Chapter 3: Squares, Square Roots, Cubes And Cube Roots

Figure 18-11 represents the amount of energy stored as organic material in each trophic level in an ecosystem. The pyramid shape of the diagram indicates the low percentage of energy transfer from one level to the next. On average, 10 percent of the total energy consumed in one trophic level is incor- porated into the organisms in the next. Why is the percentage of energy transfer so low? One reason is that some of the organisms in a trophic level escape being eaten. They eventually die and become food for decomposers, but the energy contained in their bodies does not pass to a higher trophic level. Even when an organism is eaten, some of the molecules in its body will be in a form that the consumer cannot break down and use. For example, a cougar cannot extract energy from the antlers, hooves, and hair of a deer. Also, the energy used by prey for cellu- lar respiration cannot be used by predators to synthesize new bio- mass. Finally, no transformation or transfer of energy is 100 percent efficient. Every time energy is transformed, such as during the reactions of metabolism, some energy is lost as heat. Limitations of Trophic Levels The low rate of energy transfer between trophic levels explains why ecosystems rarely contain more than a few trophic levels. Because only about 10 percent of the energy available at one trophic level is transferred to the next trophic level, there is not enough energy in the top trophic level to support more levels. Organisms at the lowest trophic level are usually much more abundant than organisms at the highest level. In Africa, for exam- ple, you will see about 1,000 zebras, gazelles, and other herbivores for every lion or leopard you see, and there are far more grasses and shrubs than there are herbivores. Higher trophic levels con- tain less energy, so, they can support fewer individuals.A population is a group of organisms that belong to the same species and live in a particular place at the same time. All of the bass living in a pond during a certain period of time make up a pop- ulation because they are isolated in the pond and do not interact with bass living in other ponds. The boundaries of a population may be imposed by a feature of the environment, such as a lake shore, or they can be arbitrarily chosen to simplify a study of the population. The humans shown in Figure 19-1 are part of the pop- ulation of a city. The properties of populations differ from those of individuals. An individual may be born, it may reproduce, or it may die. A population study focuses on a population as a whole—how many individuals are born, how many die, and so on. Population Size A population’s size is the number of individuals that the population contains. Size is a fundamental and important population property but can be difficult to measure directly. If a population is small and composed of immobile organisms, such as plants, its size can be determined simply by counting individuals. Often, though, individ- uals are too abundant, too widespread, or too mobile to be counted easily, and scientists must estimate the number of individuals in the population. Suppose that a scientist wants to know how many oak trees live in a 10 km2 patch of forest. Instead of searching the entire patch of forest and counting all the oak trees, the scientist could count the trees in a smaller section of the forest, such as a 1 km2 area. The scientist could then use this value to estimate the population of the larger area. SECTION 1 OBJECTIVES ● Describe the main properties that scientists measure when they study populations. ● Compare the three general patterns of population dispersion. ● Identify the measurements used to describe changing populations. ● Compare the three general types of survivorship curves. VOCABULARY population population density dispersion birth rate death rate life expectancy age structure survivorship curve FIGURE 19-1 A population can be widely distributed, as Earth’s human population is, or confined to a small area, as species of fish in a lake are. Copyright © by Holt, Rinehart and Winston. All rights reserved. 382 CHAPTER 19 If the small patch contains 25 oaks, an area 10 times larger would likely contain 10 times as many oak trees. A similar kind of sampling technique might be used to estimate the size of the pop- ulation shown in Figure 19-2. To use this kind of estimate, the sci- entist must assume that the distribution of individuals in the entire population is the same as that in the sampled group. Estimates of population size are based on many such assumptions, so all esti- mates have the potential for error. Population Density Population density measures how crowded a population is. This measurement is always expressed as the number of individuals per unit of area or volume. For example, the population density of humans in the United States is about 30 people per square kilome- ter. Table 19-1 shows the population sizes and densities of humans in several countries in 2003. These estimates are calculated for the total land area. Some areas of a country may be sparsely popu- lated, while other areas are very densely populated. Dispersion A third population property is dispersion (di-SPUHR-zhuhn). Dispersion is the spatial distribution of individuals within the popu- lation. In a clumped distribution, individuals are clustered together. In a uniform distribution, individuals are separated by a fairly con- sistent distance. In a random distribution, each individual’s location is independent of the locations of other individuals in the popula- tion. Figure 19-3 illustrates the three possible patterns of dispersion. Clumped distributions often occur when resources such as food or living space are clumped. Clumped distributions may also occur because of a species’ social behavior, such as when animals gather into herds or flocks. Uniform distributions may result from social behavior in which individuals within the same habitat stay as far away from each other as possible. For example, a bird may locate its nest so as to maximize the distance from the nests of other birds. These migrating wildebeests in East Africa are too numerous and mobile to be counted. Scientists must use sampling methods at several locations to monitor changes in the population size of the animals. FIGURE 19-2 TABLE 19-1 Population Size and Density of Some Countries Population size Population density Country (in millions) (in individuals/km2) China 1,289 135 India 1,069 325 United States 292 30 Russia 146 8 Japan 128 337 Mexico 105 54 Kenya 32 54 Australia 20 3 dispersion from the Latin dis-, meaning “out,” and spargere, meaning “to scatter” Word Roots and Origins Copyright © by Holt, Rinehart and Winston. All rights reserved. POPULATIONS 383 The social interactions of birds called gannets, which are shown in Figure 19-3b, result in a uniform distribution. Each gannet chooses a small nesting area on the coast and defends it from other gannets. In this way, each gannet tries to maximize its distance from all of its neighbors, which causes a uniform distribution of individuals. Few populations are truly randomly dispersed. Rather, they show degrees of clumping or uniformity. The dispersion pattern of a population sometimes depends on the scale at which the popu- lation is observed. The gannets shown in Figure 19-3b are uni- formly distributed on a scale of a few meters. However, if the entire island on which the gannets live is observed, the distribution appears clumped because the birds live only near the shore. POPULATION DYNAMICS All populations are dynamic—they change in size and composition over time. To understand these changes, scientists must know more than the population’s size, density, and dispersion. One important measure is the birth rate, the number of births occur- ring in a period of time. In the United States, for example, there are about 4 million births per year. A second important measure is the death rate, or mortality rate, which is the number of deaths in a

