NES Elementary Education Subtest 2 – Flashcards
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N = {1, 2, 3, 4, 5, 6, . . . }
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Natural Numbers
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W = {0, 1, 2, 3, 4, 5, 6, . . . }
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Whole natural numbers together with zero.
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2 + (-2) = 0
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Every whole number has a unique opposite or negative whose sum with it is 0. For example,
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Z = {. . ., -3, -2, -1, 0, 1, 2, 3, . . . }
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The set of integers consists of the whole numbers and their opposites.
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2 Ă— 1/2 = 1
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Every nonzero integer has a unique reciprocal whose product with it is one. For example,
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2/3 = 2 Ă— 1/3
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The ratio or fraction of one integer to a nonzero integer is the product of the first integer with the reciprocal of the second. For example, the ratio of 2 to 3 is
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1/2 = 0.5
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not every rational number is an integer. For example, 1/2 is a rational number that is not an integer.
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commutativity, associativity and identity.
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There are three basic properties of addition:
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When adding two numbers, the sum is the same regardless of the order in which the numbers are added. 2 + 3 = 3 + 2
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Commutative property.
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When adding three or more numbers, the sum is the same regardless of the way in which the numbers are grouped. 2 + (3 + 5) = (2 + 3) + 5
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Associative property.
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Adding zero to a number does not change it. 2 + 0 = 2
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Identity property.
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commutativity, associativity and identity.
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There are three basic properties of multiplication:
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The product of a number with a sum equals the sum of the products of the number with each term of the sum. 2 Ă— (3 + 5) = (2 Ă— 3) + (2 Ă— 5)
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Distributive property.
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Exponentiation is repeated multiplication. An exponent is often called a power. For example, the third power of 2 is 2Âł = 2 Ă— 2 Ă— 2 = 8
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Exponentiation
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(-3)0 = 1
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We define the zero power of any nonzero number to be 1. For example,
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2 (-3rd power) =1 / 2 (3rd power) = 1 / 8
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A negative exponent indicates a reciprocal. For example,
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2 (to the 1st power) = 2
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The first power of any number is itself. For example,
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2 (to the 3rd) x 2 (to the 5th) = 2 (to the eighth)
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To multiply like bases with exponents, add the exponents. For example,
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(2 to the 3rd) to the 5th = 2 to the 15th
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To exponentiate a power, multiply the exponents. For example,
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1
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10 to the 0 power
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10
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10 to the 1 power
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1 / 10 to the 2 power or 1 / 100
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10 to the -2 power
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10 to the 5 power
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10 to the 2 power x 10 to the 3 power
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2045 = (2 x 10 to the 3 power) + (0 x 10 to the 2 power) + (4 x 10 to the 1 power) + 5 x 10 to the 0 power)
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Identifying Place Value in Numbers 2045
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23.405 = (2 x 10 to the 1 power) + (3 x 10 to the 0 power) + (4 x 10 to the -1 power) + (0 x 10 to the -2 power) + (5 x 10 to the -3 power)
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Digits to the right of a decimal point correspond to negative powers of ten. For example, 23.405
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3 divided by 8 = 0.375
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Converting a fraction to a decimal. For example 3/8
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45/100
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convert 0.45 to a fraction.
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3 + 208/1000
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convert 3.208 to a mixed number.
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2/5 = .4 = 40%
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Converting a fraction to a percentage. Convert the fraction to a decimal and then convert the decimal to a percentage. For example, 2/5
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65/100
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Converting a percentage to a fraction. Convert the percentage to fraction with a denominator of 100. For example, 65%
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coordinate
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A fundamental concept of mathematics is that the set of real numbers is in one-to-one correspondence with the set of points on a line. That is, each real number corresponds to exactly one point on a line, and each point on a line corresponds to exactly one real number, called the _____ of the point
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2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, ...
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It is worthwhile to memorize the first several prime numbers.
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composite
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A natural number is _____ if it is greater than 1 and not prime.
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To find the prime factorization of a number, it is helpful to know a few tests for divisibility.
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Divisibility Tests
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If the last digit is even, then the number is divisible by 2. For example, 158 is divisible by 2 since its last digit is 8.
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Divisibility by 2.
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If the sum of the digits is divisible by 3, then the number is also. For example, 177 is divisible by 3 since the sum of its digits is 15 (1 + 7 + 7 = 15), and 15 is divisible by 3.
