ILTS Elementary Education (305-Content Test) 2024/2025 100% VERIFIED SOLUTIONS, Study Guides, Projects, Research of Education Planning And Management

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ILTS Elementary Education (305-Content Test) 2024/2025 100% VERIFIED SOLUTIONS Nouns A person, place, thing, or idea Common Noun The class or group of people, places, and things (not capitalized) Proper Nouns The names of a specific person, place, or thing (capitalized) General Nouns The names of conditions or ideas Specific Nouns Names people, places, and things that are understood by using your senses Collective Nouns The names for a person, place or thing that may act as a whole Pronouns Words that are used to stand in for a noun Nominative Nouns and Pronouns The case for nouns and pronouns that are the subject of a sentence Objective Nouns and Pronouns The case for nouns and pronouns that are an object in a sentence Possessive Nouns and Pronouns The case for nouns and pronouns that show possession or ownership How can Pronouns be Grouped? -Intensive (I myself, you yourself, he himself, she herself, the itself, we ourselves, you yourselves, they themselves) -Relative (which, who, whom, whose) -Interrogative (what, which, who, whom, whose) -Demonstrative (this, that, these, those) -Indefinite (all, any, each, everyone, either/neither, one, some, several) -Reciprocal (each other, one another) Transitive Verbs A verb whose action points to a receiver Intransitive Verbs A verb that does not point to a receiver of an action Action Verbs A verb that shows what subject is doing in a sentence Linking Verbs Link the subject of a sentence to a noun or pronoun or link a subject with an adjective Transitive Verbs-Active Voice The subject of the sentence is doing the action Transitive Verbs-Passive Voice The subject receives the action Past Verbs The action happened in the past Present Verbs The action happens at the current time Future Verbs The action is going to happen later Past Perfect Verbs The second action started in the past and the first action came before the second Present Perfect Verbs Indirect Objects A word or group of words that show how an action had an influence on someone or something Predicate Nominatives The word (noun or pronoun) that gets linked to the subject in the predicate that describe or define the subject Predicate Adjectives The word (adjective) that gets linked to the subject in the predicate that describe or define the subject Pronoun-Antecedents Agreement Pronouns and their antecedents agree when they have the same number and gender Clauses A group of words that contains both a subject and a predicate Independent Clauses Contains a complete thought (stands alone) Dependent/Subordinate Clauses Includes a subject and verb (cant stand alone) Adjective Clauses A dependent clause that modifies a noun or pronoun Essential Clauses Explains or defines a person or thing (no comma) Nonessential Clauses Give more information about a person or thing but are not necessary to define them (uses comma) Adverb Clauses A dependent clause that modifies a verb, adjective, or adverb Noun Clause A dependent clause that can be used as a subject, object, or complement Subordination When 2 related ideas are not of equal importance, the ideal way to combine them is to make the more important idea an independent clause, and the less important idea a dependent or subordinate clause Phrases A groups of words that functions as a single part of speech that adds detail or explanation to a sentence, or renames something in the sentence Prepositional Phrases Begins with a preposition and ends with a noun or pronoun that is the object of the preposition Verbal Phrases Formed from a verb but does not function as a verb Types of Verbals -Participle (always functions as an objective) -Gerund (always functions as a noun) -Infinitive (functions as a noun, adjective, or adverb) Participle Phrases Come right before or right after the noun or pronoun that they modify Gerund Phrases Can be used as the subject of a sentence, the predicate nominative, or the object of a verb or preposition Infinitive Phrases Includes the verbal itself and all of its complements or modifiers Appositive Phrases Used to explain or rename nouns or pronouns Absolute Phrases Consists of a noun followed by a participle to provide context to what is being describes in the sentence Proper Parallel Structures Items and ideas must be stated in grammatically equivalent ways Complete Sentence Has a subject and a verb or predicate Fragments Sentences without a complete thought Declarative Sentences States a fact and ends with a period Imperative Sentences Tells someone to do something and ends with a period Interrogative Sentences Asks a question and ends with a question mark Exclamatory Sentences Shows strong emotion and ends with an exclamation point Simple Sentences Has 1 independent clause with no dependent clauses Compound Sentences