List MF15 MATHEMATICS (8864) MATHEMATICS (9740) MATHEMATICS (9810) LIST OF FORMULAE AND STATISTICAL TABLES PURE MATHEMATICS Algebraic series Binomial expansion: n n n (a + b) n = a n + a n −1b + a n − 2b 2 + a n − 3b3 + K + b n ‚ where n is a positive 1 2 3 n n! integer and = r r!(n − r )! Maclaurin’s expansion: x2 x n (n) f ′′(0) + K + f (0) + K n! 2! n(n − 1) 2 n(n − 1) K (n − r + 1) r x +K (1 +
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Chapter 16 Notes Lesson 1: Composition and Structure of Earth’s Oceans Water covers 70 percent of Earth’s surface. The five main bodies of water are: The Pacific Ocean is the largest and deepest ocean. It is larger than all of Earth’s combined land area. The Atlantic Ocean is half the size of the Pacific. It occupies about 20 percent of Earth’s surface. The Indian Ocean is between Africa‚ India‚ and the Indonesian Islands. It is the third largest ocean. The Southern Ocean surrounds
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EFFECT OF ORGANIC AND INORGANIC FERTILIZER ON OKRO CHAPTER ONE (1) 1.1 INTRODUCTION Okra was domesticated in West and Central Africa (Cobley and Steele‚ 1976) and known as ‘Okro’ in the Anglophone African countries as a fast growing common annual vegetable widely consumed in Africa (Schippers‚ 2000). It is one of the numerous vegetable crops cultivated in Nigeria (Anon‚ 1989) where a total of 1 – 2 million hectares
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include quantities and SI units? Did you present the steps of the procedure as a numbered list? Did you note any changes to the original procedure? Did you identify your experimental and control groups? Data Collection and Organization Did you organize all data in a clearly labeled table and/or graph? Did you check that your data is accurate and complete? Did you title any tables and graphs? Did you label rows‚ columns‚ axes‚ etc.‚ and include units? Analysis and Conclusion
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product‚ filter paper‚ and watch glass 40.2 g 42.3 43.3 Mass of dry product 0.9 g 2.00 3.00 Calculations 1. Determine the limiting reagent for each trial. Show your calculations. (Hint: See the example in the Introduction.) Example: Trial 1: Note: These should be about the same and either CaCl2 or K2CO3 can be the limiting reagent depending on their initial masses. Trial 2: Table 3: Comparison of theoretical and actual yields for CaCO3 Trial # Limiting Reagent Theoretical Yield of CaCO3
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A HISTORY OF SCIENCE AND TECHNOLOGY IN THE PHILIPPINES* by Olivia C. Caoili** Introduction The need to develop a country’s science and technology has generally been recognized as one of the imperatives of socioeconomic progress in the contemporary world. This has become a widespread concern of governments especially since the post world war II years.(1) Among Third World countries‚ an important dimension of this concern is the problem of dependence in
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The 15th of August has its own importance for us Indians. It was on this day in 1947 that India became independent. We won freedom after a hard struggle. On this day our first Prime Minister‚ Pandit Jawaharlal Nehru‚ unfurled the National Flag at the Red Fort for the first time All the people irrespective of their caste‚ colour and creed celebrate the day every year amidst great rejoicing. It is a public holiday. On this day we take a pledge to defend our freedom with all our might. The Independence
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Imagine living in one place all of your life. In this place you have a home‚ a family‚ friends‚ activities that you have committed yourself to and possibly even a car. You feel safe in this place and most likely have developed an everyday rut of doing things. Change doesn’t happen often in this place and if it does the transition of one thing to the next is uneventful. Well‚ this is all about to change. You are now going to be uprooted from your place‚ your home‚ your family‚ your friends and
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Chapter 15 – Mankiw SOLUTIONS TO TEXT PROBLEMS: Quick Quizzes 1. A market might have a monopoly because: (1) a key resource is owned by a single firm; (2) the government gives a single firm the exclusive right to produce some good; or (3) the costs of production make a single producer more efficient than a large number of producers. Examples of monopolies include: (1) the water producer in a small town‚ who owns a key resource‚ the one well in town; (2) a pharmaceutical company that is given a patent
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Sonnet 17 Explication Who will believe my verse in time to come If it were filled with your most high deserts? Though yet‚ heaven knows‚ it is but as a tomb Which hides your life and shows not half your parts. If I could write the beauty of your eyes And in fresh numbers number all your graces‚ The age to come would say “This poet lies: Such heavenly touches ne’er touched earthly faces.” So should my papers yellowed with their age Be scorned like old men of less truth than tongue‚ And
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