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Divisibility by 3.
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If the last two digits form a number divisible by 4, then the number is divisible by 4. For example, 316 is divisible by 4 since 16 is divisible by 4.
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Divisibility by 4.
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If the last digit is a 5 or a 0, then the number is divisible by 5. For example, 1995 is divisible by 5 since its last digit is 5.
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Divisibility by 5.
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If the number is divisible by both 3 and 2, then it is also divisible by 6. For example, 168 is divisible by 6 since it is divisible by 2, and it is divisible by 3.
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Divisibility by 6.
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If the last three digits form a number divisible by 8, then the number itself is also divisible by 8. For example, 1,120 is divisible by 8 since 120 is divisible by 8.
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Divisibility by 8.
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If the sum of the digits is divisible by 9, then the number itself is also divisible by 9. For example, 369 is divisible by 9 since the sum of its digits is 18 (3 + 6 + 9 = 18), and 18 is divisible by 9.
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Divisibility by 9.
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If the number ends in 0, then it is divisible by 10. For example, 670 is divisible by 10 since its last digit is 0.
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Divisibility by 10.
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0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ... beginning with 0 and 1 so that each term beginning with the third term is the sum of the two preceding terms.
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The Fibonacci Sequence. The Fibonacci sequence is the sequence
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12, 22, 32, 42, 52, 62, 72, 82, 92, 102, 112,... or 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 ...
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The Sequence of Squares. The sequence of squares of natural numbers is an important sequence.
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Constants are symbols that represent fixed values. In the expression 3x + 7, the constants are 3 and 7.
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Constants.
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Variables are symbols that stand for changing values. Most often we use letters of the alphabet for variables. In the expression 3x + 7, the letter x is a variable. The value of the expression depends on the specific number we substitute for x. For example, if we substitute 2 for x, the value of the expression is 3(2) + 7 = 13.
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Variables.
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Operators are symbols such as +, -, Ă— and / that represent operations such as addition, subtraction, multiplication, and division.
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Operators.
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Relations are symbols that compare expressions. Common relations are =, , ≤, and ≥.
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Relations.
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Grouping symbols are symbols such as parentheses ( ) and brackets [ ] that indicate the order in which we should interpret the operations and the relations in a mathematical expression.
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Grouping symbols.
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function
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A _____ f is a set of ordered pairs that pairs each element x of one set, called the domain (input) of the function, with a unique element f(x) of another set, called the range (output) of the function.
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C = 2Ď€r
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A circle with radius r has circumference, C, given by
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A = πr²
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and an area, A, given by
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d = 2r
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The diameter of circle, d, is twice the radius. That is,
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All living organisms exhibit homeostasis, or the ability to maintain a state of internal balance. For example, if the environmental temperature increases, the human body begins to perspire, and the cooling effect of evaporation decreases the surface temperature of the skin. Likewise, a disruption in any system will set off a diverse set of control mechanisms that return the organism to a state of internal balance.
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Homeostasis.
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Energy.
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Every living thing needs energy that they produce or acquire in order to exist, grow, and reproduce. Some organisms (called autotrophic organisms) are capable of harnessing energy from sunlight and using it to produce glucose, the main source of energy for the organism. Others (called heterotrophic organisms) capture energy by eating plants or other animals.
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are capable of harnessing energy from sunlight and using it to produce glucose, the main source of energy for the organism.
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autotrophic organisms)
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capture energy by eating plants or other animals.
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heterotrophic organisms)
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organelles
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Animal and plant cells contain smaller structures, called _____, which are specialized to fulfill specific functions within the cell. Mitochondria, for example, break down glucose to provide energy to the cell. Bacterial cells lack most of these organelles.
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Mitochondria
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_____, for example, break down glucose to provide energy to the cell.
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connective, epithelial, muscle, and nerve.
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Humans have four basic types of tissues:
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of or belonging to the epithelium
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epithelial
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membranous tissue covering internal organs and other internal surfaces of the body
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epithelium
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The Human body has 11 organ systems—circulatory, digestive, endocrine, excretory, immune, integumentary, muscular, nervous, reproductive, respiratory, and skeletal.
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The Human body has _____ organ systems—circulatory, digestive, endocrine, excretory, immune, integumentary, muscular, nervous, reproductive, respiratory, and skeletal.