Has 2 or more independent clauses with no dependent clauses Complex Sentences Has 1 independent clause and at least 1 dependent clause Compound-Complex Sentences Has 2 independent clauses and at least 1 dependent clause Run-On Sentences Consist of multiple independent clauses that have not been joined together properly How to Correct Run-On Sentences? -Join Clauses Properly -Split into separate sentences -Make 1 clause dependent -Reduce to 1 clause with a compound verb Dangling Modifier -After the greeting in a formal letter, to show hours and minutes, and Separate a title and subtitle Parentheses Are used for additional information When do you use Quotation Marks? -Close off a persons spoken or written words -Titles and short works -Highlight irony -Inside for periods and commas -Outside for colons and semicolons Apostrophe Use to show possession or the deletion of letters in contractions Hyphens Used to separate compound words When do you use Hyphens? -Compound numbers -Written our fractions -Adjectives that come before a noun Dashes To show a break or a change in thought in a sentence or to act as parentheses in a sentence When do you use Dashes? -To set off parenthetical statements or an appositive with internal punctuation -To show a break or change in tone or thought Ellipsis Has 3 periods to show when words have been removed from a quotation When do you use Brackets? -When placing parentheses inside of parentheses -When adding clarification or detail to quotation that is not part of the quotation Commonly Confused Words -Which (used for things only) -That (used for people and things) -Who (used for people only) Homophones Words that sound alike, but have different spellings and definitions Examples of Homophones -To, too, and two -There, their, and they're -Knew and new -its and it's -your and you're Commonly Confused Words 2 -Then (sequence or order) -Than (comparison) Forms of Affect and Effect -Affect [n] (feeling, emotion, or mood that is displayed) -Affect [v] (to alter, to change, to influence) -Effect [n] (a result, a consequence) -Effect [v] (to bring about, to cause to be) Homographs Words that share the same spelling, but have different meanings and sometimes different pronunciation Examples of Homographs -Bank -Content -Fine -Incense -Lead -Object -Produce -Refuse -Subject -Tear What should be Addressed in the First Part of an Essay? -What is the subject of the lesson? -Analogy -Cause and effect -Process Coherence Details that fit together and flow well to clearly understand the main points Transitions Guide readers from idea to idea Thesis Main idea of the story that includes the topic and comment Analogies Comparisons between items that appear to have nothing in common Paragraph of Narration Tells a story or a part of a story Descriptive Paragraph Makes a verbal portrait of a person, place, or thing Process Paragraph Related to time order Comparing 2 Things Draws attention to their similarities and indicates a number of differences Why Start a New Paragraph? -Mark off introduction and conclusion -Signal a shift to a new idea or topic -Indicate an important shift in time -Explain a point in additional detail -Highlight a comparison, contrast, or cause and effect relationship Linguistic Form Encodes the literal meaning of words and sentences Writing Style Consists of different ways of encoding the meaning and indicating figurative and stylistic meaning Basic Effects of Writing Style -Communicate meaning -Authors attitude -Express feelings Formal Writing Addressing a superior in school or work environment Informal Writing Appropriate for private letters, personal emails, and business correspondence between close associates Cliches Phrases that have been overused to the point that the phrase has no importance or has lost the original meaning Jargon Specialized vocabulary that is used among members of a trade or profession Slang Informal and sometimes private language that is understood by some individuals Colloquiums Word or phrase that is found in informal writing Tone The writers attitude towards the topic, and to the audience Concisness Writing that you need to get your message across in the fewest words possible Figurative Language Language that goes beyond the literal meaning of a word or phrase Types of Figurative Language -Hyperbole (excessive exaggeration for humor) -Onomatopoeia (words that imitate the sounds they name) -Simile (compares using like or as) -Metaphor (compares without using like or as) -Personification (describing a thing or animal as a person) -Alliteration (series of words containing the same sound) -Imagery (create mental images of the story) Descriptive Language Evokes imagery in the readers mind to make a story come alive Figure of Speech Word of phrase that departs from straight forward, literal language Literacy The ability to read and write Reading Literacy Ability to read Writing Literacy Includes spelling, grammar, and sentence structure