Electrostatics The section of CBSE Class 12 Physics electrostatic potential and capacitance notes mainly deals with the in-depth analysis of electromagnetic phenomena when they are not performing any movements. Additionally, it is divided into ten further sub-topics to study the companion processes of reaching the state. These are - 1. Electric charge In this section of Physics ch 2 Class 12 notes, you get to learn about the basic features of electric charge and its expression in Physics. Along with its basics, the sections help to understand the full potential of charge. Different aspects of Charge included in Class 12 Physics Chapter 2 notes are - Definition Type: Positive and Negative Charge Unit and dimensional formula Point Charge Properties of Charge Comparison of Charge and Mass Methods of Charging Electroscope 2. Coulomb's Law Force is created when charges of opposite signs attract each other, and they repulse if the signs are the same. Coulomb's law tries to define this phenomenon through a mathematical formula, explicitly mentioned in Physics Class 12 notes Chapter 2. Moreover, there is key information about the variation of the constant k and its effect on a medium. Coulomb's law's vector form and the principle of superimposition are also explained in ch 2 Physics Class 12 notes. (Image will be uploaded soon) 3. Electric Field As stated in Class 12 Physics Chapter 2 notes, every positively or negatively charged particle has their respective electric fields. It feels a force at the time of interaction which might be attraction or repulsion. As it arises from electric charge, it is crucial to know about its different parts like - Electric field intensity Relation between electric force and electric field Super imposition of electric field Point charge Continuous charge distributions Properties of Electric Field Lines Motion of Charged Particles in an Electric field Learning more about the electric field from electric potential and capacitance notes Class 12 helps a student to get a grasp of upcoming chapters. 4. Electric Potential Energy When energy helps a charge to move from an electric field, it is known as the Electric Potential Energy. This section of electrostatic chapter Class 12 notes requires a student to study the Electron volt (eV), and the potential energy that an n number of charges can hold. 5. Electric Potential This section of Class 12 Physics Chapter 2 notes focuses on in-depth learning of Electric Potential or Voltage. Basically, it defines the potential movement of energy. 6. Relation between Electric Field and Potential Apart from knowing more about the relationship between the two values, Physics Class 12 Chapter 2 notes also discuss equipotential surfaces. 7. Electric Dipole Essentially, 'Dipoles' are two opposite points of charge represented with q and –q, with their distance between each other being 2a. Electric Dipoles are crucial in your study of Physics Class 12 Chapter 2 notes to learn more about electric fields and their potential. Additionally, Class 12 Physics Chapter 2 notes focus on the influence of electric dipoles on a uniform electric field mainly through Force and Torque, Work, and Potential Energy. In the last part of Electrostatics, further focus is on using the formulas to their fullest potential. It includes subsections of Electric Field, Electric Potential Energy, Electric Potential, and Electric Dipole. In the notes for electrostatic potential and capacitance, you will find proper solutions accompanied by clear and crisp diagrams for better understanding. 8. Gauss's Law Apart from just discussing the Gauss's Law, in Physics Class 12 ch 2 notes there is a thorough explanation of its properties and applications. The Gauss' Law states that net electric flux passing through a hypothetical closed surface is equal to the net electric charge present within the same closed surface. Being a broad part of the whole chapter, you may need to spend a little more time on it. Moving forward, it starts discussing the properties of conductors in relation to Gauss's Law. The Class 12 Physics notes Chapter 2 perfectly defines the journey to Gauss' Law from Coulomb's Law. Here is the Gauss's Law present in the Class 12 Physics ch 2 notes, (image will be uploaded soon) 9. Capacitors There is a dedicated section about Capacitors in the Class 12 Physics Chapter 2 notes elucidating its functions and importance as storage of potential electric energy. After explaining the