Math Ch. 5 Cheat Sheet

5.1

• Polynomial Degrees: Largest power of X that appears

• Polynomial Functions: Smooth and continuous graphs. Equations are such that domain is all real numbers and exponents are always nonnegative integers.

• Power Functions: f(x) = x^something

• Multiplicities: (x – number)^multiplicity

• Behavior Near a Zero: Choose numbers near a solution. i.e.: If a solution is 1, choose 0.5 1.5, 1.25, 0.75, etc...

• Turning Points: Functions have “degree – 1” turning points.

• End Behavior: Choose a high value for X (ie: 100), the solution should be a power function that determines how the graph behaves at extreme values.

5.2

• Rational Functions: f(x) = poly. func./poly. func.

• y = 1/x^2: Similar to y = 1/x, except the “boomerang” is mirrored across the y-axis.

• Asymptotes:

  • 3 kinds: horizontal, vertical and oblique.

  • Graphs cannot intersect vertical asymptotes, but can intercept horizontal and oblique asymptotes.

  • Finding Vertical Asymptotes: When function is in lowest terms, all zeros of the denominator are vert. asymptotes in the form x = solution.

  • Finding Horizontal Asymptotes: If the degree is proper (degree of numerator is less than degree of denominator), hor. asymptote is y = 0. If improper, use long division (divide den. into num.) If the result is y = number, it is horizontal.

  • Finding Oblique Asymptotes: The degree must be improper. Use the method listed above. If the result is y = ax +b, the asymptote is oblique.

5.3

• Graphing Rational Functions

  • Step 1: Factor numerator and denominator, find domain. If the domain is 0, find y-int by finding R(0) and plot.

  • Step 2: Write fraction in lowest terms. The x-int. are the real zeros of the numerator. Plot and find behavior near the intercepts.

  • Step 3: The vertical asymptotes of the equation are the zeros of the denominator in lowest terms.

  • Step 4: Find hor. or obl. asymptotes using the method in 5.2. Plug in the values to determine if the graph intersects them.

  • Step 5: Find the behavior of the graph between negative infinity, any x-int. and vert. asymp. and positive infinity. Plot these points.

  • Step 6: Determine behavior near asymptotes. Graph.

  • Step 7: Put information together and graph.

  • Quick reference for information about the graph

    • Numerator: x-ints.

    • Denominator: restrictions on domain, vert. asymp.

    • Quotient of Numerator and Denominator: hor. or obl. asymp.;

    • Use chart to find behavior

    • Find behavior near asymptotes

    • Graph.

    • WINRAR.

5.4

• Solving Polynomial and Rational Inequalities:

  • Step 1: Make it such that f(x) (sign: “>”, “<” etc.) 0

  • Step 2: Determine zeros and undefined numbers for the function

  • Step 3: Divide a number line into segments using the zeros and undefineds.

  • Step 4: Evaluate the graph within each interval, determine the solution.

5.5

• Remainder Thm: If f(x) is divisible by x – c, the remainder is f(c).

  • Application: Finding remainders of poly. equations

• Factor Thm: x – c is a factor of f(x) if and only if f(c) = 0

  • Application: Seeing if f(x) has a factor x – c.

• Descartes' Rule of Signs:

  • Number of positive real zeros in an equation f(x): number of variation in signs in the equation or the number of variations – an even integer

  • Number of negative real zeros in an equation: use f(-x). number of variation in signs in the equation or the number of variations – an even integer

• Rational Zeros Thm: When rational eq. is in lowest terms, p is a factor of the constant (last number) and q is a factor of the coefficient of the first number (2x^2, q = 2). Using this, p/q = a potential rational zero of the equation

• Finding Real Zeros of a Poly. Func.:

  • Step 1: Determine maximum number of real zeros (degree)

  • Step 2: Use Descartes' Rule of Signs to find number of pos. and neg. zeros.

  • Step 3: Either use the Rational Zeros Thm or synthetic/long division to find working solutions.

  • Step 4: Reduce and factor, if possible.

• Bounds on Zeros: Bound of a poly. func. is the smaller of the two numbers Max {1, sum of
  |coefficients|} (where max means choose the greatest value) or 1+ Max {sum of |coefficients|}

• Intermediate Value Thm: If a < b and if f(a) and f(b) have opposite signs, there is at least 1 real zero between a and b.

5.6

• Fundamental Theorem of Algebra: Every function of degree > or = 1 has at least one complex zero.