Phonological Awareness The ability to perceive sound structures in a spoken language Phonemes The sounds represented by the eaters in the alphabet Classroom Activities that Teach Phonological Awareness -Clapping to the sounds of individual words, names, or all words in a sentence -Print runs from left to right or top to bottom -The book has parts -The book has an author and contains a story -The illustrations can carry meaning -Letters and words are different -Words and sentences are separated by spaces and punctuation -There are different text forms -Print represents spoken language -How to hold a book Facts Children should know about Letters -Letters are distinct in appearance -Direction and shapes must be used to make each letter -Each letter has a name -There are 26 letters in the alphabet -Letters represent sounds of speech -Words are composed of letters and have meaning -To read, one must be able to correspond letters and sounds Decoding Method or strategy used to make sense of printed words and figure out how to correctly pronounce them Phonics Process of learning to read by learning how spoken language is represented by letters Fluency The goal of literacy development, to read accurately and quickly Vocabulary The list of words that students understand and comprehend How can Teacher Promote Vocabulary Development? -Prior knowledge -Defining Words -Context clues -Prefixes, roots, and suffixes -Dictionaries and thesaurus -Allow for practice -Print rich environment -Group Words into single subject Affixes Syllables attached to the beginning or end of a word to make a derivative or inflectional form of a word Prefixes Syllables that appear at the beginning of a word Root Words The base of a word to which affixes can be added Suffixes Syllables that appear at the end of a word Types of Suffixes -Noun suffix -Verb suffix -Adjective suffix Strategies to Improve Reading Comprehesion -Illustrations and questions -Predictions -Relating or connecting -Retelling Prior Knowledge Something from a students long term memory Effective Classroom Practices for Second Language Acquisition -Understandable instruction -Relate instruction to cultures -Increase interactive activities -Cover all curriculum areas -Use consistent routines -Verbal summaries Teaching Strategies for ESL Student -Partner ESL students and native English speakers together -Encourage questions -Dictate key sentences -Alternate difficult and easy tasks -Ask to label objects Epic Poems Recount heroic deeds and adventures, using stylized language and combining dramatic and lyrical conventions Epistolary Poems Written and read as letters Ballards Structured with rhyme and meter to focus on subjects such as love, death, and religious topics Elegies Mourning poems written in lament, praise of the deceased, and solace for loss Odes Evolved from songs to the typical poems, expressing strong feelings and contemplative thoughts Pastoral Poems Idealize nature and country living Epigrams Memorable rhymes with 1 or 2 lines Limericks 2 lines of iambic diameter followed by 2 lines of iambic diameter and another of iambic triameter Haikus Poems that have 17 syllables (5-7-5) that are distributed across 3 lines and have a pause after line 1 or 2 Sonnets Poems with 14 lines of iambic pentameter, tightly organizes around a theme Novels of Manners Fictional stories that observe, explore, and analyze the social behaviors of a specific time and place. Epistolary Novels Told in the form of letters written by their characters rather than in narrative form Pastoral Novels Lyrically idealize country life as idyllic and utopian, akin to the Garden of Eden Bildungsroman Describes apprenticeship novels focusing on coming of age stories and is German for education novel Roman à Clef Refers to books that require a real life frame of reference or key, for full comprehension and is French for novel with a key Realism A literacy form with the goal of representing reality as faithfully as possible Satire Uses sarcasm, irony, and/or humor as social criticism to lampoon human folly William Shakespeare A poet and play writer who lived in England and wrote poems, sonnets, and plays Types of Dramatic Comedies -The farce (zany and goofy type of comedy that includes pratfalls and slapstick humor) -The romantic comedy (includes humor and a happy ending with love) -The satirical comedy (mock and lampoon human foolishness and vices) Aristotle's 5 Critical Terms Relative to Tragedy -Anagnorisis (tragic recognition) -Hamartia (tragic flaw) -Hubris (tragic overstepping) -Nemesis (tragic punishment) -Peripateia (tragic turning) Hegel's Theory of Tragedy A tragedy must involve some circumstance in which 2 values or right are fatally at odds with one another and conflict directly Predictions Conclusions that readers make based on what will happen in the text Inferences Conclusions that readers make based on observations and previous knowledge Connections Help readers