and Hofer and by Sternberg and Williams) that for long-range criteria of practical interest, such as graduation, the validities of the GRE are virtually zero. These findings cannot be dismissed as being due to random error. In contrast to the dubious figures reported for commercial IQ tests, such as the Wechsler and the Stanford–Binet, the sample sizes for the SAT, ACT, and GRE often range in the millions.
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Multivariate Linear Regression
S. Ganesh, in International Encyclopedia of Education (Third Edition), 2010
We may consider three distinguished cases, also indicated by Rencher (2002), according to the number of response and regressor variables:
- 1.
-
Simple linear regression. Here, the interest is on one response Y and one regressor X; for example, predicting college freshman grade-point average (GPA) based on the student’s SAT score.
Usually, a model is postulated by relating the response variable to the regressor variable with unknown parameters. A model that is linear in these parameters is called the simple linear regression model. This model, also referred to as a straight line model, is fitted via a technique known as the least squares and takes the form Y = β0 + β1X, where β0 and β1 are the so-called intercept and slope parameters. The reader may read any intermediate-level statistics textbook for further details (e.g., Ott and Longnecker, 2001).
- 2.
-
Multiple linear regression. Multiple regression analysis is used whenever we wish to model the relationship between one response variable and more than one regressor variable. In the preceding example, we could attempt to improve our prediction of college GPA by using, for example, high school GPA, Scholastic Aptitude Test (SAT) scores, and rating of school.
Many different forms of relationship are possible, but the overwhelming emphasis in practical applications is on the linear relationship Y = β0 + β1X1 + β2X2 + … + βpXp, known as the multiple linear regression model. The regression coefficients β0, β1, …, βp are model parameters whose values need to be estimated from the given data.
- 3.
-
Multivariate (multiple) linear regression. Multivariate multiple regression analysis arises when we have more than one response variable, and we wish to model the relationship between these variables and a set of regressor variables. Attention is again focused almost exclusively on linear relationships. In the preceding example, we may wish to predict freshman college GPA (in the sciences, arts, and humanities) as well as the number of years of college the student will complete based on high school GPA, SAT, and rating of school.
Note that, in multivariate multiple linear regression, multivariate refers to the response variables and multiple represents the independent variables so that (2) above can be regarded as univariate linear regression. The focus of this article is on multivariate linear regression and the main aim is to give a detailed exploration of the topic including examples.
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Statistical Conclusion Validity
P.L. Busk, in International Encyclopedia of Education (Third Edition), 2010
Restriction of Range
Restriction of range affects both correlation coefficients and the power of statistical tests. If the sample on which a correlation is based is homogeneous with respect to the variables being measured, then the correlation between the variables will be much less than if the sample were more heterogeneous. This phenomenon of range restriction is problematic for researchers trying to predict performance based on a sample that has a restricted range, for example, predicting performance for the first year in college based on applicants to that college or predicting performance for first year in college based on high-school students who take the Scholastic Aptitude Test (SAT) or American College Testing (ACT). Given that not all high-school students have college aspirations or will be attending a college that requires the SAT or ACT for admission and, further, not all students who take the test are admitted to colleges or universities, the range of scores is restricted for both variables and, hence, the correlation on which the prediction is based is restricted. Glass and Hopkins (1995) provided a formula for correcting the correlation coefficient for restricted variability in one of the samples. This equation should be used only for large samples and only where the conditions of linearity and homoscedasticity are met.
The range restriction on the dependent variable lowers the power of statistical tests. Researchers may be studying restricted samples that will result in floor or ceiling effects for the dependent variable. For example, if severely depressed individuals are studied, their data will result in floor effects as scores will cluster near the highest scores on a measure of depression, and, if highly anxious individuals are studied, their data will result in ceiling effects as their scores will cluster near the highest scores on a measure of anxiety. Researchers conducting studies with homogeneous samples should compensate for low power with larger sample sizes.
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Normal Random Variables
Sheldon M. Ross, in Introductory Statistics (Third Edition), 2010
Example 6.1
Test scores on the Scholastic Aptitude Test (SAT) verbal portion are normally distributed with a mean score of 504. If the standard deviation of a score is 84, then we can conclude that approximately 68 percent of all scores are between 504 – 84 and 504 + 84. That is, approximately 68 percent of the scores are between 420 and 588. Also, approximately 95 percent of them are between 504 – 168 = 336 and 504 + 168 = 672; and approximately 99.7 percent are between 252 and 756.
The approximation rule is the theoretical basis of the empirical rule of Sec. 3.6. The connection between these rules will become apparent in Chap. 8, when we show how a sample mean and sample standard deviation can be used to estimate the quantities μ and σ.
By using the symmetry of the normal curve about the value μ, we can obtain other facts from the approximation rule. For instance, since the area between μ and μ + σ is the same as that between μ – σ and μ, it follows from this rule that a normal random variable will be between μ and μ + σ with approximate probability 0.68/2 = 0.34.