• Conjugate Pairs Theorem: For every r = a + bi that is a solution of a poly. func., its conjugate, r = a – bi, is a solution.

http://docs.google.com/Doc?id=dcppjfrr_8gj96pp

Biology 35.1 Cheet Sheet

• Main function of the digestive system is to disassemble the food you eat into its component molecules so your body can use it for energy

• Your mouth breaks food down into smaller pieces for digestion

  • Chewing is mechanical digestion

  • Chemical digestion also occurs in the mouth, with the release of the enzyme amylase to break down polysaccharides into smaller molecules.

• Swallowing your food sends it into the esophagus, which connects the mouth to the stomach.

  • The esophagus uses peristalsis to move the food down into the stomach

    • Contractions occur in waves

      • circular muscles relax and longitudinal muscles contract, then vice versa

  • Epiglottis prevents food from going into respiratory system

• The stomach is a muscular, pouchlike enlargement of the digestive tract

  • Muscles work to break down the food in the stomach and chemical cocktails work to break the molecules of food into usable substances .

    • The cocktail is called “gastric juice”

      • It includes pepsin and hydrochloric acid

        • Pepsin processes proteins in food.

          • Pepsin works best in an acidic environment

  • Stomach does not dissolve itself with gastric juices due to the mucus lining of the inner stomach

  • Food remains the the stomach for two to four hours

• The small intestine is a muscular tube about 6 m long and 2.5 cm wide.

  • Muscle and chemical reactions further break down the food in the SI

  • Carbohydrates and proteins are also changed by enzymes produced by the pancreas and liver.

  • The first 25 cm of the SI is called the duodenum.

    • Most enzymes and chemicals in the duodenum are produced from the pancreas, liver, and gallbladder.

      • The pancreas is a soft, flattened gland that secrets digestive enzymes and hormones.

        • It helps to break down carbs, proteins, and fats.

        • Alkaline pancreatic juices help to neutralize the acidic food's pH, stopping pepsin as well.

      • The liver is a large, complex organ that produces bile.

        • Bile is a chemical substance that helps to break down fats.

        • The gallbladder stores bile

        • Bile breaks apart fats into smaller droplets

        • If the bile concentration is too high, or there is too much cholesterol in the person's diet, or if the gallbladder becomes inflamed, gallstones can form.

• Villus absorb food

  • A villus is a small projection on the lining of the small intestine.

  • The allow for a higher absorption rate and small enough molecules are absorbed directly into the cells of the villi.

• The large intestine is a muscular tube that is also known as a colon.

  • It is 1.5 m long and 6.5 cm wide.

  • The appendix is attached to the large intestine.

  • The large intestine absorbs and recycles water.

• The rectum is the last stop in the digestive system. Here, waste is eliminated from the organism.

Biology 15.2 Cheet Sheet

• Populations, not individuals, evolve

• gene pool – picture of all the alleles of the population's genes

• allelic frequency – percentage of alleles in a gene pool

• genetic equalibrium – when a population's genes remain the same through many generations

• Evolution results from a disruption of a population's genetic equilibrium

  • Mutations are disrutptions

  • genetic drift – alteration of allelic frequencies by chance

    • Individuals leaving and joining a population are part of genetic drift

    • Isolation causes genetic drift

• Population's genetic pool will change over time due to population

• Three natural selection mechanics

  • Stabilizing

    • favors average individuals in a population

  • Directional

    • favors extreme variations of a trait

  • Disruptive

    • favors organisms with either extreme variation of a trait

• speciation – evolution of new species

  • occurs when members of a species can no longer interbreed to produce fertile offspring

  • Geographic isolation – when a physical barrier divides a population's

    • can result in new species

  • Reproductive isolation – when formerly interbreeding organisms can no longer mate and produce fertile offspring

    • can result in new species

  • changes in chromosomes can result in new species (nondisjuncture) by breeding with other polyploids (organisms with an abnormal set of genes) with the same gene set

    • occurs most frequently in plants, polyploidal animals generally do not survive

  • Speed of speciation

    • Gradualism – idea that species originate from a gradual change of adaptations

    • punctuated equilibrium – speciation occurs in rapid bursts

• adaptive radiation – when an ancestral species evolves into an array of species to fit a number of diverse habitats

• divergent evolution – evolution where species that once were similar to an ancestral species diverge (become distinct)

• convergent evolution – when unrelated species evolve with similar traits

Section 14.2 CS

Section 14.2 Cheet Sheet

• Spontaneous generation – The idea that living material comes from nonliving material.