understand text better and predict what might occur next based on what they already know Kinds of Connections -Text to self -Text to text -Text to world Summarize Helps readers identify important information and organize it in their minds Paraphrase Antonyms Words that mean the opposite of one another Setting The place in which the story as a whole is set Time Frame The period in which the story is set Theme What the reader learns from the text or the passage Types of Conflict -Man vs man -Man vs nature -Man vs self Syntax Sentence structure Allusion Incited but recognizable reference to something else Comic Relief Use of comedy by an author to break up a dramatic or tragic science and infuse it with a bit of lightheartedness Mood A story's atmosphere or the feeling the reader gets from reading it First Person Narration Narrator expresses inner feelings and thoughts Second Person Narration Narrator expresses other people's thoughts and actions Third Person Narration Narrator expresses other people's feelings, thoughts, and actions Story Plot Characters, places, and events originating in the authors mind Discourse How the author arranges and sequences events Irony The opposite of what is said or done Types of Irony -Verbal irony (uses words opposite of what is said or done) -Situational irony (what happens contrasts with that was expected) -Dramatic irony (narrative informs audiences of more than its characters know) Technical Language Impersonal language found in scientific texts Common Core Anchor Standards (6-12) in citing textual evidence to support informational text analysis -6 (cite textual evidence to support their inferences and analyses) -7 (identify several specific pieces of textual evidence to defend each of their conclusions) -8 (differentiate strong from weak textual evidence) -9 & 10 (cite through evidence as well as strong evidence from text) -11 & 12 (determine which things are left unclear in a text) Text Coding/Text Monitoring Active reading strategy to support student comprehension of informational texts Types of Structures or Organizational Patterns -Descriptive -Sequence and order -Comparison/contrast -Cause and effect -Problem and solution Text Features -Title of a text -Table of contents -Appendix -Index -Glossary -Boldface print -Headings and subheadings -Footnotes -Bullet point -Sidebar -Illustrations -Captions -Charts, tables, and diagrams Irrational Numbers Cannot be written as fractions or decimals because the number of decimal places is infinite and there is no recurring pattern of digits within the number Real Numbers The set of all rational and irrational numbers Number Lines A graph to see the distance between numbers Place Value in Word Form Each digit of a number represents how many of the corresponding place value Absolute Value The distance away from 0 a number is in the number line |3|=|-3|? Yes because the distance is the same between 0 and 3 and -3 and 0 Mathematical Expressions A combination of values and operations Operation Mathematical process that takes some values as inputs and produces and output Addition Increases the value of one quantity by the value of another quantity Subtraction The opposite operation of addition, it decreases the value of one quantity by the value of another quantity Multiplication Can be thought of as repeated addition, one number indicates how many times to add the other number to itself Division Is the opposite operation to multiplication, one number tells how many parts to divide the other number into Math Parentheses Used to designate which operation should be done first when there are multiple operations Exponent Superscript number placed next to another number at the top right, Indicating how many times the bass number is to be multiplied by itself What is the Property of a^1=a? Any number to the power of one is equal to itself What is the Property of 1^n=1? The number one raised to any power is equal to one What is the Property of a^0=1? Any number raised to the power of zero is equal to one What is the Property of a^n x a^m=a^n+m? Add exponents to multiply powers of the same base number What is the Property of a^n / a^m=a^n-m? Subtract exponents to divide powers of the same base number What is the Property of (a x b)^n=a^n x b^n and (a / b)^n=a^n / b^n? Multiplication and division operations inside parentheses can be raised to a power, this is the same as each term being raised to the power What is the Property of a^-n=1/a^n? A negative exponent is the same as the reciprocal of a positive exponent Root Another way of writing a fractional exponent with the radical symbol Perfect Square A number that has an integer for its square root Order of Operations A set of rules that dictate the order in which we must perform each operation in an expression so that we evaluate it PEMDAS -Parentheses -Exponents -Multiplication -Division -Addition -Subtraction Regrouping Subtraction When subtracting, borrow a unit from the