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Metric Predicted Variable with Multiple Metric Predictors
John K. Kruschke, in Doing Bayesian Data Analysis (Second Edition), 2015
18.1.3 The posterior distribution
Figure 18.5 shows the posterior distribution from the SAT data in Figure 18.3 and model in Figure 18.4. You can see that the slope on spending (Spend) is credibly above zero, even taking into account a modest ROPE and MCMC instability. The slope on spending has a mode of about 13, which suggests that SAT scores rise by about 13 points for every extra $1000 spent per pupil. The slope on percentage taking the exam (PrcntTake) is also credibly non-zero, with a mode around −2.8, which suggests that SAT scores fall by about 2.8 points for every additional 1% of students who take the test.
Figure 18.5. Posterior distribution for data in Figure 18.3 and model in Figure 18.4. Scatter plots reveal correlations among credible parameter values; in particular, the coefficient on Spending (“Spend”) trades off with the coefficient on Percentage taking the exam (“PrcntTake”), because those predictors are correlated in the data.
The scatter plots in the bottom of Figure 18.5 show correlations among the credible parameter values in the posterior distribution. (These are pairwise scatter plots of credible parameter values from the MCMC chain; these are not scatter plots of data.) In particular, the coefficient for spending (Spend) trades off with the coefficient on percentage taking the exam (PrcntTake). The correlation means that if we believe that the influence of spending is smaller, then we must believe that the influence of percentage taking is larger. This makes sense because those two predictors are correlated in the data.
Figure 18.5 shows that the normality parameter for these data is fairly large, suggesting that there are not many outliers for this particular selection of predictors. It is worth noting that values of y are not inherently outliers or nonoutliers; they are only outliers relative to a spread of predicted values for a particular model. A value of y that seems spurious according to one set of predictors might be nicely linearly predicted by other predictors.
Finally, Figure 18.5 also shows a posterior distribution for a statistic labeled R2, which is called the proportion of variance accounted for in traditional least-squares multiple regression. In least-squares regression, the overall variance in y is algebraically decomposed into the variance of the linearly predicted values and the residual variance: ∑i(yi−y¯)2=∑i(yi−y^i)2+∑i(y^i−y¯)2, where y^i is the linearly predicted value of yi. The proportion of variance accounted for is R2=∑i(y^i−y¯)2/∑i(yi−y¯)2 when y^i is the linear prediction using coefficients that minimize ∑i(yi−y^i)2. If that makes no sense to you because you have no previous experience with least-squares regression, do not worry, because in Bayesian analysis no such decomposition of variance occurs. But for people familiar with least-squares notions who crave a statistic analogous to R2, we can compute a surrogate. At each step in the MCMC chain, a credible value of R2 is computed as R2=∑jζjry,xj, where ζj is the standardized regression coefficient for the jth predictor at that step in the MCMC chain, and ry,xj is the correlation of the predicted values, y, with the jth predictor values, xj. These correlations are constants, fixed by the data. The equation for expressing R2 in terms of the regression coefficients is used merely by analogy to least-squares regression, in which the equation is exactly true (e.g., Hays, 1994, Equation 15.14.2, p. 697). The mean value in the distribution of R2, when using vague priors, is essentially the least-squares estimate and the maximum-likelihood estimate when using a normal likelihood function. The posterior distribution reveals the entire distribution of credible R2 values. The posterior distribution of R2, defined this way, can exceed 1.0 or fall below 0.0, because R2 here is a linear combination of credible regression coefficients, not the singular value that minimizes the squared deviations between predictions and data.
Sometimes we are interested in using the linear model to predict y values for x values of interest. It is straight forward to generate a large sample of credible y values for specified x values. At each step in the MCMC chain, the combination of credible parameter values is inserted into the model and random y values are generated. From the distribution of y values, we can compute the mean and highest density interval (HDI) to summarize the centrally predicted y value and the uncertainty of the prediction. As was the case for simple linear regression, illustrated back in Figure 17.3 (p. 481), the uncertainty in predicted y is greater for x values outside the bulk of the data. In other words, extrapolation is more uncertain than interpolation.
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Noncognitive Measures for Higher Education Admissions
W.E. Sedlacek, in International Encyclopedia of Education (Third Edition), 2010
Keeping Up with Change
The world is much different than it was when the SAT and other tests were developed in the last century. International students, women, people of color, gays, lesbians, and bisexuals, among others, are participating in higher education in more extensive and varied ways (Knapp et al., 2002). Commonly employed tests have not kept up with these changes (Sedlacek, 2004).
We need a fresh approach. It is not good enough to feel constrained by the limitations of our current ways of conceiving of tests. Instead of asking, “How can we make the SAT and other such tests better?” we need to ask, “What kinds of measures will meet our needs now and in the future?” The purpose of this article is to present the underlying logic and research supporting a method that yields such measures. We do not need to ignore our current tests, we need to add some new measures that expand the potential we can derive from assessment.