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xylem and phloem
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The plants discussed in this section are vascular plants; they have a system of tubes (_____ _____ _____) that are used to transport nutrients and water.
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chloroplast
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Chlorophyll, which is contained within a cell organelle called the ______, captures the light from the Sun;
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6 CO2 + 6 H2O → C6H12O6 + 6 O2 Carbon dioxide + Water + Light energy → Glucose + Oxygen
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The chemical formula for photosynthesis is:
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Scientists believe that there are over 10 million different kinds of life forms, or species, on Earth.
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Scientists believe that there are over _____ million different kinds of life forms, or species, on Earth.
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The system currently used by taxonomists is called the Linnaean taxonomic system, in honor of Swedish biologist Carolus Linnaeus (1707-1778), one of the founders of the modern system of biological classification.
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The system currently used by taxonomists is called the _____ taxonomic system, in honor of Swedish biologist Carolus Linnaeus (1707-1778), one of the founders of the modern system of biological classification.
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Eukaryotes consist of all organisms with cells that have true nuclei and membrane-bound organelles. Four kingdoms—animals, plants, protists, and fungi—fit into this domain.
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Eukaryotes.
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Prokaryotes have neither nuclei nor organelles with membranes. True bacteria fit in this domain.
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Prokaryotes.
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Archaea are microorganisms similar to bacteria in form but genetically so vastly different from everything else on the planet that they deserve their own unique branch on the tree of life. Archaea are often found in extreme environments including acidic conditions, boiling hot springs, deep ocean vents, or polar ice.
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Archaea.
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Kingdom Phylum Class Order Family Genus Species
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Modern taxonomy uses genetic analysis and comparison of physical traits to classify organisms according to a hierarchy of taxonomic ranks. These include
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Eggs are laid by the adult female insect. Females lay a lot of eggs so that at least some of them will survive.
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Egg.
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Larvae hatch from the eggs and bear no resemblance to their adult parents. The larva has only one job—to eat and eat so it can grow quickly. Larvae can grow 100 times their size during this stage. Butterfly and moth larvae are caterpillars, fly larvae are maggots, and beetle larvae are grubs. Eventually, when growth is complete, the larva is transformed into a pupa.
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Larva.
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The pupa stage is usually considered a resting stage, although much activity is going on within a sealed chrysalis or cocoon. Special cells that were present in the larva are now growing rapidly and will become the legs, wings, eyes and other parts of the adult insect. After the reorganization is complete, the pupa splits to reveal the mature adult with functional wings. This stage can last a few weeks, a month, or even several years.
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Pupa.
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See the last four
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Complete Metamorphosis
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About 12 percent of all insects go through incomplete metamorphosis. These include stinkbugs, earwigs, crickets, grasshoppers, cockroaches, ants, praying mantis, and dragonflies. Incomplete metamorphosis has only three life cycle stages: egg, nymph, and adult. The nymph looks similar to, but is a smaller version of, the adult. The nymph is also wingless. As nymphs grow, they shed their hard exoskeletons, a process called molting. There is no pupal stage during incomplete metamorphosis.
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Incomplete Metamorphosis
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egg, nymph, and adult.
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Incomplete metamorphosis has only three life cycle stages: ____ ____ ____
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Heredity is defined as the transmission of characteristics carried by the genetic code from one generation to the next. Characteristics may be physical, physiological, or psychological as long as they are carried by the genes. Heredity explains why offspring look like their parents and why dogs always give birth to puppies and never guppies or butterflies. Through heredity, living things inherit traits from their parents.
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Heredity
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Chromosomes are microscopic, threadlike structures that contain the genes that carry hereditary information from one generation to the next. Each chromosome contains many genes. Different organisms may have different numbers of chromosomes. In sexually reproducing organisms, chromosomes occur in pairs—one chromosome of each pair comes from the mother and one from the father. Humans have 23 pairs of chromosomes. One pair, consisting of two X chromosomes (XX) in females or an X and a Y chromosome (XY) in males determines the gender of the offspring. The other 22 pairs are called somatic chromosomes because their genes produce proteins for building the body rather than determining gender. In eukaryote organisms, chromosomes, and their genes are found in the nucleus, which is surrounded by its own membrane. In bacteria, no nucleus is present and the chromosomes are found in the cytoplasm of the cell.
