High

1. Times Tables (1-10 and squares through 20)

2. Mental math (addition, subtraction, multiplication, division(divisibility rules))

3. Order of Operations

4. Basic algebraic equations

5. Fraction operations and Friendly Fractions

Medium

1. Pythagorean triples

2. Volume and surface area calculations

3. Cell organelles

4. Planetary moons and other astronomical bodies

5. Famous mathematicians

Low

1. Plant classification and parts

2. Clouds and weather

3. Animal phyla

4. Parts of an atom, periodic table

5. Types of rocks and classifications

Full Math and Science Curriculum Outline

1.     Famous Mathematicians

·       The work of Isaac Newton (1643-1727, English) in pure math includes generalizing the binomial theorem to non-integer exponents, doing the first rigorous manipulation with power series, and creating "Newton's method" for the finding roots. He is best known, however, for a lengthy feud between British and Continental mathematicians over whether he or Gottfried Leibniz invented calculus (whose differential aspect Newton called "the method of fluxions"). It is now generally accepted that they both did, independently.

·       Euclid (c. 300 BC, Alexandrian Greek) is principally known for the Elements, a textbook on geometry and number theory, that was used for over 2,000 years and which grounds essentially all of what is taught in modern high school geometry classes. Euclid is known for his five postulates that define Euclidean (i.e., "normal") space, especially the fifth (the "parallel postulate") which can be broken to create spherical and hyperbolic geometries. He also proved the infinitude of prime numbers.

·       Carl Friedrich Gauss (1777-1855, German) is considered the "Prince of Mathematicians" for his extraordinary contributions to every major branch of mathematics. His Disquisitiones Arithmeticae systematized number theory and stated the fundamental theorem of arithmetic. He also proved the fundamental theorem of algebra, the law of quadratic reciprocity, and the prime number theorem. Gauss may be most famous for the (possibly apocryphal) story of intuiting the formula for the summation of an arithmetic series when given the busywork task of adding the first 100 positive integers by his primary school teacher.

·       Archimedes (287-212 BC, Syracusan Greek) is best known for his "Eureka moment" of using density considerations to determine the purity of a gold crown; nonetheless, he was the preeminent mathematician of ancient Greece. He found the ratios between the surface areas and volumes of a sphere and a circumscribed cylinder, accurately estimated pi, and presaged the summation of infinite series with his "method of exhaustion."

·       Gottfried Leibniz (1646-1716, German) is known for his independent invention of calculus and the ensuing priority dispute with Isaac Newton. Most modern calculus notation, including the integral sign and the use of d to indicate a differential, originated with Leibniz. He also invented binary numbers and did fundamental work in establishing boolean algebra and symbolic logic.

·       Pierre de Fermat (1601-1665, French) is remembered for his contributions to number theory including his "little theorem" that ap - a will be divisible by p if p is prime. He also studied Fermat primes (those of the form 22n+1) and stated his "Last Theorem" that xn + yn = zn has no solutions if x, y, and z are positive integers and n is a positive integer greater than 2. He and Blaise Pascal founded probability theory. In addition, he discovered methods for finding the maxima and minima of functions and the areas under polynomials that anticipated calculus and inspired Isaac Newton.

·       Leonhard Euler (1707-1783, Swiss) is known for his prolific output and the fact that he continued to produce seminal results even after going blind. He invented graph theory with the Seven Bridges of Königsberg problem and introduced the modern notation for e, the square root of -1 (i), and trigonometric functions. Richard Feynman called his proof that eiπ = -1 "the most beautiful equation in mathematics" because it linked four of math's most important constants.

·       Kurt Gödel (1906-1978, Austrian) was a logician best known for his two incompleteness theorems proving that every formal system that was powerful enough to express ordinary arithmetic must necessarily contain statements that were true, but which could not be proved within the system itself.

·       Andrew Wiles (1953-present, British) is best known for proving the Taniyama-Shimura conjecture that all rational semi-stable elliptic curves are modular. This would normally be too abstruse to occur frequently in quiz bowl, but a corollary of that result established Fermat's Last Theorem.

·       William Rowan Hamilton (1805-1865, Irish) is known for extending the notion of complex numbers to four dimensions by inventing the quaternions, a non-commutative field with six square roots of -1: ±i, ±j, and ±k with the property that ij = k, jk = i, and ki = j.

2.         Types of Computational Problems

• Pythagorean Triples. Almost certainly, the most important things to know are the basic sets of integers that satisfy the Pythagorean Theorem (a2 + b2 = c2) and could be the side lengths of a right triangle. These are called Pythagorean Triples and the simplest ones are 3-4-5, 5-12-13, 7-24-25, and 8-15-17. Note that any multiple of a Pythagorean Triple is also a Pythagorean Triple so that 6-8-10, 15-20-25, and 300-400-500 are also ones by virtue of 3-4-5 being one.
• Solids. Teams should be able to calculate the volume and surface area of simple geometric figures including the sphere, cone, cylinder, pyramid, hemisphere, prism, and parallelepiped.
• Plane Figures. Teams should be able to calculate the areas of triangles (especially equilateral triangles), trapezoids, parallelograms, rhombi, and circles using different angles and lengths.
• Similar Figures. The areas of similar figures are related by the square of any corresponding length and the volumes are related by the cube of any corresponding length. For instance, if a square has a diagonal that is 30% longer than another square, it has an area that is (1.30 x 1.30 = ) 1.69 times as great (69% greater). Similar reasoning applies to perimeters, side lengths, diameters, and so forth.
• Permutations. Teams should be able to compute the number of permutations and combinations of n objects taken m at a time. They should also have memorized the first eight (or so) values of the factorial function to make this easier.
• Divisibility Rules. Teams should be able to quickly apply the divisibility rules for small integers (2 through 11) to large integers.
• Polynomial Math. Teams should be able to quickly add, subtract, multiply, divide, factor, and find the roots of low-degree polynomials.