  • Was disproved by Francesco Redi and Louis Pasteur

    • Redi did the meat/fly experiment

    • Pasteur did the broth experiment

• Biogenesis – Life comes from life

• Simple organic molecules must have been formed on early Earth for life to arise.

  • Water vapor, carbon dioxide, nitrogen, and methane and ammonia in the atmosphere may have joined together via energy from the sun, lightning, and Earth's heat to form organic molecules.

  • These molecules would “brew” in a “primordial soup” until simple life arose called protocells.

  • Stanley Miller and Harold Urey tested the hypothesis and created organic molecules.

• The first life might have been heterotrophs, eating organic molecules found in the oceans, and anaerobic, because there was not an abundant amount of oxygen in the atmosphere.

• After all the food had been devoured by these heterotrophs, autotrophs would be favored by natural selection and would have evolved, called archaebacteria. These autotrophs would be photosynthetic, producing oxygen.

• These autotrophs increased the concentration of oxygen in the Earth's atmosphere and allowed aerobically energy producing organisms to evolve.

  • Lightning also may have converted much of the oxygen in the atmosphere to ozone, forming a shield from the dangerous ultraviolet radiation from the sun, which enabled more complex organisms to evolve.

• Lynn Margulis proposed a theory for how eukaryotes may have evolved, called the endosymbiont theory.

  • Mitochondria evolved from energy making bacteria.

Science, Section 14.1 Cheat Sheet

• Early Earth was:

  • extremely hot

    • possibly caused by:

      • surface/atmosphere heating

        • meteorites colliding with the Earth

        • volcanoes erupting

      • internal heating

        • compression of minerals

        • decay of radioactive materials

• The gas from volcanoes was the primitive atmosphere of the earth.

  • Made up of:

    • Water Vapor

    • CO2

    • Nitrogen

    • Little O2

    • Other gases

• First organisms appeared between 3.9 and 3.5 billion years ago.

• 99 percent of all organisms that were on earth are now extinct.

• Types of Fossils

  • Trace

    • Marking left by an animal

  • Cast

    • When minerals in a rock fill a space left by a decayed organism

  • Imprint

    • When a thin object falls into a sedimentary rock

  • Petrified

    • When minerals penetrate and replace the hard parts of an organism

  • Mold

    • When a dead organism is buried in sediment and decays

  • Amber/Frozen

    • When entire organisms were trapped in ice or tree sap and preserved

• Fossils can teach scientists about the organism's behavior, as well as the climate and geography of the area the fossil was found in.

• Fossils primarily occur in sedimentary rocks.

• There are two ways to find the age of fossils:

  • Relative Dating

    • If the fossil is found in an undisturbed area, the deeper the fossil is, the older it is.

    • The only way scientists can truly have an approximation of the age through this method is to know how old the rock and/or other fossilized organisms are around it.

  • Radiometric Dating

    • Radiometric dating allows scientists to get a better idea of the age of the organism.

    • Radiometric uses common radioactive materials that decay into other materials at a given rate.

    • A radioactive material's half-life is half the amount of time it takes for that material to decay into the other material.

    • Scientists can then find the age of the organism by seeing how much of the radioactive material has decayed.

• The Geologic Time Scale is a scale of time based on the study of rocks in the Earth.

  • Precambrian – 3.5 billion years ago.

    • 87% of Earth's history.

    • Simple bacterias at first, then to eukaryotes by about 1.8 billion years ago, and by the end, contained multicellular, aquatic eukaryotes like sponges and jellyfish.

  • Paleozoic (Cambrian) – ended 245 million years ago.

    • Large and diverse amounts of organisms, such as fish, worms, and starfish.

    • Plants may have existed since 400 million years ago.

    • A mass extinction marked the end of the Paleozoic, which killed 70 to 90% of all life on Earth.

  • Mesozoic – Began 245 million years ago –

    • Mammals appeared, dinosaurs existed, birds evolved.

    • Three periods: Triassic, Jurassic (Age of the Dinosaurs), Cretaceous.

    • Mass extinction, during Cretaceous period, of dinosaurs in cretaceous allowed mammals and flowering plants to develop.

    • Mass extinction may have took out 2/3 of all living species.

    • Continents may have moved exponentially during this period. This is based on the concept of plate tectonics.