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Distributions of Sampling Statistics
Sheldon M. Ross, in Introductory Statistics (Fourth Edition), 2017
Review Problems
- 1.
-
The sample mean and sample standard deviation of all student scores on the last Scholastic Aptitude Test (SAT) examination were, respectively, 517 and 120. Find the approximate probability that a random sample of 144 students would have an average score exceeding
- (a)
-
507
- (b)
-
517
- (c)
-
537
- (d)
-
550
- 2.
-
Let X‾ denote the sample mean of a sample of size 10 from a population whose probability distribution is given by
P{X=i}={0.1if i=10.2if i=20.3if i=30.4if i=4
Compute
- (a)
-
The population mean μ
- (b)
-
The population standard deviation σ
- (c)
-
E[X‾]
- (d)
-
Var(X‾)
- (e)
-
SD(X‾)
- 3.
-
In Prob. 2, suppose the sample size was 2. Find the probability distribution of X‾, and use it to compute E[X‾] and SD(X‾). Check your answers by using the values of μ and σ.
- 4.
-
The mean and standard deviation of the lifetime of a type of battery used in electric cars are, respectively, 225 and 24 minutes. Approximate the probability that a set of 10 batteries, used one after the other, will last for more than
- (a)
-
2200 minutes
- (b)
-
2350 minutes
- (c)
-
2500 minutes
- (d)
-
What is the probability they will last between 2200 and 2350 minutes?
- 5.
-
Suppose that 12 percent of the members of a population are left-handed. In a random sample of 100 individuals from this population,
- (a)
-
Find the mean and standard deviation of the number of left-handed people.
- (b)
-
Find the probability that this number is between 10 and 14 inclusive.
- 6.
-
The weight of a randomly chosen person riding a ferry has expected value 155 and standard deviation 28 pounds. The ferry’s capacity is 100 riders. Find the probability that, at capacity, the total passenger load exceeds 16,000 pounds.
- 7.
-
The monthly telephone bill of a student residing in a dormitory has an expected value of $15 with a standard deviation of $7. Let X denote the sum of the monthly telephone bills of a sample of 20 such students.
- (a)
-
What is E[X]?
- (b)
-
What is SD(X)?
- (c)
-
Approximate the probability that X exceeds $300.
- 8.
-
A recent newspaper article claimed that the average salary of newly graduated seniors majoring in chemical engineering is $54,000, with a standard deviation of $5000. Suppose a random sample of 12 such graduates revealed an average salary of $45,000. How likely is it that an average salary as low as or lower than $45,000 would have been observed from this sample if the newspaper article were correct?
- 9.
-
An advertising agency ran a campaign to introduce a product. At the end of its campaign, it claimed that at least 25 percent of all consumers were now familiar with the product. To verify this claim, the producer randomly sampled 1000 consumers and found that 232 knew of the product. If 25 percent of all consumers actually knew of the product, what is the probability that as few as 232 (that is, 232 or less) in a random sample of 1000 consumers were familiar?
- 10.
-
A club basketball team will play a 60-game season. Of these games 32 are against class A teams and 28 are against class B teams. The outcomes of all the games are independent. The team will win each game against a class A opponent with probability 0.5, and it will win each game against a class B opponent with probability 0.7. Let X denote the total number of victories in the season.
- (a)
-
Is X a binomial random variable?
- (b)
-
Let XA and XB denote, respectively, the number of victories against class A and class B teams. What are the distributions of XA and XB?
- (c)
-
What is the relationship among XA,XB, and X?
- (d)
-
Approximate the probability that the team wins 40 or more games. (Hint: Recall that the sum of independent normal random variables is also a normal random variable.)
- 11.
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If X is binomial with parameters n=80 and p=0.4, approximate the following probabilities.
- (a)
-
P{X>34}
- (b)
-
P{X≤42}
- (c)
-
P{25≤X≤39}
- 12.
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Consider the following simple model for daily changes in price of a stock. Suppose that on each day the price either goes up 1 with probability 0.52 or goes down 1 with probability 0.48. Suppose the price at the beginning of day 1 is 200. Let X denote the price at the end of day 100.
- (a)
-
Define random variables X1,X2,…,X100 such that
X=200+∑i=1100Xi
- (b)
-
Determine E[Xi]
- (c)
-
Determine Var(Xi)
- (d)
-
Use the central limit theorem to approximate P{X≥210}
- 13.
-
The following are the percentages of U.S. residents, classified by age, who were not covered by health insurance in 2002.
Age Percentage not covered under 18 11.6 18 to 24 29.6 25 to 34 24.9 35 to 44 17.7 45 to 64 13.5 65 and over 0.8 Suppose random samples of 1000 people in each age category are selected. Approximate the probability that
- (a)
-
At least 100 of those under 18 are not covered.
- (b)
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Fewer than 260 of those 25 to 34 years old are uncovered.
