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- Cambridge International AS and A Level Mathematics Statistics
- Cambridge International AS and A Level Mathematics (9709) Ebooks
- Cambridge International as & a Level Mathematics: Probability & Statistics 1 Coursebook
It dawned on me that their fight had seemed like a show, like they were actors playing parts in a made-up story.
Cambridge International AS and A Level Mathematics Statistics
English Pages  Year Written for international students with suitable content and language levels - Ensures ease of teaching and student prog. This new edition for the revised syllabus has been endorsed by Cambridge International Examinations. Table of contents : Cover Title page Copyright Contents Series introduction How to use this book Acknowledgements 1 Representation of data 2 Measures of central tendency 3 Measures of variation Cross-topic review exercise 1 4 Probability 5 Permutations and combinations Cross-topic review exercise 2 6 Probability distributions 7 The binomial and geometric distributions 8 The normal distribution Cross-topic review exercise 3 Practice exam-style paper The standard normal distribution function Answers Glossary Index.
Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. Cambridge Assessment International Education bears no responsibility for the example answers to questions taken from its past question papers which are contained in this publication.
C w ge U R ev ie w rs C ity op Pr y Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Information regarding prices, travel timetables, and other factual information given in this work is correct at the time of first printing but Cambridge University Press does not guarantee the accuracy of such information thereafter.
In examination, the way marks would be awarded to answers like these may be different. On the one hand, it is a facilitating subject: there are many university courses that either require an A Level or equivalent qualification in mathematics or prefer applicants who have it. On the other hand, it will help you to learn to think more precisely and logically, while also encouraging creativity.
Doing mathematics can be like doing art: just as an artist needs to master her tools use of the paintbrush, for example and understand theoretical ideas perspective, colour wheels and so on , so does a mathematician using tools such as algebra and calculus, which you will learn about in this course.
But this is only the technical side: the joy in art comes through creativity, when the artist uses her tools to express ideas in novel ways. Mathematics is very similar: the tools are needed, but the deep joy in the subject comes through solving problems. This is a very good question, and many people have offered different answers. You might like to write down your own thoughts on this question, and reflect on how they change as you progress through this course.
One possible idea is that a mathematical problem is a mathematical question that you do not immediately know how to answer.
Such a problem will take time to answer: you may have to try different approaches, using different tools or ideas, on your own or with others, until you finally discover a way into it. This may take minutes, hours, days or weeks to achieve, and your sense of achievement may well grow with the effort it has taken. The new examinations may well include more unfamiliar questions than in the past, and having these skills will allow you to approach such questions with curiosity and confidence.
It is very common to be faced with problems, be it in science, engineering, mathematics, accountancy, law or beyond, and having the confidence to systematically work your way through them will be very useful.
As you study this course, you will work on many problems. Exploring them or struggling with them together with a classmate will help you both to develop your understanding and thinking, as well as improving your mathematical communication skills. There are many situations where people need to make predictions or to understand what is happening in the world, and mathematics frequently provides tools to assist with this.
Mathematicians will look at the real world situation and attempt to capture the key aspects of it in the form of equations, thereby building a model of reality.
They will use this model to make predictions, and where possible test these against reality. If necessary, they will then attempt to improve the model in order to make better predictions. Examples include weather prediction and climate change modelling, forensic science to understand what happened at an accident or crime scene , modelling population change in the human, animal and plant kingdoms, modelling aircraft and ship behaviour, modelling financial markets and many others.
In this course, we will be developing tools which are vital for modelling many of these situations. They require thought and deliberation: some introduce a new idea, others will extend your thinking, while others can support consolidation. The activities are often best approached by working in small groups and then sharing your ideas with each other and the class, as they are not generally routine in nature.
This is one of the ways in which you can develop problemsolving skills and confidence in handling unfamiliar questions.
They are designed to support you in preparing for the new style of examination. They may or may not be harder than other questions in the exercise. It is also the way that professional mathematicians usually write about mathematics.
The new examinations may well present you with unfamiliar questions, and if you are used to being active in your mathematics, you will stand a better chance of being able to successfully handle such challenges. These high-quality resources have the potential to simultaneously develop your mathematical thinking skills and your fluency in techniques, so we do encourage you to make good use of them.
Copyright Material - Review Only - Not for Redistribution vii y ve rs ity ni w ge C U How to use this book ev ie q am br id p q op p S c ve rs ity display numerical data in stem-and-leaf diagrams, histograms and cumulative frequency graphs interpret statistical data presented in various forms select an appropriate method for displaying data.
Construct and interpret histograms with equal and unequal intervals. The column widths are 3 cm and 4 cm, and the column heights are 8 cm and 6 cm, respectively. What do we know about the frequencies of these two classes? Determine, by drawing a cumulative frequency diagram, how many trees have heights: ie ev -R Pr ity y ni op li Answer The 5 is a repeated digit, so we must investigate three situations separately.
