Science Exam Term 4 Study Notes PDF

Science Exam Term 4 Study Notes Genetics: When does the body need new cells? - Growth - Repair - Reproduction How does the body produce new cells? The body is constantly producing new cells from old cells. This process is called cell division. Cell division occurs extremely quickly. Mitosis...

Science Exam Term 4 Study Notes Genetics: When does the body need new cells? - Growth - Repair - Reproduction How does the body produce new cells? The body is constantly producing new cells from old cells. This process is called cell division. Cell division occurs extremely quickly. Mitosis- The type of cell division that makes animals and plants grow is called mitosis In Mitosis a parent cell divides into two identical daughter cells. The daughter cell is divided into two and so on. Mitosis is also the way in which old and damaged cells are replaced. All the genes and chromosomes from the parent cells must be copied and passed onto the daughter cells. Before dividing a cell must duplicate all its chromosomes. Duplicating Chromosomes A cell chromosome is usually long, thin strands. Just before the cell divides, however, the chromosomes become shorter, thicker and more visible. They are said to condense. Each chromosome duplicates and becomes two strands, each one called a chromatid. The two chromatids are joined at the centromere. Stages of Mitosis: 1. Two pairs of chromosomes are visible 2. Chromosomes are doubled 3. Chromosomes line up along the equator of the cell 4. Chromosomes separate and move to the ends of the cell 5. Membranes form to produce two new cells Copying of DNA - When a cell divides by mitosis, the entire DNA inside the cell first needs to be copied; this is called DNA replication. - DNA replication results in two identical DNA molecules. Each molecule is made up of an original strand and a new strand. - The parent DNA molecule starts to ‘unzip’ at one end - Copying of the DNA molecule has begun with complementary bases attaching to both strands of the DNA  - Replication results in two identical strands of DNA What is DNA for? The information in DNA is stored as a series of nucleotides. A long series of nucleotides is a gene. One gene makes one protein. Proteins make up the components of our body and control our growth and ageing. Many genes are arranged end to end on a chromosome. How does DNA work? DNA remains in the nucleus of the cell. In order to obtain the information,part of the DNA is unzipped and “read”. The code is copied onto a carrier molecule called RNA (ribonucleic acid). RNA is similar to DNA, except that: - It has a different sugar:ribose instead of deoxyribose - One of the bases is different U instead of T - It does not form a double helix: it is a single strand of nucleotides Combinations of the four spell the names= of amino acids that form proteins. Amino acids are molecules that combine to form proteins.Amino acids and proteins are the building blocks of life. Meiosis- What is Meiosis? Meiosis is a type of cell division in sexually reproducing organisms that reduces the number of chromosomes in gametes (the sex cells, or egg and sperm). Sex cells in animals and plants are called gametes in animals, the gametes are eggs (ova) and sperm. Fertilisation is the stage of sexual reproduction when gametes fuse. This is the first step in the creation of a new life. - When an egg cell is fertilised, it becomes a zygote. This Zygote divides by mitosis many times and becomes an embryo. The embryo continues to grow and develop into a foetus. Stages of Meiosis: 1. Two pairs of chromosomes are visible 2. Chromosomes are doubled but attached at a point called the centromere 3. Homologous chromosomes line up along the ‘equator’ of the cell 4. One of each pair of chromosomes moves to the ends of the cell 5. Chromosomes line up along the ‘equator’ of each cell 6. Chromosomes separate and move to the ends of each cell 7. Membranes form to produce four daughter cells. Cell Division- Diploid Cell - A cell with a full set of chromosomes, containing two of each chromosome Haploid Cell - A cell with half a set of chromosomes,containing one of each homologous pair Mitosis vs Meiosis Mitosis Meiosis Type of cells produced Body cells Sex cells Function Growth and reproduction repair Number of stages 1 2 Number of daughter cells 2 4 Number of chromosomes in parent cells (human) 46 46 Number of chromosomes in daughter cells (human) 46 23 Are daughter cells identical to parent cells? Yes No Are daughter cells identical to each other? Yes No Type of daughter cells Diploid Haploid Mitosis - Exact copies - Asexual reproduction Meiosis - New cells are different - Sex cells Inheritance- Genetics is the study of traits (characteristics) that living things inherit from their parents True -breeding Plants are those that consistently produce offspring the same as the parents for a particular trait. For example: plants with yellow pods that always produce plants with yellow pods would be considered true breeding. Genes- Genes are located on chromosomes. Chromosomes exist in pairs; one is inherited from each parent. Each individual therefore has two copies of every gene. Dominant alleles are given a capital letter Recessive alleles are given a lowercase letter Homozygous and heterozygous- If the alleles are the