structure of a capacitor, it points out the different types, parallel plate, spherical and cylindrical. The section of Chapter 2 notes of Physics Class 12 is further divided into subheads like: Properties of an ideal battery Grouping of capacitors Simple circuits (Series and Parallel) Dielectric Van de Graaff generator Combination of drops Charge distribution method Wheatstone Bridge-based circuit Extended Wheatstone Bridge Infinite network of capacitors Redistribution of charge between two capacitors Vedantu prepares the Class 12 Physics Chapter 2 notes with help from subject matter experts. In the PDF, you get a comprehensive idea of the topic along with potential answers to the most asked questions. Furthermore, the detailed explanation on each section and subsections are written in a simple language allows a student to ace their exams with wholesome knowledge. These Physics Chapter 2 Class 12 notes are going to be one of the best supplementary study materials besides a student’s textbooks. Visit the Vedantu website or download the app to get your hands on all important notes! Important Questions A charge of 4 × 10–8C is uniformly distributed on the surface of a spherical conductor, having a radius of 15 cm. Determine the electric field just outside this sphere at a point that is 15 cm from the centre of this sphere. Determine the capacitance given that the distance between the two plates has been reduced by half and the parallel plate capacitor holds a capacitance of 20 pF (where 1pF = 10-12 F) having air between the two plates. What will be the total capacitance of a combination where three capacitors, each having a capacitance of 20 pF, are connected in series. A square having a side of 10 cm has a 500 µC charge at its centre. Determine the work done to move a charge of 10 µC between two points that are diagonally opposite each other on the square. At an equatorial point, what will be the electrostatic potential because of an electric dipole? Calculate the work done to move a test charge, q, through a length of 1 cm along the equatorial axis of an electric dipole? Polarisation A capacitor has its plates enclosed in a medium that can be filled by insulating substances. A net dipole moment is then induced by an electric field in the dielectric. This event causes the field in an opposite direction. Equipotential Surface An equipotential surface is a type of surface where the potential always has a constant value. If considered as a point charge, the concentric spheres that are centred at a particular area of this charge are basically equipotential surfaces. Advantages of Vedantu's Revision Notes: A Comprehensive Resource for Effective Learning There are several reasons why one may refer to Vedantu's revision notes for studying a subject like Electrostatic Potential and Capacitance. Here are some key points: Comprehensive Coverage: Vedantu's revision notes provide a comprehensive coverage of the entire topic, ensuring that all important concepts and subtopics are included. Concise and Organized: The notes are designed to be concise, focusing on the key points and core ideas. They are organized in a structured manner, making it easy for students to navigate and revise the content. Simplified Explanation: The revision notes offer simplified explanations of complex concepts, making them more accessible and easier to understand. This helps students grasp the material more effectively. Key Formulas and Equations: The notes highlight the key formulas and equations relevant to the topic, ensuring that students have a clear understanding of the mathematical aspects of Electrostatic Potential and Capacitance. Examples and Illustrations: Vedantu's revision notes often include examples and illustrations that help clarify concepts and provide practical applications, enabling students to better relate theory to real-world scenarios. Quick Recap: The revision notes serve as a quick recap of the important points, allowing students to review the material efficiently before exams or assessments. Exam-Oriented Approach: Vedantu's revision notes are designed with an exam-oriented approach, focusing on the topics and concepts that are frequently asked in examinations. This helps students prepare effectively and increase their chances of scoring well. Accessible Anytime: Vedantu's revision notes are easily accessible online, allowing students to study at their convenience and revise the material anytime, anywhere.