- (c)
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At most 5 of those 65 and over and at most 120 of those 45 to 64 years old are uncovered.
- (d)
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More of those who are 18 to 24 years old than of those who are 25 to 34 years old are uncovered.
- 14.
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A university administrator wants a quick estimate of the average number of students enrolled per class. Because he does not want the faculty to be aware of his interest, he has decided to enlist the aid of students. He has decided to randomly choose 100 names from the roster of students and have them determine and then report to him the number of students in each of their classes. His estimate of the average number of students per class will be the average number reported per class.
- (a)
-
Will this method achieve the desired goal?
- (b)
-
If the answer to part (a) is yes, explain why. If it is no, give a method that will work.
- 15.
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Teams 1, 2, 3, 4 are all scheduled to play each of the other teams 10 times. Whenever team i plays team j, team i is the winner with probability Pi,j. If
P1,2=.6,P1,3=.7,P1,4=.75P2,1=.4,P2,3=.6,P2,4=.70
- (a)
-
approximate the probability that team 1 wins at least 20 games. Suppose we want to approximate the probability that team 2 wins at least as many games as does team 1. To do so, let X be the number of games that team 2 wins against team 1, let Y be the total number of games that team 2 wins against teams 3 and 4, and let Z be the total number of games that team 1 wins against teams 3 and 4.
- (b)
-
Are X,Y,Z independent.
- (c)
-
Express the event that team 2 wins at least as many games as does team 1 in terms of the random variables X, Y, Z.
- (d)
-
Approximate the probability that team 2 wins at least as many games as team 1.
Hint: Approximate the distribution of any binomial random variable by a normal with the same mean and variance.
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Cognitive Psychology and Educational Statistics
H.S. Kim, S. Embretson, in International Encyclopedia of Education (Third Edition), 2010
Multicomponent Latent Trait Model
Many ability and achievement tests have sources of multidimensionality in the item domain. For example, the Scholastic Aptitude Test (SAT) algebra items require multiple skills or stages to arrive at a correct response, such as prerequisite skills for symbols and conventions, algebraic manipulations, linear functions, and simultaneous equations (Gierl et al., 2007). To better explain why an examinee answers a specific item incorrectly, statistical models that can assess the sources of multidimensionality are needed.
One important aspect of multidimensionality is that the skills or processing stages in the items are often sequentially dependent. Thus, cognitive models for tasks typically postulate a flow of information from one stage to another. Four possible forms of hierarchical structures of processing stages in task performance are presented in Figure 1 (Gierl et al., 2007). In all the structures, there is a prerequisite skill (stage 1) and orderings among all or some processing stages except in Figure 1(d), which is an unstructured hierarchy.
Figure 1. Four different hierarchical structures. Reproduced from Gierl, M. J., Leighton, J. P., and Hunka, S. M. (2007). Using the attribute hierarchy method to make diagnostic inferences about examinees’ cognitive skills. In Leighton, J. P. and Gierl, M. J. (eds.) Cognitive Diagnostic Assessment for Education, pp 242–274. New York: Cambridge University Press.
The multidimensional latent trait model (MLTM; Whitely, 1980) was designed to properly reflect the sequentially dependent stages (called components in this model) based on a product of processing outcome probabilities as follows:
[10]P(Xis=1)=∏kP(Xisk)=∏kexpθsk−βik1+expθsk−βik,
where P(Xis = 1) is the probability of success for person s on item i and ∏k P(Xisk) is the product of success on each processing component k, given the correct outcome of the preceding component. The right side of the equation contains terms from the Rasch models for the probability of success on each component, where θsk is the trait level of person s on component k and βik is the difficulty of item i on component k.
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An Overview of Statistics in Education
S. Sinharay, in International Encyclopedia of Education (Third Edition), 2010
Analysis of Variance, Analysis of Covariance, and Multivariate Analysis of Variance
Analysis of variance (ANOVA) is the statistical procedure of comparing the means of a variable across several groups of individuals. For example, ANOVA may be used to compare the average SAT critical reading scores of several schools. The name of the technique arises from the fact that the first step in an ANOVA is to partition the variance present in the observations into several components. The ANOVA method was the second most frequently used data-analysis procedure in a survey of articles published between 1971 and 1998 in three reputed educational-research journals (Hsu, 2005). Generalizability theory (Cronbach et al., 1963), which is a competitor to the classical theory of reliability of tests, usually applies ANOVA procedures to test scores.
Analysis of covariance (ANCOVA) is used when, like in ANOVA, the interest is in comparing several means, but the investigator also has the values of an additional variable that influences the variable of interest. For example, ANCOVA may be used to compare the average SAT critical reading scores of several schools where the preliminary scholastic aptitude test/national merit scholarship qualifying test (PSAT/NMSQT) critical reading score of each examinee is available in addition to the SAT critical reading score. (The PSAT/NMSQT is supposed to provide firsthand practice for the SAT.)