3.         Programming Languages

• C++ is a popular, compiled, high-level language developed by Bjarne Stroustrup in 1985 at Bell Labs. C++ is similar to C, but adds object-oriented features (classes), generic programming (templates), and exception handling to the language. It is a popular language for developing business applications and, increasingly, games.
• Java is a popular high-level language developed by Sun Microsystems in the early 1990s. The language was originally named OAK and unsuccessfully used for set-top devices, but hit it big after being renamed in 1995 and introduced to the World Wide Web. It is a relatively pure object-oriented language with syntax similar to C++. Instead of being compiled to object code, it is compiled to Java bytecode, which is then interpreted or compiled on the fly. This use of machine-independent bytecode gives it its "write once, run everywhere" property. Java is principally used for client-side web application ("applets") and server-side web application ("servlets") that make use of J2EE technology. The success of Java inspired Microsoft to introduce its C# language and .NET framework.
• BASIC (Beginner's All-purpose Symbolic Instruction Code) is a high-level language developed by John Kemeny and Thomas Kurtz at Dartmouth College in the mid 1960s. It is easy to use but its relative lack of structure makes maintaining programs difficult. There have been many versions of BASIC and some more modern ones (TurboBasic, QuickBasic Visual Basic) have added advanced features. Stereotypical programs like 10 PRINT "HELLO" and 10 GOTO 10 are written in BASIC.
• C, a compiled successor to the B programming language, was developed by Dennis Ritchie in 1972. It is a high-level and highly standardized language that remains very "close to the hardware" and allows the programmer to perform useful, fast, and dangerous tricks. It is widely used for business applications, games, operating systems (particularly UNIX and Linux), and device drivers.
• Perl is an interpreted language designed principally to process text. It was written by Larry Wall and first released in 1988. It is intended to be practical and concise rather than theoretically elegant and is sometimes lampooned as "write one, read never" because of its heavy use of symbols and idiom. It is often used for web CGI scripts and parsing log files. "Perl" is an unofficial retronym for "Practical Extraction Report Language."
• ALGOL (ALGOrithmic Language) was created in the late 1950s and was the first procedural language intended for solving mathematical and scientific problems. Formalized in a report titled ALGOL 58, it progressed through ALGOL 60 and ALGOL 68 before waning in popularity. ALGOL was sufficiently advanced and respected that most modern procedural languages reflect its overall structure and design; some, like Pascal, are very closely related.
• Pascal is a high-level, compiled language built upon ALGOL. It is named after the 17th-century mathematician Blaise Pascal and was developed by Niklaus Wirth during 1967-71. Pascal is best known for its emphasis on structured programming techniques and strong typing; because of this, it was extremely popular as a teaching language in the 1980s and early 1990s, though it was never popular for business or scientific applications. The object-oriented language Delphi was based on Pascal.
• LISP (LISt Processing) is the ancestor of the family of functional languages that emphasize evaluating expressions rather than executing imperative commands. It was developed in 1950-1960 by John McCarthyand is used primarily for symbolic manipulations of complicated structures rather than numerical calculation. It and its descendants (Scheme, CommonLisp, etc.) continue to be used in academic research, particularly artificial intelligence.
• Fortran (FORmula TRANslation) is the oldest high-level language. Designed by John Backus for IBM during the late 1950s, it was once in use on virtually every computer in the world and is still used today for engineering and scientific applications because of the quality of its compilers and numerical libraries. The most popular Fortran versions are Fortran IV, 77, and 90. The name "Fortran" was originally entirely capitalized, but the ANSI Fortran Committee has since declared the "initial capital" spelling official.
• COBOL (COmmon Business-Oriented Language) was developed in 1959 by CODASYL (Conference on Data Systems Languages) under the direction of Rear Admiral Grace Hopper and is the second-oldest high-level language. It emphasized record-processing and database access and uses an English-like syntax, all attributes that led to widespread use in business, particularly the financial sector. It is characterized as especially wordy (just as C and Perl are characterized as terse). The vast majority of Year 2000 problems involved programs written in COBOL.