This is indicated in the last column of the table. Worked examples provide step-by-step approaches to answering questions. The left side shows a fully worked solution, while the right side contains a commentary explaining each step in the working.
Two digits from 7, 8 and 9 are selected and arranged with a 5. How many distinct three-digit numbers can be made from five cards, each with one of the digits 5, 5, 7, 8 and 9 written on it?
Key terms are important terms in the topic that you are learning. They are highlighted in orange bold. Try the questions to identify any areas that you need to review before continuing with the chapter. Find: s es -C y op C viii R Check your skills Obtain appropriate upper and lower bounds to solutions of simple problems when given data to a specified accuracy. D ata in a stem-andleaf diagram are ordered in rows of equal widths. This section provides a brief overview of these features.
Copyright Material - Review Only - Not for Redistribution Tip boxes contain helpful guidance about calculating or checking your answers. Rewind boxes refer to earlier learning, in case you need to revise a topic. U PS These questions focus on problem-solving.
P These questions focus on proofs. M These questions focus on modelling. Latin was used as the language of international communication, scholarship and science until well into the 18th century. Assume that the weather on any one day is independent of the weather on other days. You can use this to check your understanding of the topics you have covered. The number of marks gives an indication X Y of how long you should be spending on the question.
X You should spend more time on questions with higher mark allocations; questions with only one or two marks should not need you to spend time doing complicated calculations or writing long explanations. U 1 Each of the eight players in a chess team plays 12 games against opponents from other teams.
The total n m the whole team are denoted by X , Y and Z, respectively. You can use a calculator for these questions. You should not use a calculator for these questions. C op ni y Throughout each chapter there are multiple exercises containing practice questions. Pr es s -C Recall from Chapter 4, Section 4. If any omissions are brought to our notice, we will be happy to include the appropriate acknowledgements on reprinting.
Copyright Material - Review Only - Not for Redistribution op y ve rs ity ni C U ev ie w ge -R am br id Pr es s -C y ni C op y ve rs ity op C w ev ie Chapter 1 Representation of data y op w ge C U R ni ev ve rs w C ity op Pr y es s -C -R am br ev id ie w ge U R ie 1 id es s -C -R am br ev display numerical data in stem-and-leaf diagrams, histograms and cumulative frequency graphs interpret statistical data presented in various forms select an appropriate method for displaying data.
Pr es s y op Construct and interpret histograms with equal and unequal intervals. C op ni U ie w ge 3 The heights of 50 trees are measured: 17 trees are less than 3m; 44 trees are less than 4 m; and all of the trees are less than 5 m. Determine, by drawing a cumulative frequency diagram, how many trees have heights: -R am br ev id R b of 4 m or more.
Pr y es s -C a between 3 and 4 m ity op 2 a its least possible perimeter y ve rs ity C 1 A rectangular plot measures 20 m by 12 m, both to the nearest metre. Find: 2 A histogram is drawn to represent two classes of data.
The column widths are 3 cm and 4 cm, and the column heights are 8cm and 6cm, respectively. We display and analyse data so that we can describe the things, both physical and social, that we see and experience around us. We can also find answers to questions that might not be immediately obvious, and we can also identify questions for further investigation.
We find it in the media and from elsewhere: sports news, product advertisements, weather updates, health and environmental reports, service information, political campaigning, stock market reports and forecasts, and so on.
Quantitative data take numerical values and are either discrete or continuous. As a general rule, discrete data are counted and cannot be made more precise, whereas continuous data are measurements that are given to a chosen degree of accuracy.
This is a valuable skill that helps us to make informed decisions. Copyright Material - Review Only - Not for Redistribution ve rs ity C U ni op y Chapter 1: Representation of data am br id ev ie w ge The number of letters in the words of a book is an example of discrete quantitative data. Each word has 1 or 2 or 3 or 4 or… letters. There are no words with 3 13 or 4.
For example, United States coins have dollar values of 0. In Canada, the United Kingdom and other countries, shoe sizes such as 6 21 , 7 and 7 21 are used. Pr es s -C Continuous data can take any value possibly within a limited range , as shown in the diagram. Continuous data can take any value, possibly within a limited range. We can measure these to the nearest second, tenth of a second or even more accurately if we have the necessary equipment.
The range of times is limited to positive real numbers. The rows should have intervals of equal width to allow for easy visual comparison of sets of data. A key with the appropriate unit must be included to explain what the values in the diagram represent. The last digit of each data value appears as a leaf attached to all the other digits, which appear in a stem.
The digits in the stem are ordered vertically, and the digits on the leaves are ordered horizontally, with the smallest digit placed nearest to the stem.
R -R s -C am br ev In a back-to-back stem-and-leaf diagram, the leaves to the right of the stem ascend left to right, and the leaves on the left of the stem ascend right to left as shown in Worked example 1.