Commas Directions: Correct the sentences by adding commas where needed. 1. After the sound of the bell we realized it was a false alarm. 2. Mr. Yoshino the head of the department resigned yesterday. 3. The gentleman with the black umbrella who is an ambassador to the United States said hello to us as we were entering the hotel. 4. Even though we won the game the players unfortunately did not play their best. 5. Heather walked quickly up to the door and knocked hoping that someone would answer. Author’s Purpose 6. An author writes a story about a boy who saves his town from a flood by using his quick thinking. The author includes exciting descriptions of the boy's bravery. What is the author’s most likely purpose for writing this story? A. To inform readers about the dangers of floods B. To entertain readers with a heroic tale C. To explain how to prevent floods D. To persuade readers to prepare for emergencies 7. Which of the following is an example of an author writing to persuade? A. A science textbook chapter explaining the water cycle B. A commercial encouraging people to adopt shelter pets C. A short story about a girl who finds a magical necklace D. A recipe for making chocolate chip cookies 8. Read the following sentence: "Studies show that students who read for 20 minutes a day score higher on tests. Reading is one of the best habits you can develop for success in school and life." What is the author’s purpose in this passage? A. To entertain readers with a fun story B. To persuade readers to read more often C. To inform readers about how books are written D. To explain how to find books to read 9. An author writes a how-to guide titled 10 Easy Steps to Plant a Garden. What is the author’s primary purpose? A. To persuade readers to grow their own vegetables B. To inform readers how to plant a garden C. To entertain readers with funny garden tips 10. Read the excerpt: "Long ago, in a village surrounded by mountains, the people discovered a secret about their water well. Every full moon, the well water turned to gold for just one night. But no one knew why. This mystery brought travelers from far and wide, hoping to uncover the truth." What is the author’s purpose in this excerpt? A. To persuade readers to visit the village B. To inform readers about a historical event C. To entertain readers with a mysterious tale D. To explain the science behind the water Main Idea When I stepped out into the bright sunlight from the darkness of the movie house, I had only two things on my mind: Paul Newman and a ride home. I was wishing I looked like Paul Newman--- he looks tough and I don't--- but I guess my own looks aren't so bad. I have light-brown, almost-red hair and greenish-gray eyes. I wish they were more gray because I hate most guys that have green eyes, but I have to be content with what I have. My hair is longer than a lot of boys wear theirs, squared off in back and long at the front and sides, but I am a greaser and most of my neighborhood rarely bothers to get a haircut. Besides, I look better with long hair. 11. What is the main idea? The narrator likes movies. The narrator wishes he was Paul Newman. The narrator is content with his appearance. The narrator looks better with long hair. 12. The narrator believes. . . looks are important. he should get a haircut. green eyes are bad. that he has red hair. Once there were four girls who shared a pair of pants. The girls were all different sizes and shapes, and yet the pants fit each of them. You may think this is a suburban myth. But I know it's true, because I am one of them, one of the sisters of the Traveling Pants. We discovered their magic last summer, purely by accident. The four of us were splitting up for the first time in our lives. Carmen had gotten them from a secondhand place without even bothering to try them on. She was going to throw them away, but by chance, Tibby spotted them. First Tibby tried them; then me, Lena; then Bridget; then Carmen. By the time Carmen pulled them on, we knew something extraordinary was happening. If the same pants fit and I mean really fit the four of us, they aren't ordinary. They don't belong completely to the world of things you can see and touch. My sister, Effie, claims I don't believe in magic, and maybe I didn't then. But after the first summer of the Traveling Pants, I do. 13. What is the main idea? Four friends were connected through a special pair of pants. A pair of pants called the Traveling Pants. Carmen finding a pair of pants from a second-hand shop. The girls believing in magic. 14. The narrator included that the pants fit all of them to emphasize how the girls become friends. the girls are different sizes. why the pants are special. where the pants came from. If you are interested in stories with happy endings, you would be better off reading some other book. In this book, not only is there no happy ending, there is no happy beginning and very few happy things in the middle. This is because not very many happy things happened in the lives of the three Baudelaire youngsters. Violet, Klaus, and Sunny Baudelaire were intelligent children, and they were charming, and resourceful, and had pleasant facial features, but they were extremely unlucky, and most everything that happened to them was rife with misfortune, misery, and despair. I'm sorry to tell you this, but that is how the story goes. 15. What is the main idea? description about the story to come. A warning about the story and its sad content. A declaration about the Baudelaire family. A beginning for the end of the story. 16. The narrator believes the reader does not like sad stories. likes stories with happy endings. can’t enjoy the story. will find the story unhappy. 17. Read the following sentence: Of course you can exaggerate your story, but what you say must be based on truth. Which word means the same as exaggerate? repeat reveal overstate increase 18. What is the meaning of the word inaugurated, used in the following sentence: Less than two months after Abraham Lincoln was inaugurated President in 1861, he encountered one of the most difficult tasks ever experienced by a United States leader: civil war. elected by a vote brought into office identified by name viewed as an authority 19. What does the phrase “practice your presentation so much that you could do it in your sleep” suggest in the following sentence: The best advice is to practice your presentation so much that you could do it in your sleep. get plenty of sleep the night before giving a presentation give their presentations in front of a small audience first take advice from their teachers on how to write a presentation memorize their presentations before they give them 20. Read the following sentence: The Phoenix Mars Lander is a NASA spacecraft that landed on the Red Planet in May 2009 to study the history of water and potential for life on the planet. What is another word for potential? existence situation possibility qualification

Chapter 3

Chapter 3.

110.31.b.17.C

Topic: Reading/Vocabulary Development

STAAR English II High School 2014 - Past Paper

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