place value to the left in order to get a positive difference Prime Number Has only two factors, but other numbers can have many factors Common Factor A number that divides exactly into two or more other numbers Prime Factor Also a prime number Greatest Common Factor The largest number that is a factor of two or more numbers Multiples Integer increments of a given factor Least Common Multiple The smallest number that is a multiple of two or more numbers Fraction A number that is expressed as one integer above another integer Quotient The answer to a division problem Numerator The top number in a fraction Denominator The bottom number in a fraction Reducing a Fraction When you divide both numbers by a common factor The sum of a single variable term, where the variable has no exponent and a constant Linear Expression The sum of any number of variable terms so long as none of the variables have an exponent One Variable Linear Equations Equations that can be written as ax+b=0, where a does not equal 0 Solution Set The set of all solutions of a equation Empty Set When an equation has no true solutions Equivalent Equations Equations with identical solutions Identity A term whose value or determine is equal to one Standard Form Equation Ax+By=C Slope Intercept Form Equation y=mx+b Point Slope Form Equation y-y1=m(x-x1) Two Point Form Equation y-y1 / x-x1 = y2-y1 / x2-x1 Intercept Form x/x1 + y/y1 = 1 Like Terms Terms in an equation that have the same variable, regardless of whether or not they have the same coefficient Combining Like Terms Adding or subtracting like terms to reduce sets of like terms to a single term Isolate a Variable Manipulate the equation so that the variable appears by itself on one side of the equation Linear Equation An equation in which variables only appear by themselves Spurious Solution Squaring both sides of an equation as a step in solving it or under certain other operations on the equation Conditional Inequalities Certain values for the variable that will make the condition true and other values for the variable where the condition will be false Absolute Inequalities Any real number as the value for the variable to make the condition true, while there is no real number value for the variable that will make the condition false Double Inequalities Situations where two inequality statements apply to the same variable expression Compound Inequalities An equality that consists of 2 Inequalities combined with and or or Cartesian Coordinate Plane 2 number lines placed perpendicular to each other and intersecting at the 0 point Systems of Equations Sets of simultaneous equations that all use the same variables Consistent Systems Have 1 solution Inconsistent Systems Have no solution Trace Feature on Calculator Rewrite each equation, isolating the y variable on one side of the equal sign Monomial A single variable or product or variables Polynomial Algebraic Expressions that use addition and subtraction to combine 2 or more monomials Binomial 2 terms Trinomial 3 terms Degree of a Monomial The sum of the exponents of the variables Degree of a Polynomial The highest degree of any individual term Coefficient The number part FOIL Method F- Multiply the first terms of each binomial O- Multiply the outer terms I- Multiply the inner terms L- Multiply the last terms of each binomial Rational Expressions Fractions with polynomials in both the numerator and denominator Quadratic Formula x = -b ± √(b² - 4ac)/2a Variables Expresses functional relationships Coordinates Values on a graph written as (x,y) Relation Set of data in which there is not a unique y value for each x value in the data set Function A function that can be constructed as a ratio of 2 polynomial expressions: f(x)= p(x)/q(x) and q(x)= 0 Square Root Functions A function that contains a radical and is in the format f(x)= √2x+1 Step Functions The double brackets in a equation, such as f0(x)=[[x]] Exponential Functions Equations that have the format y=b^2, where b>0 and b doesn't = 1 Geometric Sequences an= a1 x r^n-1, where an is the value of the nth term, a1 is the initial value, r is the common ratio, and n is the number of terms Population Growth f(t)=ae^rt, where f(t) is the population at time is greater than or equal to zero, a is the initial population, e is the mathematical constant known as Euler's number, and r is the growth rate Compound Interest f(t)=P(1+r/n)^nt, where f(t) is the account value at a certain number of time periods t is greater than or equal to 0, P is the initial principle balance, r is the interest rate, and n is the number of times the interest is applied per time period General Exponential Growth or Decay f(t)=a(1+r)^t, where f(t) is the future count, a is the current or current count, r is the growth or decay rate, and t is the time Logarithmic Functions Equations that have the format y=logb x or f(x)=logb x logb 1=0 The log of one is equal to zero for any base logb b=1 The log of the base