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Genes
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22
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The other _____ pairs are called somatic chromosomes because their genes produce proteins for building the body rather than determining gender.
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sun → grass → grasshopper → toad → snake → hawk → bacteria of decay
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A simple food chain might look like this:
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In a commensal relationship, members of different species live together, and one member benefits without seriously affecting the other party. As a rule, the animal that benefits is usually the physically smaller of the two. The commensal organism may depend on its host for food, shelter, support, or transportation. The animal that benefits is known as the commensal, or symbiont, while the nonbenefitting species is known as the host. For example, some flatworms live attached to the gills of the horseshoe crab, obtaining bits of food from the horseshoe crab's meals; the horseshoe crab is apparently unaffected.
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Commensalism.
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In mutualism, members of two different species benefit by associating together. For example, many plant species require an animal to visit its flowers for pollination. The animal benefits in this relationship by having a source of food (nectar or pollen), while the plant benefits by having its ovules fertilized.
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Mutualism.
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In parasitic relationships, one species receives a benefit from the relationship to the detriment of the other species. For example, there are parasitic fishes, such as the lamprey, that attach themselves to other fishes and suck their body fluids. Similiarly, tapeworms may attach to the intestines of host humans in their intestines. They constantly take in nutrients and can eventually cause organ and tissue damage.
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Parasitism.
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quark
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At the present time, scientists believe that the most fundamental particle of matter is the _____.
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118, 95
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In total, _____ elements have been observed as of March 2010, and new elements continue to be discovered. Of these, _____ occur naturally; the others are produced in laboratories.
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Compounds
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_____ are groups of two or more elements that are bonded together through chemical change.
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Law of Conservation of Matter
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Atoms are neither gained nor lost during a chemical change. This is the _____ ______ _____ _____ _____ ; matter can neither be created nor destroyed in a chemical reaction. In a chemical change, however, a new substance is formed, and there may be accompanying clues that a chemical reaction has taken place, such as light, heat, color change, gas production, odor, or sound.
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Newton's First Law of Motion states that an object at rest will remain at rest and a body moving with a constant speed in a straight line will maintain its motion unless acted upon by an unbalanced external force. An example of force that opposes the motion of a body is friction.
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Newton's First Law.
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Any change in motion involves acceleration, or how much the velocity of an object changes in a certain time. This is where Newton's Second Law applies; it gives us the relationship between force, mass, and acceleration. Using Newton's Second Law, force is expressed by the mathematical equation, F=ma or Force=Mass Ă— Acceleration. The greater the mass of the object being accelerated, the greater the amount of force needed to accelerate the object.
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Newton's Second Law.
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Newton's Third Law states that all forces in the universe occur in equal but oppositely directed pairs; for every action, there is an equal and opposite reaction. Rockets and jet planes capitalize on Newton's Third Law. Each discharge hot gases in one direction (an action force so as to produce thrust (a reaction force). In both rocket and jet engines, chemical energy is changed to the energy of motion.
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Newton's Third Law.
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An inclined plane is a slanted surface used to raise an object. A ramp is an inclined plane. When an object is moved up an inclined plane, less effort is needed than if you were to lift it straight up, but you must move the object over a greater distance.
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Inclined plan.
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A wedge is an inclined plane which moves. Most wedges (but not all) are combinations of two inclined planes. A knife, axe, razor blade, and teeth are all good examples of wedges. Generally, it can be anything that splits, cuts, or divides another object including air and water.
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Wedge.
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A screw, like a wedge, is another form of an inclined plane. A screw is an inclined plane wrapped around a cylinder to form a spiral.
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Screw.
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A lever has three parts: a fulcrum, an effort arm, and a resistance arm. There are three types, or classes, of levers. In all first class levers, the Fulcrum is between the Effort and Resistance (ex., seesaw). In all second class levers, the Resistance is between Fulcrum and the Effort (ex., wheelbarrow). In all third class levers the Effort is between the Resistance and Fulcrum (ex., baseball bat and tweezers).
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Lever.
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A pulley is a chain, belt or rope wrapped around a wheel. The mechanical advantage of a pulley system is approximately equal to the amount of supporting ropes or strands. A rig on a flagpole or a sailing mast are examples of pulleys.
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Pulley.