    • Plate tectonics is the idea that Earth's is actually several large “plates”, which are floating on magma, which is moving as well. These plates move and collide to create the surface on which we currently live.

  • Cenozoic – Began 66 Million years ago

    • Modern era

    • Primates evolved

    • Modern humans appeared 200,000 years ago.

Science - Chapter 11 Cheet Sheet

Final Version

DNA Cheat Sheet

11.1

• DNA controls you by giving the necessary instructions your body needs to produce the proteins you need.

• DNA stands for Deoxyribo-Nucleic Acid.

• DNA is a double helix.

• Nucleotides are made of:

  • A simple sugar (ribose)

  • A phosphate group

  • A nitrogen base

    • Nitrogen base – carbon ring structure that contains one or more atoms of nitrogen

    • 4 possible base types: Adenine, Guanine, Cytosine, and Thymine

      • Pairing: Good Cats : Annihilate Tacos! GC, AT

      • Purines: Good Angels are pure (G and A)

      • Pyrimidines: Thebes the Cat's pyramid (T and C)

  • Nucleotides bond by connecting phosphate and deoxyribose molecules.

• Important people in DNA discovery:

  • Watson

  • Crick

  • Franklin

  • Chargaff

• The sequence of nucleotides is the genetic code of an organism.

• DNA replication is the process of copying DNA.

  • Steps

    • 1. DNA is seperated with DNA Polymerase (an enzyme)

    • 2. Nucleotides in the nucleoplasm bond with the separated DNA strands.

    • 3. Another enzyme joins the nucleotides and already constructed strand together.

    • 
      

11.2

• DNA codes for all the proteins your body makes.

• RNA makes the protines

  • Differences between RNA and DNA

    • RNA is single stranded.

    • The sugar in RNA is ribose (DNA has deoxyribose)

    • RNA has uracil instead of thymine.

• Three types of RNA

  • messenger RNA (mRNA)

    • contains information for making proteins

    • is made via transcription (process like DNA replications, but instead RNA is formed and breaks off into a single strand instead of a double)

  • transfer RNA (tRNA)

    • has anti-codons

    • chains together amino acids with peptide bonds

  • ribosomeal RNA (rRNA)

    • RNA on the ribosome for translation

• Codon – 3 nitrogen bases that get made into an amino acid

• All organisms have the same genetic code for amino acids.

• The process of converting RNA to proteins is called translation.

  • Step 1: tRNA's anti-codon temporarily bonds with a corresponding mRNA codon.

  • Step 2:

• REMEMBER: Things must be transcripted before they can be translated.

11.3

• Changes in DNA sequences are called mutations

• Mutated organisms are called mutants

• Mutation can occur

  • as a result of changes in the DNA of sex cells

  • from environmental sources (radiation, mutagens)

• Cancer can result from mutations

• Point mutations are mutations where a single base pair is changed in DNA.

• Frameshift mutations are mutations in which a single base is added or deleted from DNA.

• Chromosomal mutations are changes in chromosomes, such as nondisjunction.

  • These changes occur frequently in plants.

  • Few chromosomal mutations are passed on to the future generations.

    • Most CM organisms are either sterile (cannot reproduce) or die at birth.

  • 4 chromosomal mutations:

    • deletion: part of chromosome is left out

    • insertion: part of a sister chromatid attaches itself to the other sister chromatid

    • inversion: parts in the chromosome are exchanged

    • translocation: parts of a chromosome are attached to a completely different chromosome

• Any agent that causes a change in DNA is called a mutagen.

  • Radiation, chemicals, and sometimes high temperatures are all mutations.

    • Radiation can delete bases.

    • Chemical mutagens usually result in a substitution mutations.

• DNA can repair itself with special enzymes.

Section 10.2

• Diploid – Normal cell with 2n number of chromosomes from either parent organism

• Haploid – only one kind of chromosome (n). These cells are gametes usually.

• Homologous chromosomes – chromosomes that determine the phenotype of an organism's cells that will have the same genes for a trait but not in the same order, necessarily.

• If sex cells had the number of chromosomes that a normal cell has, the amount of chromosomes would increase over time. This is why meiosis occurs.

• Meiosis Cycle, easy way to remember:

  • Prophase (Please) – Spindle fibers form, tetrads form, crossing over may occur

  • Metaphase (Make) – Tetrads attach to spindle fibers, move to equator

  • Anaphase (Another) – Tetrads split into double stranded chromosomes and move to opposite ends

  • Telephase (Taco) – Spindle breaks down, chromosomes uncoil, cytoplasm divides

• Meiosis II = EXACTLY THE SAME EXCEPT: It yields 4 gametes instead of two normal cells.