4.         Animal Phyla

• Porifera (pore-IH-fer-ah; 5,000 species) The sponges are all water-dwellers (98% marine, 2% freshwater), and are sometimes classified separately from other animals because of their asymmetric bodies and lack of distinct tissues. They are sessile (immobile) except in early dispersing stages, and collect food particles via the sweeping motions of flagellated cells called choanocytes [koh-ANN-oh-sites].
• Cnidaria (nih-DARE-ee-ya; 10,000 species) Also called Coelenterata [se-LEN-ter-AH-tah], the cnidarians develop from a diploblastic (two-layered) embryo, and have two separate tissue layers and radial body symmetry. Many cnidarians have two life stages, the mobile, usually bell-like medusa and the sessile polyp. All cnidarians have nematocysts, or stinging cells, for capturing prey, and some can inflict painful stings on swimmers. Examples include the hydras, sea anemones, corals, jellyfishes, and Portuguese man-o-war (which is actually an aggregation of colonial cnidarians).
• Platyhelminthes (PLAT-ee-hel-MIN-theez; 15,000 species) The flatworms are the most primitive phylum to develop from a triploblastic (three-layered) embryo. They have bilateral body symmetry, and are acoelomate (lacking a true body cavity), so that the space between the digestive tract and the body wall is filled with tissue. As the name implies, they are generally flat-bodied. They have a true head and brain, but the digestive system has only one opening that functions as both mouth and anus. Most are hermaphroditic. This phylum includes parasites such as the tapeworms and flukes, as well as free-living (i.e., non-parasitic) organisms such as the planarians.
• Nematoda (NEM-ah-TOE-dah; 15,000 species) The roundworms are unsegmented worms that live in a variety of habitats. They are pseudocoelomate; the three tissue layers are concentric, but the body cavity is not lined with tissue derived from the mesoderm (middle embryonic layer). They include both free-living and parasitic species; human parasites include hookworms and the causative agents of elephantiasis, trichinosis, and river blindness. Soil nematodes may be crop pests, while others are beneficial predators on other plant pests. The nematode species Caenorhabdis elegans is a common subject in genetics and developmental-biology labs.
• Annelida (AN-el-LEE-dah; 11,500 species) The annelids are segmented worms and represent the first lineage of truly eucoelomate (having a body cavity lined with mesoderm-derived tissue) animals; their body cavities are lined with tissue derived from the embryonic mesoderm. Annelid classes include the marine Polychaeta, as well as the mostly terrestrial Oligochaeta (including the earthworms, Lumbricus) and the mostly-aquatic Hirudinea, or leeches. Characteristics of annelids include nephridia (kidney-like structures), blood vessels, and, in some classes, hermaphroditism.
• Arthropoda (ar-THROP-oh-dah or AR-thro-POE-dah; over 800,000 species described; estimates of actual diversity vary but go as high as 9 million species) The most diverse and successful animal phylum on earth (incorporating about 75% of all described animal species), the Arthropoda are characterized by jointed legs and a chitinous exoskeleton. Like annelids, they are segmented, but unlike annelids, their segments are usually fused into larger body parts with specialized functions (such as the head, thorax, and abdomen of an insect). Arthropods are often divided into four subphyla: Uniramia (insects, centipedes, millipedes);Chelicerata (arachnids, sea spiders, horseshoe crabs); Crustacea (shrimps, lobsters, crabs, crayfish, barnacles, pillbugs), and Trilobitomorpha (the trilobites, now extinct).
• Cycliophora (CY-clee-oh-FORE-ah; 1 species) The most recently named phylum; its only known member is Symbion pandora, a tiny invertebrate first identified in 1995 when a Danish biologist found specimens on the mouthparts of a Norwegian lobster. It is believed to be closely related to the marine phyla Entoprocta and Ectoprocta (Bryozoa), which are not discussed here.
• Mollusca (mol-LUS-kah; 50,000 species) The molluscs are second in diversity only to the arthropods. Body plans within this phylum are diverse, but general characteristics include a soft body covered by a thin mantle, with a muscular foot and an internal visceral mass. There are two fluid-filled body cavities derived from mesodermal tissue; a small coelom and a large hemocoel that functions as an open circulatory system. Many molluscs have a shell composed of calcium carbonate and proteins, secreted by the mantle. Familiar groups within the Mollusca include the classes Gastropoda (slugs, snails), Bivalvia (clams, oysters, scallops), and Cephalopoda (nautilus, squids, octopi).
• Echinodermata (ek-KY-no-der-MAH-tah; 6,500 species) Characteristics of this phylum include an endoskeleton composed of many ossicles of calcium and magnesium carbonate, a water vascular system (WVS), a ring canal around the esophagus, and locomotion by tube feet connected to the WVS. Unique to echinoderms is the five-fold radial symmetry obvious in sea stars (seafish), sea urchins, and sea lilies. Others, like sea cucumbers, have varying degrees of bilateral symmetry. In the echinoderm body plan, a true head is absent; the anatomical terms oral (mouth-bearing) and aboral (away from the mouth) are used to describe orientation of the body surfaces. Feeding adaptations include particle feeding through the WVS, everting the stomach to engulf prey (sea stars), and a scraping device called Aristotle's lantern (sea urchins).
• Chordata (kor-DAH-tah; 44,000 species) Our home phylum is divided into three subphyla: Urochordata, the sea squirts; Cephalochordata, the lancelets, and the true vertebrates (Vertebrata, the most diverse subphylum). Defining traits of chordates include pharyngeal gill slits, a notochord, a post-anal tail, and a dorsal hollow nerve cord. In vertebrates, some of these structures are found only in embryonic stages. The lancelet Amphioxus (Branchiostoma) is often used as a demonstration organism in biology labs.

5.         Planetary Moons

• Charon (Pluto) Named for the mythical boatman of the Greek underworld. Its expected pronunciation of "KAIR-en" is not the correct one, which is actually "SHAHR-en", in honor of Charlene Christy, wife of Jim Christy, its discoverer. The largest moon relative to the size of its orbiting planet, Charon not only is in synchronous orbit with Pluto, but the two show the same face toward each other at all times. The relative sizes of the two bodies has led some to call Charon and Pluto a double planet system. Charon's surface is believed to be water ice.
• Deimos and Phobos (Mars) Named for two sons of Ares and Aphrodite. Phobos and Deimos (Greek for "fear" and "panic") are the two moons of Mars and both were discovered in 1877 by Asaph Hall. Phobos orbits closer to the planet and has as its most prominent feature the crater Stickney (Hall's wife's maiden name). Unlike the Earth's moon, it rises in the west and sets in the east, about twice per Martian day. This is due to it being below the radius for synchronous orbit. This position also means it will either impact Mars or break into a ring in around 50 million years. Deimos is the smallest moon in the solar system. It was discovered two days before Phobos. Deimos was likely an asteroid brought into Mars' orbit after being disturbed by Jupiter.  Like Phobos, Deimos is heavily cratered, rich in carbon, and believed to have water ice.
• Europa (Jupiter) One of the Galilean moons, discovered in 1610 by Galileo (the others are Callisto, Ganymede, and Io). It resembles Io, and to a degree, Earth, in its composition of silicate rocks. However, it is coated in a thin layer of ice, which causes it to be exceedingly smooth. This ice layer may also provide a thin atmosphere as hydrogen and oxygen are released when the planet is exposed to sunlight. There is the possibility of an active sea of liquid water beneath the surface. The most striking feature of the surface is a series of dark streaks that may be due to geysers or volcanic eruptions.
• Ganymede (Jupiter) The largest satellite in the solar system, this Galilean moon is larger than Mercury, but has only half its mass. Based on the observations of the Galileo spacecraft, it is thought to have a three-layer structure of a molten iron core, silicate mantle, and ice exterior. Its surface is marked by older, dark, highly cratered regions, mixed with lighter, grooved regions. These grooves indicate tectonic activity, but Ganymede does not appear to have undergone recent tectonic shifts.
• Io (Jupiter) Like Europa, Io (named for a lover of Zeus) is primarily formed of silicate rock. Its surface, however, is unlike any other satellite. Rather than craters, Io is dotted with active volcanoes, calderas, and other signs of geological activity. The eruptions are believed to consist of sulfurous compounds that comprise Io's thin atmosphere. The tremendous activity is due to tidal warming from the gravity of Jupiter and other satellites. Additionally, as Io orbits it is heated electrically from currents produced by Jupiter's magnetic field. This action strips material from Io, producing a radiation field and increasing Jupiter's magnetosphere.
• Nereid (Neptune) Discovered by Gerard Kuiper (who also discovered Miranda, Titan's atmosphere, and an asteroid belt), Nereid (named for the daughters of Nereus and Doris) has the most eccentric orbit of any known satellite, ranging from 1.3 million kilometers to 9.6 million. The oddity of this orbit indicates it is likely a captured asteroid.
• Oberon (Uranus) Named for the King of the Fairies in A Midsummer Night's Dream (all of Uranus' satellites are named for literary, rather than mythological, characters), Oberon is both the second largest of Uranus' satellites, and the outermost of its large satellites. Like all large Uranian moons, its structure is about half water ice, half rock. Large faults are visible across its southern hemisphere, but its surface is heavily cratered, indicating long-term tectonic stability. Some craters have dark floors that could possibly indicate post-impact upwellings of water.
• Titan (Saturn) The largest of Saturn's satellites, Titan might be the largest satellite in the solar system, but this awaits more accurate measurements. Those measurements are difficult because of Titan's major characteristic: It is the only satellite to have a substantial atmosphere. Its significant atmosphere, a mix of nitrogen (80%), methane (20%), and argon (trace), also makes it unique among satellites.
• Titania (Uranus) Another of Herschel's discoveries, Titania is named for Oberon's wife, the Queen of the Fairies, and is the largest of the Uranian satellites. Its surface is an odd mix of craters and valleys. One theory regarding this is that it began as a liquid, then cooled surface first. Once ice had formed, the interior, freezing forced surface cracks which formed the valleys. This also accounts for the appearance of some craters, where ice appears to have melted and filled in.
• Triton (Neptune) By far the largest of Neptune's satellites, Triton is also unusual for its retrograde orbit, which indicates that it was not part of the natural formation of Neptune's other moons. It also features seismic activity in the form of ice volcanoes, a tenuous nitrogen-methane atmosphere, and a southern hemisphere "ice cap" of nitrogen and methane. All of these may be caused by Triton's odd rotational axis, which tends to alternate polar and equatorial regions facing the sun.