same, the individual is homozygous for that gene If the alleles are different, the individual is heterozygous for that gene Example: height of a plant T= gene for tallness t= gene for shortness There are two alleles for each trait (characteristic) Homozygous (pure) tall plant= TT Heterozygous (hybrid) tall plant = Tt Homozygous (pure) short plant = tt Incomplete Dominance- In incomplete dominance, the heterozygous offspring have a phenotype intermediate between the phenotypes of the two homozygous organisms. Example: In snapdragons, allele R produces red flowers and allele W produces white flowers. The genotype RW produces pink flowers. Red (RR) + White (WW) = Pink (RW) Codominance- In codominance , the heterozygous genotype produces a phenotype that is a combination of the phenotypes of the homozygous organisms. Example: In shorthorn cattle, allele R produces cattle with red coats and allele B produces cattle with white coats. The genotype RW produces roan cattle, which have coats containing both red and white. Red (RR) + White (WW) = Roan (RW) Incomplete dominance = In between Codominance = Combination Genotype refers to the genetic makeup of an individual eg TT, Tt or tt Phenotype refers to the actual appearance of the individual, e.g tall or short. Punnett squares: Mutations- Mistakes can happen as DNA is copied. The base sequence is changed and this results in changes in their proteins. This type of change is called a mutation. If the mutation occurs in the gametes, then there I chance it will be passed onto the next generation. Types of Mutations: - Single Base Mutations - Mutations involving sections of DNA Examples of mutations and genetic disorders in humans: - Albinism - Cystic Fibrosis - Duchenne Muscular Dystrophy - Haemophilia - Huntington Disease - Phenylketonuria (PKU) - Tourette Syndrome Genetic Diseases- Chromosomal Chromosomal disorders can occur when chromosomes fail to separate during the first mitotic division. As a result, one gamete may contain both chromosomes of one pair and the other has none. Delections can also occur when a whole chromosome or part of a chromosome becomes lost. Radiation,some chemicals and excessive heat may cause mistakes to occur during meiosis. These diseases are caused by chromosomal abnormalities - Down Syndrome - Cri du Chat Syndrome - Fragile X Syndrome - Turner Syndrome - Klinefelter Syndrome Biotechnology- Developing vaccines: Vaccines work by causing your body to react as if it had been infected by a pathogen (disease causing organism). Traditional approach: Taking a small amount of poison produced by the bacteria and making it inactive or using dead bacteria. Modern approach: Inactive poison and dead bacteria are harmless but your body responds to them by making antibodies and you become immune to the disease caused by the pathogen. - The first step in producing a vaccine is for scientists to complete the genome of the bacteria to identify the genetic code that causes the surface proteins to be produced. What is genetic engineering? Genetic engineering involves changing an organism's genetic material. This can result in a change in the organism's characteristics. Stages of genetic engineering - Select the product or characteristics needed - Isolate genes from specialist cells - Insert the genes into target cells - Replicate the new organism Advantages Disadvantages - Completely different species can be - Bacteria can’t produce complex combined proteins - Organisms shows only the desired - Difficult to insert genes without characteristic damaging the host cell. - Larger quantities can be produced - Might produce harmful by products - Easier to purity product - Possible release of GM organisms - Faster than selective breeding into the environment - Expensive What is selective breeding? - Selective breeding or artificial selection is a process where people try to improve plants and animals by selecting and breeding only those that have desirable characteristics. Examples of why animals and plants might selective breed - A farmer might chose the two largest cattle in his hers to produce getting more cattle/meet - Breeding sheep to produce wool. Breeding wheat to produce more grain. Give two reasons why bacteria are genetically engineered to produce useful chemicals  - Bacteria are often genetically engineered to prince useful chemicals because their DNA isd loose in the cytoplasm,making it easy to modify; they also grow and replicate very quickly. Stem Cells- What is an embryonic stem cell? When an embryo is a few days old, it contains cells that are pluripotent. Pluripotent cells are capable of becoming any one of the 220 different cell types found in the human body. These cells are known as embryonic stem cells. What does it mean when stem cells have differentiated? In the late stage embryo,the cells have differentiated (chnaged_ and became sized as skin cells, cardiac muscle cells or nerve cells in the brain. Where are adult stem cells found? Adult stem cells lie deep within organs that need a constant supply of new cells such as the skin. What can stem cells possibly be used for? Stem cells give rise to the different types of blood cells and stem cells in the skin to regrow skin and hair. Scientists believe that stem cells have the potential to treat and possibly cure diseases