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A wheel and axle is a lever that rotates in a circle around a center point, or fulcrum. The larger wheel (or outside) rotates around the smaller wheel (axle). Bicycle wheels, Ferris wheels and gears are all examples of a wheel and axle. Wheels can also have a solid shaft with the center core as the axle such as a screwdriver or drill bit or the log in a log rolling contest.
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Wheel and axle.
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are two or more simple machines working together. A wheelbarrow is an example of a complex machine that uses a lever and a wheel and axle. Machines of all types make work easier by changing the size or direction of an applied force.
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Compound machines
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electromagnetic (EM) radiation
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Visible light, or the light energy we see, is only one small portion of a family of waves called _____ _____ _____. If you listen to the radio, watch television, have your teeth x-rayed, talk on a cell phone, or use a microwave oven, you are making use of different types of electromagnetic radiation. Electromagnetic waves are generated by accelerating electric charges. For example, if an electric charge oscillates back and forth, it will radiate energy in the form of an electromagnetic wave. The quickness, or frequency at which charges oscillate, determines the type of electromagnetic radiation produced.
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A measure of the distance between a wave's crest and trough
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Amplitude.
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The number of oscillations the wave undergoes in a certain amount of time
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Frequency.
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electromagnetic spectrum
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The entire range of electromagnetic waves is referred to as the _____ _____
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radio waves, microwaves, infrared, visible, ultraviolet, X-rays, and gamma-rays.
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The wavelengths in the electromagnetic spectrum vary in size from very long radio waves the size of buildings, to very short gamma-rays smaller than the size of the nucleus of an atom; they include, from longest wavelength to shortest:
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the angle of incidence equals the angle of reflection. Scattering is merely a reflection from a rough surface. Incoming light waves are reflected at many different angles because the surface is uneven.
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the Law of Reflectance:
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convex lens
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The most commonly-seen type of lens is the _____ _____. A convex lens is a converging lens; it focuses the light passing through it to a point. A convex lens is used to bend light in a magnifying glass so objects appear larger than they really are. A concave lens spreads out light rays that have been refracted through it.
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concave
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A _____ lens is used to correct short-sightedness.
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In order to understand static electricity, it is important to review the basics of atoms. An atom consists of protons, electrons, and neutrons. Protons have a positive charge, electrons are negatively charged, and neutrons have no charge. Because atoms normally have the same number of electrons as protons, the positive and negative charges cancel each other out and, as a result, atoms usually have no charge; they are neutral. Static electricity is the result of an imbalance between negative and positive charges in an object. Normally, the protons and neutrons in the nucleus are held together very tightly. But some of the outer electrons are held very loosely; they can move from one atom to another. If an electron is removed from a neutral atom, the atom is left with more positive particles and acquires a positive charge. If an electron is added to a neutral atom, the atom has more negative particles and acquires a negative charge. The more positive atoms or negative electrons you have, the stronger the attraction for the other. For example, rubbing a shoe against a carpet creates an excess of electrons. When reaching and touching a doorknob a shock, or tiny spark, is felt or seen; excess electrons are released to recreate a balance of electrons and protons in atoms. Lightning is also a result of static electricity.
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Static electricity.
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Current electricity comes from a stream of electrons moving through a conductor, such as copper. Some materials allow charges, usually electrons, to flow through the material. These materials are called conductors, and the flow of charge is called current. Some materials are better conductors than others; they offer very little resistance to the flow of electrons. Most metals are very good conductors—copper, silver, gold, aluminum, or steel, for example. However, not all substances are good conductors. Materials that do not conduct electricity well are called insulators. Rubber, plastic, wood, cloth, glass, and dry air are good insulators; they have very high resistance to the flow of electrons.
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Current electricity.
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insulators
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Materials that do not conduct electricity well are called_____.
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closed
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In a circuit, electrons travel along a conductor in _____ loops.
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circle
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The word circuit means _____
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A magnet is any object that has the ability to attract ferrous objects like iron, steel, nickel, and cobalt. Magnetite, called lodestone for many years, is a naturally occurring iron ore that has this ability. Most permanent magnets we use are manufactured and are a combination or alloy of aluminum, nickel, cobalt, and iron, although none of these metals is naturally magnetic. The magnetic field in a permanent magnet is a result of electron spin. A magnetic field is produced by spinning electrons in an atom. Every atom is essentially a small magnet with a north pole and a south pole. In nonmagnetic materials, electrons spin in random directions, so the magnetic field is not noticeable. In magnets, however, the electrons all spin in the same direction—they are aligned—and create a north pole and a south pole. When a bar magnet is suspended at its center by a string, it will rotate until one end points north. That end is called the north pole of the magnet and the end that points south is called the south pole. In magnets, unlike poles attract, and like poles repel. Either pole, however, can attract iron objects such as pins and paper clips. That is because under the influence of a nearby magnet, each pin or paper clip becomes a temporary magnet, with its poles arranged in a way appropriate to magnetic attraction.