Multivariate analysis of variance (MANOVA) is used to compare means of several variables simultaneously across several groups of individuals. For example, one could apply MANOVA to simultaneously compare the average scores on several subjects across several schools. Longford (1990) provides such an example.
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Overview of the Generalized Linear Model
John K. Kruschke, in Doing Bayesian Data Analysis (Second Edition), 2015
15.1.1 Predictor and predicted variables
Suppose we want to predict someone’s weight from their height. In this case, weight is the predicted variable and height is the predictor. Or, suppose we want to predict high school grade point average (GPA) from Scholastic Aptitude Test (SAT) score and family income. In this case, GPA is the predicted variable, while SAT score and income are predictor variables. Or, suppose we want to predict the blood pressure of patients who either take drug A, or take drug B, or take a placebo, or merely wait. In this case, the predicted variable is blood pressure, and treatment category is the predictor.
The key mathematical difference between predictor and predicted variables is that the likelihood function expresses the probability of values of the predicted variable as a function of values of the predictor variable. The likelihood function does not describe the probabilities of values of the predictor variable. The value of the predictor variable comes from outside the system being modeled, whereas the value of the predicted variable depends on the value of the predictor variable.
Because the predicted variable depends on the predictor variable, at least mathematically in the likelihood function if not causally in the real world, the predicted variable can also be called the “dependent” variable. The predictor variables are sometimes called “independent” variables. The key conceptual difference between independent and dependent variables is that the value of the dependent variable depends on the value of the independent variable. The term “independent” can be confusing because it can be used strictly or loosely. In experimental settings, the variables that are actually manipulated and set by the experimenter are the independent variables. In this context of experimental manipulation, the values of the independent variables truly are (in principle, at least) independent of the values of other variables, because the experimenter has intervened to arbitrarily set the values of the independent variables. But sometimes a non-manipulated variable is also referred to as “independent,” merely as a way to indicate that it is being used as a predictor variable.
Among non-manipulated variables, the roles of predicted and predictor are arbitrary, determined only by the interpretation of the analysis. Consider, for example, people’s weights and heights. We could be interested in predicting a person’s weight from his or her height, or we could be interested in predicting a person’s height from his or her weight. Prediction is merely a mathematical dependency, not necessarily a description of underlying causal relationship. Although height and weight tend to co-vary across people, the two variables are not directly causally related. When a person slouches, thereby getting shorter, she does not lose weight. And when a person drinks a glass of water, thereby weighing more, she does not get taller.
Just as “prediction” does not imply causation, “prediction” also does not imply any temporal relation between the variables. For example, we may want to predict a person s sex, male or female, from his or her height. Because males tend to be taller than females, this prediction can be made with better-than-chance accuracy. But a person s sex is not caused by his or her height, nor does a person s sex occur only after their height is measured. Thus, we can “predict” a person s sex from his or her height, but this does not mean that the person s sex occurred later in time than his or her height.
In summary, all manipulated independent variables are predictor variables, not predicted. Some dependent variables can take on the role of predictor variables, if desired. All predicted variables are dependent variables. The likelihood function specifies the probability of values of the predicted variables as a function of the values of the predictor variables.
Why we care: We care about these distinctions between predicted and predictor variables because the likelihood function is a mathematical description of the dependency of the predicted variable on the predictor variable. The first thing we have to do in statistical inference is identify what variables we are interested in predicting, on the basis of what predictors. As you should recall from Section 2.3, p. 25, the first step of Bayesian data analysis is to identify the data relevant to the analysis, and which variables are predictors and which variable is predicted.
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Psychometrics of Intelligence
Peter H. Schonemann, in Encyclopedia of Social Measurement, 2005
Predictive Validities of College Admission Tests
Over the decades, these tests have been refined by infusing ever more sophisticated theoretical and computational advances. However, this did not help improve them in terms of traditional measures of test efficiency. For example, it has been well-known virtually since its inception that the SAT has validities for First Year College GPA (GPA1) that hover around 0.4, approximately 10 correlation points below those of High School Rank (HSR). A tabulation published by the College Board shows that over the time span from 1964 through 1982, the HSR validities varied little (between 0.46 and 0.54, thus explaining approximately 25% of the criterion variance). For the SAT, they range between 0.37 and 0.46 (17%). To make matters worse, Humphreys showed in 1968 that the ACT validities drop into the 0.20s (4%) once the prediction interval is extended to the eighth semester GPA (GPA8). Similarly, it has repeatedly been shown (e.g., by Horn and Hofer and by Sternberg and Williams) that for long-range criteria of practical interest, such as graduation, the validities of the GRE are virtually zero. These findings cannot be dismissed as being due to random error. In contrast to the dubious figures reported for commercial IQ tests, such as the Wechsler and the Stanford–Binet, the sample sizes for the SAT, ACT, and GRE often range in the millions.
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Multivariate Linear Regression
S. Ganesh, in International Encyclopedia of Education (Third Edition), 2010
We may consider three distinguished cases, also indicated by Rencher (2002), according to the number of response and regressor variables:
- 1.