Copyright Material - Review Only - Not for Redistribution The diagram should have a bar chartlike shape, which is achieved by aligning the leaves in columns. It is advisable to redraw the diagram if any errors are noticed, or to complete it in pencil, so that accuracy can be maintained.
Cambridge International AS and A Level Mathematics (9709) Ebooks
Chapter 1 pdf Chapter 2 pdf Chapter 3 pdf Chapter 4 pdf Chapter 5 pdf nbsp AS Level Mathematics Pure Mathematics 1 Practice Book University of Cambridge International Examinations bears no responsibility for the example answers nbsp If you are working on your own there are answers in the back of the book. The series is edited by David Rayner whose clear practice based approach is trusted around the world to build students mathematical and analytical skills. Typical UK university entrance requirements are above three passes at grade C for academic courses in established universities. It explores major themes of mathematics from humankind 39 s earliest study of prime numbers to the cutting edge mathematics used to reveal the shape of the universe. Read online Pure Mathematics 1 International Cambridge book pdf free download link book now. Click Download or Read Online button to get pure mathematics 1 international book now. Develop exam confidence Cambridge past paper questions Cambridge AS and A Level Mathematics is a revised series to ensure full syllabus coverage.
Advanced level applied mathematics by Lambe, C. Your privacy is important to us. It can be writter in straightforward terms instead of confusing. To reflect … This is an elegantly composed reading material which has been revived with later past paper questions. This reading material gives full scope of Pure Mathematics 2 and 3 P2 and 3. A-Level Past Papers.
English Pages  Year Written for international students with suitable content and language levels - Ensures ease of teaching and student prog. This new edition for the revised syllabus has been endorsed by Cambridge International Examinations. Table of contents : Cover Title page Copyright Contents Series introduction How to use this book Acknowledgements 1 Representation of data 2 Measures of central tendency 3 Measures of variation Cross-topic review exercise 1 4 Probability 5 Permutations and combinations Cross-topic review exercise 2 6 Probability distributions 7 The binomial and geometric distributions 8 The normal distribution Cross-topic review exercise 3 Practice exam-style paper The standard normal distribution function Answers Glossary Index. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. Cambridge Assessment International Education bears no responsibility for the example answers to questions taken from its past question papers which are contained in this publication. C w ge U R ev ie w rs C ity op Pr y Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
Cambridge International as & a Level Mathematics: Probability & Statistics 1 Coursebook
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Go to our other sites. Endorsed by Cambridge Resources align to the syllabus they support, and have been through a detailed quality assurance process. In-depth coverage of Mechanics. Extensive and varied practice sections build the key mathematical skills along with a focus on mathematics in life and work.
This single coursebook comprehensively covers all four modules of the syllabus and helps support students in their studies and develops their mathematical skills. Authored by experienced teachers of Further Mathematics, the coursebook provides detailed explanations and clear worked examples with practice exercises and exam-style questions. Answers are at the back of the book. With topics including national security, technology, marriage, race, economics, the environment, and globalization, among others, this anthology is sure to engage students and inspire them to think critically and write well.
Новый порядок букв показался не более вразумительным, чем оригинал. P F Е Е S Е S N R Е Т М Р F Н А I R W E О О 1 G М Е Е N N R М А Е N Е Т S Н А S D С N S I 1 А А I Е Е R В R N К S В L Е L О D 1 - Ясно как в полночь в подвале, - простонал Джабба. - Мисс Флетчер, - потребовал Фонтейн, - объяснитесь.
Однажды вечером на университетском представлении Щелкунчика Сьюзан предложила Дэвиду вскрыть шифр, который можно было отнести к числу базовых. Весь антракт он просидел с ручкой в руке, ломая голову над посланием из одиннадцати букв: HL FKZC VD LDS В конце концов, когда уже гасли огни перед началом второго акта, его осенило. Шифруя послание, Сьюзан просто заменила в нем каждую букву на предшествующую ей алфавите. Для расшифровки Беккеру нужно было всего лишь подставить вместо имеющихся букв те, что следовали непосредственно за ними: А превращалось в В, В - в С и так далее.
Кажется, чуточку дороговато, не правда. - Да уж, - застонал. - Чуточку. - Это как будто деление на ноль.
Фонтейна это позабавило. - Вы знаете, кто. - Какая разница? - огрызнулся светловолосый. - Позвольте вам сразу кое-что объяснить, - сказал директор. Секунду спустя оба, залившись краской, делали доклад директору Агентства национальной безопасности.
Танкадо отдал кольцо? - скептически отозвалась Сьюзан. - Да. Такое впечатление, что он его буквально всучил - канадцу показалось, будто бы он просил, чтобы кольцо взяли.
Жила. - Да. Кошачья жила. Из нее делают струны для ракеток.
В главный банк данных попал вирус, - сказал Бринкерхофф. - Я знаю, - услышала Сьюзан собственный едва слышный голос. - Нам нужна ваша помощь.