such as cancer, diabetes,heart disease,spinal cord injuries where cells have been damaged. In-vitro fertilisation- What is IVF? In-vitro fertilisation is the process of fertilising eggs outside the human body then placing the developing embryo back into the woman’s uterus. When is IVF used? IVF is used to treat couples who are infertile or who have trouble conceiving a child naturally. When was IVF developed? IVF techniques were trialled on rabbits in the 1940s and 1950s and in humans from 1965. Evolution: Life on Earth: - It is estimated that there are about 10 million species on Earth - A species is a group of similar organisms that can produce fertile offspring - It is thought that at some point there have been about (4 000 000 000 000) 4 trillion different species that have at one time inhabited the Earth. - The Earth’s 4.7 billion year history is summarised in the Geological Time Scale.  - The geological time scale is divided into eras, periods and epochs based on the geological structure of the Earth over time. How do fossils form? Fossils refer to the preserved remains, impressions or trace of any one living organism from a part geological age. Fossils can form in many ways. One type of fossil creation is called permineralization. Formation of Fossils: 1. Ammonite dies and falls to the bottom of the sea. There it is covered by sediments and protected from being eaten by other animals. The soft parts of the ammonite’s body decay leaving just the shell. 2. More and more sediment covers and squeezes the shell. The shell may remain or be replaced with minerals such as quartz or limestone. These minerals seep into it in solutions before the original shell dissolves. 3. After millions of years, movement in Earth’s crust may thrust the layer of sedimentary rock containing the fossil upwards. 4. Weathering and erosion may eventually wear away some of the rock to expose part of the fossil, Fossils are often found in road cuttings or quarries. Law of Superposition: The law of superposition is one of the principles of geology scientists use to determine the relative ages of rock strata, or layers. This principle states that layers of rock are superimposed, or laid down one on top of another. The oldest rock strata will be on the bottom and the youngest at the top. Earth Calendar: One year represents 4.7 billion years old The universe is about 14 billion years old 3 earth calendars are needed to represent the total history of the universe How long were invertebrates on Earth for before the first Vertebrates emerged? - first invertebrates (worms and jellyfish) Nov 5th -First fish (vertebrates) Nov 20= 15 days = 193.5 million years Dating Techniques: Relative dating is a technique that compares the age of a line fossil or rock with another to determine which is older. Relative dating relies on two basic facts - Sedimentary rocks from in layers - Fossils are the same age as the rocks in which they are found \ Sedimentary rocks form in layers called Strata. A single layer is called a stratum Radioactive dating: What is an isotope? Isotopes are atoms of an element that have different numbers of neutrons and so have different atomic masses. Radioactive elements Decay at a known rate. The elements that Decay turn into new elements, the amount of which can be measured. This Decay allows scientists to estimate how long ago the rocks was laid down What is Half-Life? The Half-Life is the time it takes for half of a Radioactive sample to decay. Give some examples of radioactive isotopes that are used for dating fossils Carbon 14 and potassium 40 What is a fossil record? The fossil record is the fossil evidence of past life. It is incomplete. only a tiny fraction of all the plants and animals that have ever lived have been fossilised. What does the fossil record provide evidence of? - a vast number of species and varieties have emerged from the earliest life forms - organisms existing today have resulted from a progressive series of changes in pre-existence species line - Often more than one new species have formed from a pre-existing species - new forms of life have developed at a very slow and uneven rates new line and - environmental conditions have changed over time new line whole groups of organisms have appeared becoming abundance and then disappeared new line - Continual change What is evolution? Evolution is the slow change in a population of living things over many generations The theory of evolution states that the life on earth has changed over time and that different species have gradually developed from a common ancestor new line What is the scientific theory? A scientific theory is an evidence-based explanation for a set of observed facts Evidence for Evolution Palaeontology- The most direct evidence for Evolution comes from the fossil record. It provides evidence of continual change and shows that the earliest life forms have spread and diversified into the vast number of species that are now on Earth. What is the law of superposition? Sedimentary rocks are Deposited on top of each other. older layers are further down, younger layers are closer to the surface. If Evolution has occurred we would expect to find an orderly sequence of fossils from simple to more complex forms as we go from auto to more recent Rocks. we should also find one