6.         Organelles

• Nucleus The nucleus is the "command central" of the cell because it contains almost all of the cell's DNA, which encodes the information needed to make all the proteins that the cell uses. The DNA appears as chromatin through most of the cell cycle but condenses to form chromosomes when the cell is undergoing mitosis. Commonly seen within the nucleus are dense bodies called nucleoli, which contain ribosomal RNA. In eukaryotes, the nucleus is surrounded by a selectively-permeable nuclear envelope.
• Ribosomes Ribosomes are the machines that coordinate protein synthesis, or translation. They consist of several RNA and protein molecules arranged into two subunits. Ribosomes read the messenger RNA copy of the DNA and assemble the appropriate amino acids into protein chains.
• Mitochondria The "mighty mitos" are the powerhouses of the cell. Mitochondria are double-membrane-bound organelles that are the site of respiration and oxidative phosphorylation, processes that produce energy for the cell in the form of ATP. The inner membrane of a mitochondrion forms folds called cristae [KRIS-tee], which are suspended in a fluid called the matrix. The mitochondrial matrix contains DNA and ribosomes.
• Endoplasmic Reticulum (ER) The ER is a network of tube-like membranes continuous with the nuclear envelope that comes in rough (with ribosomes) and smooth (without ribosomes) varieties. In the ER, proteins undergo modifications and folding to yield the final, functional protein structures.
• Golgi Apparatus The stack of flattened, folded membranes that forms the Golgi apparatus acts as the "post office of the cell." Here proteins from the ribosomes are stored, chemically modified, "addressed" with carbohydrate tags, and packaged in vesicles for delivery.
• Lysosomes Lysosomes are membrane-bound organelles that contain digestive enzymes that break down proteins, lipids, carbohydrates, and nucleic acids. They are important in processing the contents of vesicles taken in from outside the cell. It is crucial to maintain the integrity of the lysosomal membranes because the enzymes they contain can digest cellular components as well.
• Chloroplasts Found only in plants and certain protists, the chloroplast contains the green pigment chlorophyll and is the site of photosynthesis. Like the mitochondrion, a chloroplast is a double-membrane-bound organelle, and it has its own DNA and ribosomes in the stroma. Chloroplasts contain grana, which are stacks of single membrane structures called thylakoids on which the reactions of photosynthesis occur.
• Vacuoles Found mainly in plants and protists, vacuoles are liquid-filled cavities enclosed by a single membrane. They serve as storage bins for food and waste products. Contractile vacuoles are important for freshwater protists to rid their cells of excess water that accumulates because of salt imbalance with the environment.
• Cilia/Flagella Cilia and flagella are important organelles of motility, which allow the cell to move. Flagella are long, whip-like structures, while cilia are short hair-like projections. Both contain a 9 + 2 arrangement of microtubules in cross section and are powered by molecular motors of kinesin and dynein molecules.
• Centrioles Not found in plant cells, centrioles are paired organelles with nine sets of microtubule triplets in cross section. They are important in organizing the microtubule spindle needed to move the chromosomes during mitosis.

7.   Rocks and Minerals

A.        Rock Classifications

1.         Sedimentary: Sedimentary rocks are types of rock that are formed by the deposition of material at the Earth's surface and within bodies of water. Sedimentation is the collective name for processes that cause mineral and/or organic particles (detritus) to settle and accumulate or minerals to precipitate from a solution. Particles that form a sedimentary rock by accumulating are called sediment. Before being deposited, sediment was formed by weathering and erosion in a source area, and then transported to the place of deposition by water, wind,ice, mass movement or glaciers which are called agents of denudation.The sedimentary rock cover of the continents of the Earth's crust is extensive, but the total contribution of sedimentary rocks is estimated to be only 8% of the total volume of the crust.[1] Sedimentary rocks are only a thin veneer over a crust consisting mainly of igneous and metamorphic rocks. Sedimentary rocks are deposited in layers as strata, forming a structure called bedding. The study of sedimentary rocks and rock strata provides information about the subsurface that is useful for civil engineering, for example in the construction of roads,houses, tunnels, canals or other constructions. Sedimentary rocks are also important sources of natural resources like coal, fossil fuels,drinking water or ores.

2.     Igneous:  Igneous rock is formed through the cooling and solidification of magma or lava. Igneous rock may form with or without crystallization, either below the surface as intrusive (plutonic) rocks or on the surface as extrusive (volcanic) rocks. This magma can be derived from partial melts of pre-existing rocks in either a planet's mantle or crust. Typically, the melting is caused by one or more of three processes: an increase in temperature, a decrease in pressure, or a change in composition. Over 700 types of igneous rocks have been described, most of them having formed beneath the surface of Earth's crust.