• 70 TRILLIAN different combinations, excluding genetic crossover.

• Genetic recombination – basically, genetic crossover

• Nondisjunction – failure of chromosomes to separate during meiosis

• Trisomy – when an gamete with an extra chromosome fuses with a normal gamete

  • Many organisms with extra chromosomes will survive

• Monosomy – when a gamete misisng a chromosome fuses with a normal gamete

  • Organisms will not survive monosomy most of the time, but Turner syndrome, where females have only one X chromosome, is one non-lethal example

• Triploid – organism has three sets of chromosomes

• Tetraploid – organisms has four sets of chromosomes

• Polyploids – organisms with more than the usual number of chromosome sets

  • Animals that are polyploidal almost always die

  • Polyploidal plants usually will survive with unique characteristics, such as enlarged size and greater health.

  • Plant breeders have learned how to cause polyploidal conditions in plants using chemicals

Short Story Authors

The Most Dangerous Game – Richard Connell (like Cornell Notes, the most pointless note system ever)

The Invalid's Story – Mark Twain

The Cask of Amontillado – Edgar Allen Poe

The Man to Send Rain Clouds – Leslie Marmon Silko (like silky clouds)

The Heyday of the Blood - Dorothy Canfield Fisher (fishers get fish blood on them)

The Gift of the Magi – O. Henry (Henry is magical)

The Scarlet Ibis – James Hurst (Hurst's Castle had scarlet ibises)

The Necklace – Guy de Maupassant

Chapter 8.1 Notes

Chapter 8.1 Notes

• The plasma membrane does not limit the diffusion of water.

• Water tries to reach equal concentration on both sides of the cell.

• The diffusion of water across a selectively permeable membrane is osmosis.

• Osmosis helps the cell to maintain homeostasis

• Molecules in liquids will always try to distribute themselves evenly through all the liquid.

• If a liquid such as water is separated by a selectively permeable barrier that only lets water though and one side of the container has a higher concentration of a substance than the other, then the water molecules will even out until there is a proportional amount of water molecules and the substance for each side. This uneven distribution of particles is called the concentration gradient.

• Isotonic solution – the concentration of a substance in a cell is the same as the concentration of the of a substance outside the cell. Isotonic solutions will not damage cells.

• Hypotonic solution – the concentration of a substance in in a cell is lower than the concentration of the substance outside the cell, causing the cell to pull in more of the substance. Cells will pull in water as well if they are in a hypotonic environment. If the concentration of the substance is high enough (or if it is pure water), the cell may go through cytolysis (bursting from high internal pressure) because it is pulling in too much water with the substance. This is unique to animal cells, as the cell wall in plant cells prevents the cell from bursting and will actually make the plant more firm.

• Hypertonic solution – the concentration of a substance in a cell is higher than the concentration of the substance outside the cell, causing the cell to put the substance into the environment outside the cell. Cells will expel water in a hypertonic environment, as well as the substance. If the concentration outside the cell is low enough, the cell will begin to shrivel and rupture from water loss. Plant cells will lose water mainly from the central vacuole and the plasma membrane will shrink away from the cell wall, which causes the plant to wilt.

• The movement of substances by diffusion is called passive transportation. The passive transport of substances that are not attracted to the phopholipid bilayer or are too large can still occur via the concentration gradient.
• The aid of transport proteins in order to diffuse substances is called facilitated diffusion. This is driven by the concentration gradient and is a common method of moving sugars and amino acids across membranes. The transport proteins simply provide a passage for the substances.
• Active transport is the movement of materials against the concentration gradient. It requires energy from the cell. Specialized transport proteins in the cell known as carrier proteins have specialized shapes that fit a certain molecule or ion. Chemical energy allows the carrier protein to change shape so that once the ion or molecule is in the "grasp" of the protein, it can morph so that an opening allows the substance into the cell. After the particle flows into the cell, the protein morphs back, ready to get more of the substance from the outside.
• Endocytosis is the process by which a cell surrounds and takes in materials from its environment, done by engulfing the substance with part of the plasma membrane, which breaks away. The substance is then enclosed in a vacuole and taken to an appropriate place for processing.
• Exocytosis is the expulsion of materials from a cell.
• These two forms of material transportation are both active.