form merging into another. Only the rocks laid down during the last 600 million years ( since the cambrian period) Contains abundant fossils Why do we not see many fossils from before this time? Prior to this period most living things were soft bodies and therefore were less likely to become fossilised. From this time for onward there is succession of animal and plant fossils in successive layers of rocks the order in which plants appear is - Algae, Moses, Ferns, Gymnosperms and angiosperms The order in which vertebrates appear as fossils is - Fish, amphibians, reptiles, mammals and birds. Fossil evidence shows that life has been gradually changing from one form to another, usually from most simple to more complex forms. Living Fossils Some organisms have stayed unchanged over millions of years. it is as if their Evolution has stopped. Living organisms is the term given to organisms that exist today that are the same as their fossil forms. They are usually so well adapted to today's environment that they have not needed to change any further. Some examples of living fossils are coelacanth,horseshoe crab,crocodile,wollemi pine,nautilus Transitional forms Transitional forms of fossils that show features from two different types of organisms. They are intermediate stages that are in between the evolution of a new type from a previously existing type. The most famous transitional fossil is Archaeopteryx. This dinosaur bird dates from about 150 million years ago in the Jurassic Period. Its bones are that of a small dinosaur but are covered in feathers. it had teeth in its beak and claws on its wings. they could probably not fly well but may have climbed trees and glided down. Although transitional fossils include reptiles with fur (becoming mammals?) Ferns with seed cones (becoming conifers) fish with lungs and legs(becoming amphibians) and many more including our ancestors. Embryology Embryology is a science that deals with the formation and development of organisms before birth. The early stages of the development of all vertebrates are very similar to one another and resemble a fish embryo; they all possess a definite tail, Gill slits, a two chambered heart ( like that of a fish) and a fish-like kidney. As they grow the differences that will distinguish the embryos as an adult become more and more apparent. The similarities in the early embryos of vertebrates showed that they all initially have the same basic body plan for stop; this provides evidence that mammals, birds , reptiles and fibions and fish have descended from a common ancestor. Comparative Anatomy Comparative anatomy is a study of similarities and differences in body structures. similarities are used to determine the evolutionary relationships between different types of living things. the more similar instructional the more closely related they are. The Pentadactyl Limb The best example of comparative anatomy is the limbs of vertebrates. The front Flipper of a seal, a cat's paw, a horse's front leg, a bat wing and a human hand all look different and perform different functions. Despite this they all consist of the same number of bones ,muscles,herres. Each limb has become adapted to a specific need in that animal's environment. animals use their limbs in totally different ways for example flying, grasping , walking , running , tearing , swimming. about has longer fingers allowing them to be open to make a wing. The horse has progressively lost its toes so that it now walks on its third toe which has become its hoof. The basic pentadactyl limb can be traced back to the fence of certain fish from which the first amphibians are thought to have evolved. These similar structures are called homologous structures. How do homologous Structures provide evidence for Evolution? It suggests that all of these organisms evolved from an ancestor which had that structure to provide support for a common ancestor. Useless structures A number of structures such as a human appendix and the muscles near the ears have no apparent function. They are called vestigial organs, it is thought that they had some function in our ancestors but that Evolution has reduced the structures so much that they are no longer functional they provide no advantage or disadvantage and so humans still have them today. Some other examples of vestigial organs are Wales having pelvis bones, a Kiwi's wings, a snake hind limb bones and more rat eyes Biogeography Each continent has its own characteristic types of life. In Australia the herbivores are kangaroos, the carnivores are dingos and now the extinct (thylacine) tasmanian tiger and number and echidnas eat ants. In Africa the herbivores are zebras and wild beasts, the carnivals alliance and other large cats and aardvarks eat ants. In the other continent there are different groups of animals and plants. Only continents that are joined have the same native animals. Each plant and animal species started only once the place where it started is the Center of Origin. The southern continents were once joined as a supercontinent called Gondwana, which split into pieces that then drifted into their current places.  