3.         Metamorphic: Metamorphic rocks arise from the transformation of existing rock types, in a process called metamorphism, which means "change in form". The original rock (protolith) is subjected to heat (temperatures greater than 150 to 200 °C) and pressure (1500 bars),[1] causing profound physical and/or chemical change. The protolith may be sedimentary rock, igneous rock or another older metamorphic rock.  Metamorphic rocks make up a large part of the Earth's crust and are classified by texture and by chemical and mineral assemblage (metamorphic facies). They may be formed simply by being deep beneath the Earth's surface, subjected to high temperatures and the great pressure of the rock layers above it. They can form from tectonic processes such as continental collisions, which cause horizontal pressure, friction and distortion. They are also formed when rock is heated up by the intrusion of hot molten rock called magma from the Earth's interior. The study of metamorphic rocks (now exposed at the Earth's surface following erosion and uplift) provides information about the temperatures and pressures that occur at great depths within the Earth's crust. Some examples of metamorphic rocks are gneiss, slate, marble, schist, andquartzite. Foliation is the layering within metamorphic rocks. It occurs when a rock is being shortened along one axis during recrystallization

4.         Minerals: A mineral is a naturally occurring substance that is solid and stable at room temperature, representable by a chemical formula, usuallyabiogenic, and has an ordered atomic structure. It is different from a rock, which can be an aggregate of minerals or non-minerals, and does not have a specific chemical composition. The exact definition of a mineral is under debate, especially with respect to the requirement a valid species be abiogenic, and to a lesser extent with regards to it having an ordered atomic structure. The study of minerals is called mineralogy. There are over 4,900 known mineral species; over 4,660 of these have been approved by the International Mineralogical Association (IMA). The silicate minerals compose over 90% of the Earth's crust. The diversity and abundance of mineral species is controlled by the Earth's chemistry. Silicon and oxygen constitute approximately 75% of the Earth's crust, which translates directly into the predominance of silicate minerals. Minerals are distinguished by various chemical and physical properties. Differences in chemical composition and crystal structure distinguish various species, and these properties in turn are influenced by the mineral's geological environment of formation. Changes in the temperature, pressure, and bulk composition of a rock mass cause changes in its mineralogy; however, a rock can maintain its bulk composition, but as long as temperature and pressure change, its mineralogy can change as well. Minerals can be described by variable physical properties, which relate to its chemical structure and composition. Common distinguishing characteristics include crystal structure and habit, hardness, lustre, diaphaneity, colour, streak, tenacity, cleavage, fracture, parting, and specific gravity. More specific tests for minerals include reaction to acid, magnetism, taste or smell, and radioactivity.

5.         Crystals: A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an ordered pattern extending in all three spatial dimensions. In addition to their microscopic structure, large crystals are usually identifiable by their macroscopic geometrical shape, consisting of flat faces with specific, characteristic orientations.The scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growthis called crystallization or solidification. The word crystal is derived from the Ancient Greek word κρύσταλλος (krustallos), meaning both “ice” and “rock crystal”,[1] from κρύος (kruos), "icy cold, frost".Common crystals include snowflakes, diamonds, and table salt; however, most common inorganic solids are polycrystals. Crystals are often symmetrically intergrown to form crystal twins.

8.  Weather

A.    Cloud Classifications: In meteorology, a cloud is a visible mass of liquid droplets or frozen crystals made of water or various chemicals suspended in the atmosphere above the surface of a planetary body. These suspended particles are also known as aerosols. Clouds in earth's atmosphere are studied in the cloud physics branch of meteorology. Two processes, possibly acting together, can lead to air becoming saturated; cooling the air or adding water vapor to the air. In general, precipitation will fall to the surface; an exception is virga, which evaporates before reaching the surface. The international cloud classification system is based on the fact clouds can show free-convective upward growth like cumulus, appear in non-convective layered sheets such as stratus, or take the form of thin fibrous wisps, as in the case of cirrus. Prefixes are used in connection with clouds: strato- for low clouds with limited convection that form mostly in layers, nimbo- for thick layered clouds that can produce moderate to heavy precipitation, alto- for middle clouds, and cirro- for high clouds. Whether or not a cloud is low, middle, or high level depends on how far above the ground its base forms. Cloud types with significant vertical extent can form in the low or middle altitude ranges depending on the moisture content of the air. Clouds in the troposphere have Latin names due to the popular adaptation of Luke Howard's cloud categorization system, which began to spread in popularity during December 1802. Synoptic surface weather observations use code numbers to record and report the types of tropospheric cloud visible at each scheduled observation time based on the height and physical appearance of the clouds.

B.        Meteorological instruments

o   Thermometer (from the Greek θερμός, thermos, meaning "hot" and μἐτρον, metron, "measure") is a device that measures temperature or temperature gradient using a variety of different principles.[1] A thermometer has two important elements: the temperature sensor (e.g. the bulb on amercury-in-glass thermometer) in which some physical change occurs with temperature, plus some means of converting this physical change into a numerical value (e.g. the visible scale that is marked on a mercury-in-glass thermometer).

o   Barometer: Developed by Evangelista Torricelli in 1643 to measure atmospheric pressure. Pressure tendency can forecast short term changes in the weather. Numerous measurements of air pressure are used within surface weather analysis to help find surface troughs, high pressure systems, and frontal boundaries. A barograph is a recording aneroid barometer. A barograph is used to monitor pressure. The pointer in an aneroid barometer is replaced with a pen. It produces a paper or foil chart called a barogram that records the barometric pressure over time.

o   An anemometer is a device for measuring wind speed, and is a common weather station instrument. The term is derived from the Greek word anemos, meaning wind, and is used to describe any airspeed measurement instrument used in meteorology or aerodynamics. The first known description of an anemometer was given by Leon Battista Alberti around 1450.[1]

o   A hygrometer UK /haɪˈɡrɒmɪtə/ is an instrument used for measuring the moisture content in the environment. Humidity measurement instruments usually rely on measurements of some other quantity such as temperature, pressure, mass or a mechanical or electrical change in a substance as moisture is absorbed. By calibration and calculation, these measured quantities can lead to a measurement of humidity. Modern electronic devices use temperature of condensation, or changes in electrical capacitance or resistance to measure humidity changes.