-
Simple linear regression. Here, the interest is on one response Y and one regressor X; for example, predicting college freshman grade-point average (GPA) based on the student’s SAT score.
Usually, a model is postulated by relating the response variable to the regressor variable with unknown parameters. A model that is linear in these parameters is called the simple linear regression model. This model, also referred to as a straight line model, is fitted via a technique known as the least squares and takes the form Y = β0 + β1X, where β0 and β1 are the so-called intercept and slope parameters. The reader may read any intermediate-level statistics textbook for further details (e.g., Ott and Longnecker, 2001).
- 2.
-
Multiple linear regression. Multiple regression analysis is used whenever we wish to model the relationship between one response variable and more than one regressor variable. In the preceding example, we could attempt to improve our prediction of college GPA by using, for example, high school GPA, Scholastic Aptitude Test (SAT) scores, and rating of school.
Many different forms of relationship are possible, but the overwhelming emphasis in practical applications is on the linear relationship Y = β0 + β1X1 + β2X2 + … + βpXp, known as the multiple linear regression model. The regression coefficients β0, β1, …, βp are model parameters whose values need to be estimated from the given data.
- 3.
-
Multivariate (multiple) linear regression. Multivariate multiple regression analysis arises when we have more than one response variable, and we wish to model the relationship between these variables and a set of regressor variables. Attention is again focused almost exclusively on linear relationships. In the preceding example, we may wish to predict freshman college GPA (in the sciences, arts, and humanities) as well as the number of years of college the student will complete based on high school GPA, SAT, and rating of school.
Note that, in multivariate multiple linear regression, multivariate refers to the response variables and multiple represents the independent variables so that (2) above can be regarded as univariate linear regression. The focus of this article is on multivariate linear regression and the main aim is to give a detailed exploration of the topic including examples.
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Statistical Conclusion Validity
P.L. Busk, in International Encyclopedia of Education (Third Edition), 2010
Restriction of Range
Restriction of range affects both correlation coefficients and the power of statistical tests. If the sample on which a correlation is based is homogeneous with respect to the variables being measured, then the correlation between the variables will be much less than if the sample were more heterogeneous. This phenomenon of range restriction is problematic for researchers trying to predict performance based on a sample that has a restricted range, for example, predicting performance for the first year in college based on applicants to that college or predicting performance for first year in college based on high-school students who take the Scholastic Aptitude Test (SAT) or American College Testing (ACT). Given that not all high-school students have college aspirations or will be attending a college that requires the SAT or ACT for admission and, further, not all students who take the test are admitted to colleges or universities, the range of scores is restricted for both variables and, hence, the correlation on which the prediction is based is restricted. Glass and Hopkins (1995) provided a formula for correcting the correlation coefficient for restricted variability in one of the samples. This equation should be used only for large samples and only where the conditions of linearity and homoscedasticity are met.
The range restriction on the dependent variable lowers the power of statistical tests. Researchers may be studying restricted samples that will result in floor or ceiling effects for the dependent variable. For example, if severely depressed individuals are studied, their data will result in floor effects as scores will cluster near the highest scores on a measure of depression, and, if highly anxious individuals are studied, their data will result in ceiling effects as their scores will cluster near the highest scores on a measure of anxiety. Researchers conducting studies with homogeneous samples should compensate for low power with larger sample sizes.
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Подготовка к поступлению в американский вуз занимает время, требует определенных усилий и финансовых вложений. Да, иногда может казаться, что все против вас. Но не нужно отчаиваться! Игра стоит свеч, тем более что пример тысяч иностранных студентов, поступивших и окончивших американские колледжи и университеты вдохновляет. В этой статье мы разберем, как выбирать вузы в США, подавать заявки, где узнавать требования к абитуриентам в разных вузах, а также разберем международные стандартизированные тесты TOEFL, SAT и ACT.
Как выбрать вузы?
Для начала стоит определиться, куда вы хотите поступить в США: в коллеж или университет. Это — взаимозаменяемые понятия. Колледжи предлагают степень бакалавра (в некоторых случаях, степень магистра и доктора), в то время как университеты предлагают степени бакалавра, магистра и доктора, но эти термины часто используются в США как синонимы.
Выбирая в какой вуз подать заявку, нужно ориентироваться в первую очередь, на свои академические потребности и финансовые возможности. Ответьте себе на несколько важных вопросов, которые помогут вам в поиске идеально подходящего вуза в США:
- Почему я хочу учиться в США?
- В каком университете я буду ощущать себя комфортно?
- Какой колледж или университет в США отвечает моим потребностям?
- Где мне хотелось бы жить в США?
- Каковы крайние сроки подачи документов для поступления?
В США на начальной ступени совсем не обязательно определиться со специальностью, достаточно выбрать направление вуза: медицина, право, инженерия, естественные науки, искусство и т. д. Изучите подробно сайты вузов, почитайте отзывы других студентов, и у вас сложится свое понимание, какое направление вам больше подходит.