DNA shows that flatless birds of the southern continent are all related when Gondwana split the flightless birds went with their consonants carrying their ancestors or DNA with them. DNA studies show that the emu is mostly related closely to the Castaway and then kiwi as a second cousin. The Thea and ostrich are more distantly related. This matches the order in which the continents of thought have separated. Biochemistry The basic chemical substances in all living things are extremely similar. These include proteins, carbohydrates, fats and water. The chemicals in more closely related animals are more similar. For example, the chemicals in the blood of a human and a chimpanzee are very similar while some similar in some different chemicals are found in the blood of a horse. - All living things are composed of cells. The type of chemical reactions occurring within all cells are similar; this indicates that all cells have a common Origin. - All the proteins in living things are made from the same 20 amino acids. Apart from some viruses all organisms use the same basic genetic code to encode these proteins to stop the genetic code being planetary, suggesting that all living things are related and have evolved from a common ancestor. Comparisons of DNA are used to provide evidence of how closely different species are related. For example, the genetic makeup of a chimpanzee is 98.5% identical to that of a human. Gorilla DNA has a 95.4% match with human DNA and will stop the genetic makeup of other primates that is also similar to humans. Natural selection in Bacteria: Bacteria become resistant to antibodies by natural selection. When you take the antibiotic,it kills all the bacterial cells that are not resistant. Any resistant ones may survive and reproduce,forming resistant offspring. Bacteria produce by dividing in half,producing two copies of themselves. Evidence for natural selection: The effects of natural selection only became obvious after many generations. The effects of natural selection are easier to observe in organisms that produce many generations in a short time. Lamark’s theory of evolution: According to Lamark organisms have altered their behaviour in response to environmental change. Darwin’s theory of evolution: Darwin proposed that species can change over time, that new species came from pre-existing species and that all species share a common ancestor. What is a species? In the past a test for a species was to see if two organisms could interbreed to produce fertile offspring under natural conditions. - A biological species is a group of organisms that can reproduce with one another in nature and produce fertile offspring. Speciation: Speciation is the process by which one species splits into two or more separate species. S The Universe: Cosmology:Cosmology is the study of the universe-how it started, how it works,and how it might end. It looks at things like galaxies, stars and space to understand the universe’s big picture. Edwin Hubble: Edwin Hubble was an American astronomer who made ground breaking discoveries about the universe. He showed that the universe is expanding by observing that distant galaxies are moving away from us, a discovery that supported the Big Band Theory. Red Shift:Red shift is when light from an object,like a galaxy,shifts to longer (redder) wavelengths as it moves away from us. This means the object is moving away and it helps scientists understand that the universe is expanding. The more red shafted the light,the faster the object is moving away. Blue shift: Blue shift is one example of the Doppler effect. It is the opposite effect to redshift. Doppler blueshift is caused by movement of a source towards the observer. The term applies to any decrease in wavelength caused by relative motion, even outside the visible spectrum. The doppler effect: Doppler effect in physics is defined as the increase (or decrease) in the frequency of sound, light, or other waves as the source and observer move towards (or away from) each other. Cosmic microwave background radiation: The cosmic microwave background radiation is the faint remnant glow of the big bang. This false colour image, covering about 2.5 percent of the sky, shows fluctuations in the ionised gas that later condensed to make superclusters of galaxies. Galaxy: A galaxy is a huge collection of gas, dust, and billions of stars and their solar systems. A galaxy is held together by gravity. Our galaxy, the Milky Way, also has a supermassive black hole in the middle. Black hole: A black hole is a place in space where gravity pulls so much that even light can not get out. The gravity is so strong because matter has been squeezed into a tiny space. This can happen when a star is dying. Plasma: Plasma is superheated matter so hot that the electrons are ripped away from the atoms forming an ionised gas. It comprises over 99% of the visible universe. In the night sky, plasma glows in the form of stars, nebulas, and even the auroras that sometimes ripple above the north and south poles. The milky way: The Milky Way is a huge collection of stars, dust and gas. It's called a spiral galaxy because if you could view it from the top or bottom, it would look like a spinning pinwheel. The Sun is located on one of the spiral arms, about 25,000 light-years away from the centre of the galaxy. What is Gravity? Gravity is the force of attraction experienced between any two objects in the universe. It is the force that drives the