is equal to one logb bp=p The log of the base raised to a power is equal to the power logb MN=logb M +logb N The log of a product is the song of the log of each factor logb M/N=logb M -logb N The log of a quotient is equal to the log of the dividend minus the log of the divisor logb M^p=plogb M The log of a value raised to a power is equal to the power times the log of value Trigonometric Functions Periodic, they repeat the same form over and over Sin Opposite side/Hypotenuse Cos Adjacent side/Hypotenuse Tan Opposite side/Adjacent side Translation When values are added to or subtracted from the X or Y values Stretching, Compression, and Reflection When different parts of a function are multiplied by different groups of constants Fundamental Theorem of Algebra Every non-constant, single variable polynomial has exactly as many roots as the polynomials highest exponent Remainder Theorem Useful for determining the remainder when a polynomial is divided by a binomial Factor Theorem Related to the remainder theorem states that if f(a)=0 then (x-a) is a factor of the function Rational Root Theorem Any rational root of a polynomial function f(x)= anX^n +an-1X^n-1 + ... + a1X +a0 with integer coefficients will, when reduced to its lowest terms, be a positive or negative fractions such as the numerator is a factor of a0 in the denominator is a factor of an Composite of 2 Functions (f o g) (x), which means that the output of the second function is used as the input of the first Precision How reliable and repeatable a measurement is Accuracy How close the data is to the correct data Appropriate Error The amount of error in a physical measurement Maximum Possible Error Half the magnitude of the smallest unit used inn the measurement Rounding Reducing the digits in a number while still trying to keep the value similar Estimation Rounding each number in the calculation to the level indicated or the level that makes sense for the numbers involved Estimating Sums All numbers must be rounded to the same level Scientific Notation A way of writing large numbers in a shorter form, ax10^n Metric Prefixes -Giga (one billion) -Mega (one million) -Kilo (one thousand) -Deci (one tenth) -Centi (one hundreth) -Milli (one thousandth) Line Segment A portion of a line that has definite endpoints Ray A portion of a line that extends from a single point on that line in one direction along the line Perpendicular Lines Lines that intersect at right angles Parallel Lines lines in the same plane that have no points in common and never meet Transversal A line that intersects at least 2 other lines, which may or may not be parallel to one annother Bisector A line or line segment that divides another line segment into 2 equal lengths Perpendicular Bisector A line segment is composed of points that are equidistant from the endpoints of the segment it is dividing Projection of a Point on a Line The point at which a perpendicular line drawn from the given point to the given line intersects the line Projection of a Segment on a Line A segment whose endpoints are the points formed when perpendicular lines are drawn from the endpoints of the given segment to the given line Planes 2 dimensional flat surface defined by three non-collinear points Conic Sections Forms when a plane intersects a circular conic surface Angle Fromed when 2 lines or line segments meet at a common point Vertex The point at which 2 segments or rays meet to form an angle Types of Angles -Acute -Right -Obtuse -Straight -Reflex -Full -Complementary -Supplementary -Adjacent -Alternate interior -Alternate exterior Rotation A transformation that turns a figure around a point Center of Rotation The point that the figure turns around, which can be anywhere Angle of Rotation the angle between 2 lines connected by a vertex Translation A transformation which slides a figure from one position in the plane to another position in the plane Dilation A transformation that stretches or shrinks a figure by a scale factor Line of Reflection A perpendicular bisector of any line segment drawn from a point on the original figure to its reflected image Point of Reflection The midpoint of a line segment which connects a point in the figure to its image Polygons A closed, 2 dimensional figure with 3 or more straight line segments Types of Polygons -Triangle -Quadrilateral -Pentagon -Hexagon -Heptagon -Octagon -Nonagon -Decagon -Dodecagon Apothem A line segment from the center of a polygon that is perpendicular to a side of the polygon Radius Square Perimeter 4s Hierarchy of Quadrilaterals Center of Circle The single point from which every point on the circle is equidisant Circle Radius A line segment that joins the center of the circle and any one point on the circle Cirlce Diameter A line segment that passes through the center of the circle and has both endpoints on the circle Circle Area πr² Circle Circumference 2πr Prism Surface Area LA+2B Pyramid or Cone Surface Area LA+B Sphere