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Magnetism
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Magnetite
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_____, called lodestone for many years, is a naturally occurring iron ore that has this ability.
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magnetic field
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Surrounding all magnets is a region called the _____ _____.
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related
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Electricity and magnetism are closely _____. The movement of electrons creates a magnetic field, so electric current creates a magnetic field. This magnetic property can be used to make powerful electromagnets. You can make an electromagnet by simply coiling wire around a thin rod made of iron or steel (a nail will work, too). When an electric current moves through the wire, it makes a magnetic field. The strength of the magnetic flow is dependent on the number of times the wire is coiled around the rod, and the value of the current is dependent on the flow through the conductor. The strength of the electromagnet becomes greater as the number of loops of wire around the core is increased.
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Energy stored in bonds of atoms and molecules is described as chemical energy. Gasoline and coal contain stored chemical energy.
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Chemical energy.
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Electrical energy is produced by the movement of electrically-charged particles (electrons). The movement of electrons through a conductor, such as a wire, is called current (or circuit) electricity. Lightning is an example of a giant spark of static electricity, or the sudden movement of electrons from a cloud to another surface.
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Electrical energy.
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Heat energy is created by the random movement of molecules from a warm substance to a cool substance. Temperature, measured in degrees, is an indication of the average kinetic energy of the moving molecules—the speed at which they move. If the molecules in a substance move slowly, the substance has a low temperature. If the molecules move rapidly, the substance has a high temperature. Heat energy is transferred in three ways.
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Heat energy.
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Conduction is the process by which energy is transferred through matter by collisions between particles. It is the transfer of heat energy from atom to atom within a substance. As one molecule is heated, it begins to vibrate. As it does, it passes some of its energy to other molecules around it. Through this process, all the molecules of an object pass energy from one to another, until they are all hot. This is conduction. For example, a metal spoon in a cup of hot soup becomes warmer because the molecular motion of the hot soup molecules is transferred, via collisions, along the length of the spoon, to the molecules in the metal spoon.
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Conduction.
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Convection is the transfer of heat in a gas or liquid by the circulation of currents from one region to another. In convection, the molecules get heated and rise up; the cold molecules sink and get reheated. Then they rise again to continue the cycle. For example, heat leaves a coffee cup as the currents of steam and air rise. During convection, mass is transferred from one location to another.
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Convection.
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Radiation is the transfer of energy by electromagnetic waves through space. Sunlight is a form of radiation that is radiated through space to our planet through a vacuum.
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Radiation.
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Nuclear energy is stored in the nucleus of an atom—the energy that holds the nucleus together. Energy is released when nuclei are combined or split apart. Einstein showed that this energy is equivalent to mass. Nuclear power plants produce energy by splitting the nuclei of uranium atoms through a process called nuclear fission.
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Nuclear energy.
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The phases, or changes in appearance of the moon, depend on its position relative to the position of the sun. When the moon is between the sun and Earth, the side of the moon facing the Earth is dark. This is called a New Moon. As the moon travels eastward in its orbit, more of its sunlit side becomes visible to Earth and the moon is said to be waxing. As the moon orbits Earth, the side of the moon facing Earth eventually becomes fully lit. This is called a Full Moon phase. As the moon continues to around in its orbit, the lit portion of the moon visible to Earth becomes smaller, so the moon is now said to be waning. As it completes its revolution around Earth, the moon starts the cycle again as a New Moon. The four phases are illustrated in Figure 6.13.
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Moon phases.
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Earth's geosphere can be divided into three main layers—the crust, mantle, and core. Physical conditions in Earth's interior vary from layer to layer partly because, as temperature and pressure increase with depth, and the properties of rocks and minerals change.
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The Geosphere
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Project 2061
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_____ _____ proposes two principal reasons for including knowledge of science history as part of any discussion of the tenets, goals, and values of science.