o   A rain gauge (also known as an udometer or a pluviometer or an ombrometer or a cup) is a type of instrument used by meteorologistsand hydrologists to gather and measure the amount of liquid precipitation over a set period of time.The first known rain records were kept by ancient greeks in 500 B.C.

o   The ultraviolet index or UV Index is an international standard measurement of the strength of the ultraviolet (UV) radiation from the sun at a particular place on a particular day. It is a scale primarily used in daily forecasts aimed at the general public, and is now available as an hourly forecast as well. Its purpose is to help people to effectively protect themselves from UV light, of which excessive exposure causes sunburns, eye damage such as cataracts, skin aging,immunosuppression,[1] and skin cancer (see the section health effects of ultraviolet light).

o   Disdrometer for measuring drop size distribution

o   Transmissometer for measuring visibility

o   Ceilometer for measuring cloud ceiling

o   Wind sock and weather vane measure wind direction

·             Types of Severe Weather

o   Tornadoes: A dangerous rotating column of air in contact with both the surface of the earth and the base of a cumulonimbus cloud (thundercloud) or acumulus cloud, in rare cases. Tornadoes come in many sizes but typically form a visible condensation funnel whose narrowest end reaches the earth and surrounded by a cloud of debris and dust.[17]Tornadoes wind speeds generally average between 40 miles per hour (64 km/h) and 110 miles per hour (180 km/h). They are approximately 250 feet (76 m) across and travel a few miles (kilometers) before dissipating. Some attain wind speeds in excess of 300 miles per hour (480 km/h), may stretch more than a mile (1.6 km) across, and maintain contact with the ground for dozens of miles (more than 100 km).[5][18][19]Tornadoes, despite being one of the most destructive weather phenomena are generally short lived. A long-lived tornado generally lasts no more than an hour, but some have been known to last for 2 hours or longer (for example, the Tri-State Tornado). Due to their relatively short duration, less information is known about the development and formation of tornadoes.[20]

o   Downburst: Downbursts are created within thunderstorms by significantly rain-cooled air, which, upon reaching ground level, spreads out in all directions and produce strong winds. Unlike winds in a tornado, winds in a downburst are not rotational but are directed outwards from the point where they strike land or water.

o   Squall Line: A squall line is an elongated line of severe thunderstorms that can form along or ahead of a cold front.[27][28] The squall line typically contains heavy precipitation, hail, frequent lightning, strong straight line winds, and possibly tornadoes or waterspouts.[

o   Tropical Cyclone: Very high winds can be caused by mature tropical cyclones (called hurricanes in the United States and Canada and typhoons in eastern Asia). A tropical cyclone’s heavy surf created by such winds may cause harm to marine life either close to or upon the surface of the water, such as coral reefs.[35] Coastal regions may receive significant damage from a tropical cyclone while inland regions are relatively safe from the strong winds, due to their rapid dissipation over land. However, severe flooding can occur even far inland because of high amounts of rain from tropical cyclones and their remnants.

o   Waterspouts: Tornadoes that form over water that cause damage if they cross land or as a result of the hurricane force winds they form.

o   Dust Storm: An unusual form of windstorm that is characterized by the existence of large quantities of sand and dust particles carried by moving air.[40] Dust storms frequently develop during periods of droughts, or over arid and semi-arid regions. Dust storms have numerous hazards and are capable of causing deaths. Visibility may be reduced dramatically, so risks of vehicle and aircraft crashes are possible. Additionally, the particulates may reduce oxygen intake by the lungs,[41] potentially resulting in suffocation. Damage can also be inflicted upon the eyes due to abrasion.Dust storms can produce many issues for agricultural industries as well. Soil erosion is one of the most common hazards and decreases arable lands. Dust and sand particles can cause severe weathering of buildings and rock formations. Nearby bodies of water may be polluted by settling dust and sand, killing aquatic organisms. Decrease in exposure to sunlight can affect plant growth, as well as decrease in infrared radiation may cause decreased temperatures.

o   Hail Storms: Any form of thunderstorm that produces precipitating hailstones is known as a hail storm.[52] Hailstorms are generally capable of developing in any geographic area where thunderclouds (Cumulonimbus) are present, although they are most frequent in tropical and monsoon regions.[53] The updrafts and downdrafts within cumulonimbus clouds cause water molecules to freeze and solidify, creating hailstones and other forms of solid precipitation.[54] Due to their larger density, these hailstones become heavy enough to overcome the density of the cloud and fall towards the ground. The downdrafts in cumulonimbus clouds can also cause increases in the speed of the falling hailstones. The term "hailstorm" is usually used to describe the existence of significant quantities or size of hailstones. Hailstones can cause serious damage, notably to automobiles, aircraft, skylights, glass-roofed structures, livestock, and crops.[55]Rarely, massive hailstones have been known to cause concussions or fatal head trauma. Hailstorms have been the cause of costly and deadly events throughout history. One of the earliest recorded incidents occurred around the 12th century in Wellesbourne,Britain.[56] The largest hailstone in terms of maximum circumference and length ever recorded in the United States fell in 2003 inAurora, Nebraska, USA The hailstone had a diameter of 7 inches (18 cm) and a circumference of 18.75 inches (47.6 cm).

o   Ice Storm: Ice storms are also known as a Silver storm, referring to the color of the freezing precipitation.[84] Ice storms are caused by liquidprecipitation which freezes upon cold surfaces and leads to the gradual development of a thickening layer of ice.[84] The accumulations of ice during the storm can be extremely destructive. Trees and vegetation can be destroyed and in turn may bring down power lines, causing the loss of heat and communication lines.[85] Roofs of buildings and automobiles may be severely damaged. Gas pipes can become frozen or even damaged causing gas leaks. Avalanches may develop due to the extra weight of the present. Visibility can be reduce dramatically. The aftermath of an ice storm may result in severe flooding due to sudden thawing, with large quantities of displaced water, especially near lakes, rivers, and bodies of water.