Area 4πr² Sphere Volume 4/3πr³ Prism Volume Bh Rectanglar Prism Volume lwh Rectanglar Prism Surface Area 2lw+2hl+2wh or 2(lw+hl+wh) Cube Volume s^3 Cube Surface Area 6s^2 Cylinder Volume πr^2h Cylinder Surface Area 2πr^2 + 2πrh Pyramid Volume 1/3Bh Pyramid Surface Area B+1/2Phs Cone Volume 1/3πr^2h Cone Surface Area πrs + πr^2 Triangle Types -Scalene (no congruent sides) -Acute (3 angles less than 90*) -Isosceles (2 angles equal) -Equilateral (3 angles equal) -Obtuse (1 angle greter than 90*) -Right (1 angle equals 90*) Types of Similar Triangles -AAA (angle, angle, angle) Types of Congruent Triangles -SSS (side, side, side) -SAS (side, angle, side) -ASA (angle, side, angle) -AAS (angle, angle, side) -HL (hypotenuse, leg) Triangle Inequality Theorem The sum of the measures of any 2 sides of a triangle is always greater than the measure of the third side Triangle Legs The other 2 sides of the triangle, not the hypotenuse Hypotenuse The side of a triangle opposite the right angle Pythagorean Theorem a²+b²=c² 6 Trigonometric Ratios -Sin (opposite side/hypotenuse) -Cos (adjacent side/hypotenuse) -Tan (opposite side/adjacent side) -Cosecant (hypotenuse/opposite side) -Secant (hypotenuse/adjacent side) -Cotangent (adjacent side/opposite side) Laws of Sines sinA/a = sinB/b = sinC/c, where A, B, and C are the angles of a triangle and a, b, and c are the sides oppostire their respective angles Laws of Cosines Independent Events 2 or more events whose outcomes do not affect one another Dependent Events 2 or more events in whose outcomes affect one another Certain Outcome probability of outcome is 100% or 1 Impossible Outcome probability of outcome is 0% or 0 Mutually Exclusive Outcomes 2 or more outcomes whose criteria cannot all be satisfied in a single event Random Variable Refers to all possible outcomes of a single event which may be discrete or continuous Theoretical Probability The likelihood of an outcome occuring, or the probability of an outcome occuring Theroretical Probability Equation Number of acceptable outcomes/number of possible outcomes Experimental Probability An estimate of the likelihood of a certain outcome based on repeted experiments or collected data Objective Probability Based on mathematical formulas and documented evidence Subjective Probability Based on personal or professional feelings and judgments Sample Space The total set of all possible results of a test or experiment Distribution Function that assigns a real number probability, from 0-1, to each outcome How to Determine the Outcome? -Tree Diagrams -List Charts Mutually Exclusive Events that have no outcomes in common Independent 2 events have no bearing on each other so that one event occuring has no influence on the probability of another event occuring Dependent The outcome of 1 event does affect the probability of the second event Odds in Favor of an Event The number of times the event will occur compared to the number of times the event will not occur Odds in Favor of an Event Formula P(A)/1-P(A) Odds Against an Event The number of times the event will not occur compared to the number of times the event will occur Odds Against an Event Formula 1-P(A)/P(A) Permutation An arrangement of a specific number of a set of objects in a specific order Permutation Formula nPr = n!/(n-r)! Combinations An arrangement of a specific number of a set of objects in no specific order Combination Formula nCr = n!/r!(n-r)! Union (symbol U) The set of elements found in all sets Intersection (symbol n) The set of common elements found in all sets Complement of an Event The possibility of something not happening Complement of an Event Equation P(not occuring)=1-P(occuring) Addition Rule Formula P(A or B)=P(A)+P(B)-P(A and B) Conditional Probability The probability that an event will occur, given that the other event has occured Multiplication Rule P(A and B)=P(A)xP(B) Expected Value A method of determing expected outcome in a random situation Data The collective name for pieces of information Quantitive Data Measurements that provide information about quantities in numbers Qualitative Data Information that cannot be measured using numbers Discrete Data Information that can be expressed only by a specific value Continuous Data Information that can be expressed by any value within a given range Primary Data Information that has been collected directly from a survey, investigation, or experiment Secondary Data Information that has been collected, sorted, and processed by the researcher Ordinal Data Information that can be placed in numerical order Nominal Data Information that cannot be placed in numerical order Population The entire collection of people, plants, etc., that data can be collected from Parameter Unimodal Distribution with a single peak Bimodal Distribution with 2 peaks Uniform Distribution Distribution with no distinct peaks Outlier An extremely high or low value in the data set Simple Regression Using an equation