Что касается финансовой составляющей, то в США надо быть готовыми оплатить обучение в вузе, проживание, питание, покупку книг, транспортные расходы и медицинскую страховку. Однако не стоит пугаться, нужно помнить три правила экономии средств:
- Во-первых, искать вузы, стоимость обучения в которых существенно ниже, чем в других. В США это совсем не влияет на качество образования, дешевый вуз — не означает плохой.
- Во-вторых, рассмотреть вариант обучения в Community Colleges с программами «2+2». То есть, вы оплачиваете два года в этом колледже США, а затем переводитесь в 4-годичный колледж или в университет. Система популярна среди американцев, так как позволяет сэкономить значительные средства на обучение в вузе.
- В-третьих, иностранным студентам американские вузы выделают разные виды финансовой поддержки. Если вуз оценит ваши компетенции, он может взять на себя или часть расходов, или оплатить их полностью. Такие программы есть не в каждом вузе, поэтому стоит обратить внимание на их наличие еще на стадии выбора.
Как подать заявку для поступления?
Итак, вы определились с вузом? Обратите внимание на сроки! В США существует несколько принципов приема заявок в вузы:
- regular decision (RD) — обычная система приема заявок в вуз с дедлайном 1 или 15 января;
- early decision (ED) — ранняя система с дедлайном 1-15 ноября. В случае поступления, абитуриент должен внести оплату, как доказательство серьезности своих намерений или будет вычеркнут из списков вуза;
- early action (EA) — ранняя система с дедлайном 1-15 ноября. В отличие от ED, абитуриент может принять решение 1 мая, что дает люфт для ожидания результатов из других вузов США;
- rolling admissions (RA) — плавающая система с подачей заявок в вузы в течение всего года и дедлайном весной.
Что дают ED или EA? Некоторые скидки при оплате обучения в вузах США. Это как купить квартиру на стадии строительства — дешевле, чем после сдачи дома.
Какие документы нужны к моменту подачи заявки?
В стандартный пакет входит:
- Форма, предложенная вузом США;
- Application fee — оплата за подачу документов и их рассмотрение вузом;
- Транскрипт с указанием всех предметов, оценок и часов, включая зачеты, курсовую, дипломную работы и практику (для студентов). Все должно быть переведено на английский язык и заверено печатью учебного заведения;
- GPA (Grade Point Average) — средний балл успеваемости;
- Мотивационное письмо в форме эссе;
- Рекомендательные письма от преподавателей, переведенные на английский язык;
- Сертификат о сдаче языкового теста TOEFL или IELTS;
- Сертификат о сдаче стандартизированного теста SAT / ACT (для поступления в вуз США на степень бакалавра);
- Доказательства платежеспособности: наличие денежных средств на оплату первого года обучения и проживания в США;
- Подтверждение достижений во внеучебной деятельности, например, работа волонтером, победы в спортивных соревнованиях, опыт практической работы, связанной с направлением обучения, или стажировки — опционально (он добавляет баллы при оценке вашей формы заявки в вуз).
Какие требования к абитуриентам?
Одно из требований, на которые следует обратить внимание, — успеваемость. Чем лучше ваши оценки, тем интереснее вузу США ваша кандидатура. Вы работаете несколько лет на оценки, а затем они работают на вас.
Второе обязательное требование — владение языком. Международные стандартизированные тесты проверяют ваш уровень владения английским языком. Практически все вузы США принимают результаты теста TOEFL, но наряду с ним могут приниматься результаты тестов IELTS или Duolingo. У каждого вуза в США свой проходной балл. Но расслабляться не стоит, так как для поступления и получения финансовой поддержки от вуза нужно продемонстрировать на экзамене высокий результат.
Третье требование — сданный стандартизированный экзамен SAT или ACT. В настоящее время результаты этих тестов просят не все учебные заведения США. Во время подготовки к поступлению нужно узнавать подробности в конкретном выбранном вузе.
Четвертое требование опционально. Иногда вузы США могут не запрашивать у абитуриента результаты SAT или ACT, но попросить прохождения тестов или экзаменов, составленных самим вузом. Пятое негласное, но очень важное требование — прохождение онлайн собеседования, в случае, если вуз его назначает в дополнение к экзаменам. Нужно быть естественным, живым, владеть интересующим вас материалом, уметь рассказать о себе, своем выборе и ответить на любые вопросы. Здесь главное не волноваться и, как ни банально звучит, быть собой.
Какие нужны международные экзамены для поступления?
Как уже было отмечено, вузы США признают результаты TOEFL и IELTS, но вам нужно уточнять на сайте вузов результаты какого экзамена принимает вуз. Тесты платные, поэтому лучше сразу сдать тот, который обязательно примут при поступлении. Ниже мы детально рассмотрим тест TOEFL.