o   Drought: Another form of severe weather is drought, which is a prolongued period of persistently dry weather (that is, absence of precipitation).[87]Although droughts do not develop or progress as quickly as other forms of severe weather,[88] their effects can be just as deadly; in fact, droughts are classified and measured based upon these effects.[87] Droughts have a variety of severe effects; they can cause crops to fail,[88] and they can severely deplete water resources, sometimes interfering with human life.[87] A drought in the 1930s known as the Dust Bowl affected 50 million acres of farmland in the central United States.[87] In economic terms, they can cost many billions of dollars: a drought in the United States in 1988 caused over $40 billion in losses, exceeding the economic totals of Hurricane Andrew, the Great Flood of 1993, and the 1989 Loma Prieta earthquake.[88] In addition to the other severe effects, the dry conditions caused by droughts also significantly increase the risk of wildfires

o   Heat Waves: Although official definitions vary, a heat wave is generally defined as a prolonged period with excessive heat.[89] Although heat waves do not cause as much economic damage as other types of severe weather, they are extremely dangerous to humans and animals: according to the United States National Weather Service, the average total number of heat-related fatalities each year is higher than the combined total fatalities for floods, tornadoes, lightning strikes, and hurricanes.[90] In Australia, heat waves cause more fatalities than any other type of severe weather.[89] As in droughts, plants can also be severely affected by heat waves (which are often accompanied by dry conditions) can cause plants to lose their moisture and die.[91] Heat waves are often more severe when combined with high humidity

9. Atoms, Elements, and Molecules

The atom is the basic unit of matter composed of a nucleus surrounded by an electron cloud according to the model introduced by Niels Bohr in 1913. The electrons are held in “orbit” around the nucleus by electrostatic forces.

A.        Parts of an Atom

o   Neutrons: The neutron is a subatomic hadron particle which has the symbol n or n0, no net electric charge and a mass slightly larger than that of a proton. The number of neutrons in an atom (mass number) is equal to the atomic mass-number of protons. James Chadwick discovered neutrons in 1932.

o   Protons: The proton is a subatomic particle with the symbol p or p+ and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom. The number of protons in each atom is its atomic number. Ernest Rutherford is given credit for discovering the proton. Protons belong to a class of particles called baryons which means each is composed of 3 quarks.

o   Electrons: The electron (symbol: e−) is a subatomic particle with a negative elementary electric charge. An electron has no known components or substructure. It is generally thought to be an elementary particle.[2] An electron has amass that is approximately 1/1836 that of the proton. Discovered by J.J. Thompson in 1897. Neutral atoms have an equal number of protons and electrons. Electrons are arranged in “shells” around an atom. The outermost electrons are called valence electrons and are responsible for all chemical activity. Electrons belong to a class of elementary particles called leptons which when uncharged are called neutrinos.

o   A quark (pron.: /ˈkwɔrk/ or /ˈkwɑrk/) is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei.[1] Due to a phenomenon known as color confinement, quarks are never directly observed or found in isolation. Most of what we know about quarks has come from studying hadrons themselves such as the efforts of the Large Hadron Collider at CERN in Switzerland.

o   Hadrons are any particles made out of quarks (alternatively, any particle affected by the strong nuclear force). Generally, this means the baryons and the mesons. All hadrons are colorless (in the sense of the combined color of their constituent quarks). The name "hadron" comes from the Greek for "thick."

• Gluons  carry the strong nuclear force and bind hadrons together. Gluons have no charge and no mass, but do have color (in the sense of quarks). This color cannot be observed directly because the gluons are part of the larger hadron. The name comes from their role in "gluing" quarks together.

B. Types of Reactions

Ions form when an atom loss or gains electrons. Anions are negatively charged because they have gained electrons. Cations are positively charged because they have lost electrons.

Ionic compounds form due to an attraction between ions of opposite charges. Covalent compounds form when electrons are shared between 2 atoms.

1) Combustion: A combustion reaction is when oxygen combines with another compound to form water and carbon dioxide. These reactions are exothermic, meaning they produce heat. An example of this kind of reaction is the burning of napthalene:

C10H8 + 12 O2 ---> 10 CO2 + 4 H2O

2) Synthesis: A synthesis reaction is when two or more simple compounds combine to form a more complicated one. These reactions come in the general form of:

A + B ---> AB

One example of a synthesis reaction is the combination of iron and sulfur to form iron (II) sulfide:

8 Fe + S8 ---> 8 FeS

3) Decomposition: A decomposition reaction is the opposite of a synthesis reaction - a complex molecule breaks down to make simpler ones. These reactions come in the general form

AB ---> A + B

One example of a decomposition reaction is the electrolysis of water to make oxygen and hydrogen gas:

2 H2O ---> 2 H2 + O2

4) Single displacement: This is when one element trades places with another element in a compound. These reactions come in the general form of:

A + BC ---> AC + B

One example of a single displacement reaction is when magnesium replaces hydrogen in water to make magnesium hydroxide and hydrogen gas:

Mg + 2 H2O ---> Mg(OH)2 + H2

5) Double displacement (metathesis): This is when the anions and cations of two different molecules switch places, forming two entirely different compounds. These reactions are in the general form:

AB + CD ---> AD + CB

One example of a double displacement reaction is the reaction of lead (II) nitrate with potassium iodide to form lead (II) iodide and potassium nitrate:

Pb(NO3)2 + 2 KI ---> PbI2 + 2 KNO3

6) Acid-base: This is a special kind of double displacement reaction that takes place when an acid and base react with each other. The H+ ion in the acid reacts with the OH- ion in the base, causing the formation of water. Generally, the product of this reaction is some ionic salt and water:

HA + BOH ---> H2O + BA

One example of an acid-base reaction is the reaction of hydrobromic acid (HBr) with sodium hydroxide:

HBr + NaOH ---> NaBr + H2O

Periodic Table

Russian chemistry professor Dmitri Mendeleev and German chemist Julius Lothar Meyer independently published their periodic tables in 1869 and 1870, respectively. Mendeleev's table was his first published version; that of Meyer was an expanded version of his (Meyer's) table of 1864.They both constructed their tables by listing the elements in rows or columns in order of atomic weight and starting a new row or column when the characteristics of the elements began to repeat.

o   Electronegativity is the tendency of an atom to attract electrons.[31] An atom's electronegativity is affected by both its atomic number and the distance between the valence electrons and the nucleus. The higher its electronegativity, the more an element attracts electrons. It was first proposed by Linus Pauling in 1932.[32] In general, electronegativity increases on passing from left to right along a period, and decreases on descending a group.

o   The electron affinity of an atom is the amount of energy released when an electron is added to a neutral atom to form a negative ion. It increases across a period and decreases down a group.

o   Atomic radii vary in a predictable and explainable manner across the periodic table. For instance, the radii generally decrease along each period of the table, from the alkali metals to the noble gases; and increase down each group.

o   The first ionization energy is the energy it takes to remove one electron from an atom, the second ionization energy is the energy it takes to remove a second electron from the atom, and so on. Increases across a period and decreases down a group.