universe. What is needed for Gravity to become significant as it is a weak force? These masses need to be incredibly large for the force to become significant. What happened within a star because of gravity? When one of the objects is as massive as a star,gravity can become an extremely strong force. It also creates pressures within the star so immense that the atoms of hydrogen at the star;s centre become fused together to form atoms of helium. What two opposing forces determine the structure of a star? The structure of any star is determined by the balance between two opposing forces. - The inwards forces of gravity. Which causes the material within the star to fall towards the centre. - The outwards force that results from pressure caused by the heat radiated from nuclear fusion in the star. This pressure is called radiation pressure. What is a nebula? Gravity is also responsible for creating stars from the huge interstellar gas known as nebulae. (cloud of gas) Describe how the sun was formed from a nebula: The Sun and the planets formed together, 4.6 billion years ago, from a cloud of gas and dust called the solar nebula. A shock wave from a nearby supernova explosion probably initiated the collapse of the solar nebula. The Sun formed in the centre, and the planets formed in a thin disk orbiting around it. Describe how galaxies form: Galaxies form out of immense clouds of gas that collapse and rotate. As they evolve, stars form within them. Entire galaxies can collide, changing their appearance. Looking deep into space, we see galaxies at earlier stages in their lives, and learn more about their evolution. How many stars do galaxies contain? The size of galaxies vary greatly but all galaxies contain an enormously large number of stars,usually between 10 million and a hundred million. What is significant about the gravitational field of a black hole? A black hole forms when the mass of an object, like a star, suddenly collapses down to a tiny volume. A small object with a large mass causes a gaping dent in space time. This enormous warp creates a gravitational field so strong that nothing, not even light, can escape from it. How are black holes detected? By detecting the gravitational ripples when they collide. We can also detect black holes by detecting the ripples in space-time created when two of them crash into each other. From that signal, we can tell how massive the black holes were, how far away they were, and how fast they were travelling when they collided. What is believed to be at the centre of most galaxies? How big are they? Black holes are a class of astronomical objects that have undergone gravitational collapse, leaving behind spheroidal regions of space from which nothing can escape, including light. Observational evidence indicates that almost every large galaxy has a supermassive black hole at its centre. Where do stars come from? Stars are formed from nebulae which are giant clouds of helium gas and other particles. The most well known nebula which can be seen with the naked eye is a near orion. When the clouds contract forming a heavier company, clouds and the temperature decrease. - Plasma is a collection of charged particles that resembles a gas. Stars are seldom born alone. - Usually these massive reactions create many clusters of stars - The brightest clusters can be seen in the southern hemisphere The life of a star: Once a star stops condensing the star begins to burn at a steady rate which depends on what it is made of. At this stage it is called a main sequence star. - Main sequence stars grow brighter and brighter, all the time undergoing the nuclear reaction of converting hydrogen to energy and helium.  Nova: a star showing a sudden large increase in brightness and then slowly returning to its original state over a few months. What is a protostar? A young star, a star that's forming? The fate of a Star: How can astronomers observe neutron stars? - by detecting pulse What is the major fuel used by stars in the process of fusion?- Hydrogen What is one way astronomers can differentiate between a pulsar from a normal star? Normal stars don’t pulse Neutron Star: A neutron star is a very dense,rotating object that emits electromagnetic radiation and is called a pulsar Black Hole: A black hole is a body with an immensely strong gravitational field. What is meant by very low luminosity? Dim low light Red Giant: A red giant is a luminous giant star of low or intermediate mass (roughly 0.3–8 solar masses in a late phase of stellar evolution. White dwarf: A white dwarf is what stars like the Sun become after they have exhausted their nuclear fuel. (white stars are difficult to observe because they have very low luminosity) Black dwarf: A black dwarf is a theoretical stellar remnant, specifically a white dwarf that has cooled sufficiently to no longer emit significant heat or light. What did Lemaitre propose the universe was doing? He was the first to propose the modern Big Bang Theory, the theory that the universe began from the explosion of a small original super atom. Big Bang Theory: The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. The notion of an expanding universe was first scientifically originated by physicist Alexander Friedmann in 1922 with the mathematical derivation of the Friedmann equations.