TOEFL
Тест призван поверить уровень владения языком во всех сферах: аудирование, говорение, чтение и письмо. TOEFL длится три часа. Секции экзамена выстроены в определенной последовательности:
Секция | Время | Вопросы/задания | Описание |
Чтение | 54-72 мин | 30-40 вопросов | Прочитать тексты и ответить на вопросы |
Аудирование | 41-57 мин | 28-39 вопросов | Ответить на вопросы по прослушанной лекции или беседе на тему обучения в вузе |
Перерыв | 10 мин | ||
Говорение | 17 мин | 4 задания | Поговорить на знакомую тему и обсудить прослушанный и прочитанный материал |
Письмо | 50 мин | 2 задания | Прочитать отрывок, прослушать запись и написать эссе, а также написать эссе на заданную тему |
В России есть один вариант сдачи теста — internet-based test (iBT) или интернет-вариант.
Помните, что тесты сдаются в специальных центрах в заранее обозначенные даты. Обычно — не менее четырех раз в месяц. Сам тест стоит $260, но поздняя запись влечет за собой повышение оплаты еще на $40. Если вы захотите перенести дату сдачи, тоже придется доплатить. Из плюсов — если вас не устроил балл за «письмо» и/или «говорение», эти секции можно пересдать отдельно.
Сертификат доставляется в течение нескольких недель и действителен только два года. Если вы уверены в своих знаниях, сдавать тест лучше всего в дату, максимально близкую к подаче документов в вуз США. Это даст возможность в случае необходимости использовать сертификат при поступлении еще раз.
SAT — Scholastic Aptitude Test
Если вы иностранный абитуриент и собираетесь поступать в колледж или в бакалавриат университета, вам нужно сдать один из тестов, подтверждающих вашу подготовленность к обучению в вузе США.
SAT — стандартизированный тест по принципу российского ЕГЭ с несколькими вариантами ответа. Он выполняется письменно в бумажном варианте. Состоит из трех частей: чтение, математика и грамматика.
Секция | Время | Задание |
Чтение | 65 мин | Пять текстов разной тематики и стилистики, а также вопросы и задания к ним. Раздел призван определить, насколько точно вы умеете понимать написанную информацию. |
Грамматика и стилистика | 35 мин | 44 задания по грамматике, структуре текста и устойчивым выражениям |
Математика | 80 мин | 58 задач из алгебры, геометрии, арифметики, статистики и тригонометрии |
ACT — American College Test
Стандартизированный тест для поступления в
колледж
США. Охватывает основные сферы: английский, математику, чтение, науки. Задания предлагают варианты ответов. Опционально можно выполнить задание по письму, создав эссе в дополнительные 40 минут.
Секция | Время | Задание |
Английский | 45 мин | 75 заданий на владение языком |
Математика | 60 мин | 60 заданий по алгебре, геометрии, тригонометрии, на рассуждение и решение задач в соответствии со школьной программой США |
Чтение | 35 мин | 40 заданий на понимание прочитанного |
Науки | 35 мин | 40 заданий на умение интерпретировать, анализировать, оценивать, рассуждать и решать проблемы |
SAT vs ACT — какой экзамен выбрать?
Вузы США принимают одинаково результаты обоих стандартизированных тестов. Какой же выбрать?
SAT | ACT | |
Секции | 3 или 4 | 4 или 5 |
Время | 180 или 230 мин | 175 или 215 мин |
Предметы | Чтение, грамматика, математика. Научные вопросы могут попасться в текстах раздела «чтение» | Чтение, грамматика, математика. Науки вынесены особо |
Специфика | Фокус на конкретных дисциплинах | Фокус на общие знания абитуриента и умение принимать решения |
Максимальное число баллов | 1600 | 36 |
Частота проведения теста за пределами США | 5 раз в год | 4-6 раз в год |
Стоимость | $101 без эссе, $117 с эссе | $168.5 без эссе, $118.5 с эссе |
Срок действия сертификата | 5 лет | 3 года |
Готовь сани с лета
Мечту уехать учиться в США можно реализовать. Для этого нужен четкий план действий, составленный как можно раньше.
- Помните, что подготовка к экзаменам SAT или ACT и ожидание результатов после сдачи занимает время. Кроме того, с самого начала нужно определиться, какие тесты сдавать в соответствии с требованиями вуза в США, по срокам или стоимости.
- Время также требуется для подготовки и сдачи языкового теста TOEFL или IELTS.
- Не забывайте, что уже на подготовительном этапе нужно обладать средствами. Равно как и при подаче документов в вузы необходимы доказательства платежеспособности. А значит, можно начать откладывать на учебу в США заранее.
- И, наконец, если вы хотите видеть в аттестате нужные отметки, беритесь за ум как можно раньше, чтобы подготовиться к поступлению
Мы в свою очередь готовы ответить на любые вопросы, помочь выбрать подходящие вузы, подготовить пакет документов и проконсультировать о наличии стипендий в том или ином вузе США.