10. Plants

A. Classification

o   The flowering plants (angiosperms), also known as Angiospermae or Magnoliophyta, are the most diverse group of land plants. Angiosperms are seed-producing plants like the gymnosperms and can be distinguished from the gymnosperms by a series of synapomorphies (derived characteristics). These characteristics include flowers, endosperm within the seeds, and the production of fruits that contain the seeds. Etymologically, angiosperm means a plant that produces seeds within an enclosure; they are fruiting plants, although more commonly referred to as flowering plants.

o   Monocotyledon: 1 cotyledon or seed leaf

o   Dicotyledon: 2 seed leaves

o   The gymnosperms are a group of seed-producing plants that includes conifers, cycads, Ginkgo, and Gnetales. The term "gymnosperm" comes from the Greek word gymnospermos (γυμνόσπερμος), meaning "naked seeds", after the unenclosed condition of their seeds (calledovules in their unfertilized state). Their naked condition stands in contrast to the seeds and ovules of flowering plants (angiosperms), which are enclosed within an ovary. Gymnosperm seeds develop either on the surface of scales or leaves, often modified to form cones, or at the end of short stalks as in (Ginkgo).

o   Conifers: They are cone-bearing seed plants with vascular tissue; all extant conifers are woody plants, the great majority being trees with just a few being shrubs. Typical examples of conifers include cedars, Douglas firs, cypresses,firs, junipers, kauri, larches, pines, hemlocks, redwoods, spruces, and yews.[

o   Deciduous means "falling off at maturity" or "tending to fall off", and is typically used in reference to trees or shrubs that lose their leavesseasonally, and to the shedding of other plant structures such as petals after flowering or fruit when ripe.

o   In botany, an evergreen plant is a plant that has leaves in all seasons. This contrasts with deciduous plants, which completely lose their foliage during the winter or dry season. There are many different kinds of evergreen plants, both trees and shrubs. Evergreens include:

§  most species of conifers (e.g., hemlock, blue spruce, red cedar, and white/scots/jack pine)

§  live oak, holly, and "ancient" gymnosperms such as cycads

§  most angiosperms from frost-free climates, such as eucalypts and rainforest trees

B. Anatomy

Xylem is one of the two types of transport tissue in vascular plants (phloem is the other). The word xylem is derived from the Greekword ξύλον (xylon), meaning "wood"; the best-known xylem tissue is wood, though it is found throughout the plant. Its basic function is to transport water, but it also transports some nutrients through the plant.

In vascular plants, phloem is the living tissue that carries organic nutrients (known as photosynthate), in particular, sucrose,[1] a sugar, to all parts of the plant where needed. In trees, the phloem is the innermost layer of the bark, hence the name, derived from theGreek word φλόος (phloos) meaning "bark". The phloem is concerned mainly with the transport of soluble organic material made during photosynthesis. This is called translocation.

11. Simple Machines

A. A lever (pron.: /ˈlɛvər/ or UK /ˈliːvər/) is a machine consisting of a beam or rigid rod pivoted at a fixed hinge, or fulcrum. It is one of the sixsimple machines identified by Renaissance scientists. The word comes from the French lever, "to raise", cf. a levant. A lever amplifies an input force to provide a greater output force, which is said to provide leverage. The ratio of the output force to the input force is theideal mechanical advantage of the lever.

B. The wheel and axle is generally considered to be a wheel attached to an axle so that these two parts rotate together in which a force is transferred from one to the other. In this configuration a hinge, or bearing, supports the rotation of the axle. Hero of Alexandria identified the wheel and axle as one of five simple machines used to lift weights.[2] This is thought to have been in the form of the windlass which consists of crank or pulley connected to a cylindrical barrel that provides mechanical advantage to wind up a rope and lift a load such as a bucket from a well.

C. A pulley is a wheel on an axle that is designed to support movement of a cable or belt along its circumference.[1] Pulleys are used in a variety of ways to lift loads, apply forces, and to transmit power. A pulley is also called a sheave or drum and may have a groove between two flanges around its circumference. The drive element of a pulley system can be a rope, cable, belt, or chain that runs over the pulley inside the groove.

D. An inclined plane is a flat supporting surface tilted at an angle, with one end higher than the other, used as an aid for raising or lowering a load. Inclined planes are widely used to move heavy loads over vertical obstacles; examples vary from a ramp used to load goods into a truck, to a person walking up a pedestrian ramp, to an automobile or railroad train climbing a grade.

E. A wedge is a triangular shaped round tool, a compound and portable inclined plane, and one of the six classical simple machines. It can be used to separate two objects or portions of an object, lift an object, or hold an object in place. It functions by converting a force applied to its blunt end into forces perpendicular (normal) to its inclined surfaces.

F. A screw is a mechanism that converts rotational motion to linear motion, and a torque (rotational force) to a linear force.[1] It is one of the six classical simple machines. The most common form consists of a cylindrical shaft with helical grooves or ridges called threads around the outside.[2][3] The screw passes through a hole in another object or medium, with threads on the inside of the hole that mesh with the screw's threads. When the shaft of the screw is rotated relative to the stationary threads, the screw moves along its axis relative to the medium surrounding it; for example rotating a wood screw forces it into wood. In screw mechanisms, either the screw shaft can rotate through a threaded hole in a stationary object, or a threaded collar such as a nut can rotate around a stationary screw shaft.[4][5]Geometrically, a screw can be viewed as a narrow inclined plane wrapped around a cylinder.[1]

Divisibility Rules