to represent a realtion between an independent and dependent variable Line of Best Fit The line that best shows the trends of the data Line of Best Fit Equation y=ax+b Correlation Coefficent The numerical value that indicates how strong the relationship is between the two variable of a linear regression equation Z Scores An indication of how many standard deviations aa given value falls from the mean Z Score Formula (x-mean)/standard deviation Central Limit Theorem The distribution of the means tend to get closer and closer to a normal distributionas the sample size gets larger and larger Frequency Tables Shows how frequently each unique value appearss in a set Relative Frequency Table Shows the proportions of each unique value compared to the entire set Circle Graph Provide a visual depiction of the relationship of each data compared to the whole sert of data Pictograph A graph, generally in the horizontal orientation, that uses pictures or symbols to represent the data Line Graphs One or more lines of varying styles to show the different values for a set of data Line Plot Plotted pointss that are not connected by line segments Stem and Leaf Plot Usedul for depicting groups of data that fall into a range of values Bar Graph A graph with a bar drawn to represent the exact value of data Histogram A bar graph that has one continuous bar for each range of data Bivariate Data Data from 2 different variables Scatter Plots Useful in determining the type of function represented by the data and finding the siple regression 5 Number Summary Gives a very informative picutre of the set Box and Whisker Plot A graphical representation of the 5 number summary 68-95-99.7 Rule Describes how a normal distribution of data should appear when compared to the mean 4 Basic Laws of Thermodynamics -Zeroth Law (2 objects in therodynamic equilibrium with a 3rd object are also in equilibrium with each other -First Law (neither madd nor energy can be destroyed, only converted from one form to another) -Second Law (the entropy of an isolated system ca only increase) -Third Law (as temperature approaches absolute 0, entropy approaches a constant minmum) Heat Energy transsfer from one body to another due to thermal contact Temperature A measurement of an objects stored heat energy Mass Measures how much of a substance is in an obkject Density A measurement of the amont of mass per unit volume Weight Measures the gravitational pull of the earth on an object Density Equation D=m/v Volume Measures the amount of space taken up Specific Gravity Meausres the ratio of a substances density to the density of water Thermal Contact Energy transferred to a bodyby a means other than work What can you Model? -Flow of electric current -Potental -Circuts Magnetic Field Sound A pressure disturbance that moves through a medium in the form of mechanical waves, which transfer energy from one particle to the next Pitch The quality of sound determined by frequency Loudness A humans perception of sound intensity Sound Intensity Measure as the sound power per unit area, and can be expressed in decibels Timbre A humans perception of the type or quality of sound Oscillation A measurement against a basic value, equilibrium, or rest point Doppler Effect The effect that relative motion of the source of the wave and the location of the observer has on waves Waves Have energy and can transfer energy when they interact with matter Mechanical Waves Transmit energy through matter Electromagnetic waves Transmit energy through a vacuum Transverse Wave Provides a good illustration of the features of a wave Electromagnetic Spectrum All of the frequencies or wavelengths of electromagnetic radiation Electromagnetic Spectrum Waves -Electromagnetic -Radio -Microwave -Infrared -Visible -Ultraviolet -Xrays -Gamma Reflection The rebound of a light wave from a surface back toward the medium from where it came Refraction The change in the direction of a light wave when it passes through transparent medium with a different optical density from the one in which the wave had been traveling Atomic Number The number of protons in the nucleus of an atom Neutrons Uncharged atomic particles contained within the nucleus Nucleon Both the neutrons and protons Element Matter with one partical type of atom First Conceptualization of the Atom Developed by Democritus inn 400BC Atom Structure Consists of a nucleus and electrons Nucleus Structure Consists of protons and neutrons Molecules Atoms that bonded together through a chemical bond Atomic Radius The average distance between the nucleus and the outermost electron Electron Cloud Electrons swarm around the nucleus Atom One of thr most basic units of matter Electrons Negatively charged and orbit the nucleus Protons Positively charged and make up the nucleus Valence Layer Outermost layer of valence electrons Covalent Bond Formed when atoms share electrons Ionic Bond Formed when an atom transfers an election to another atom Hydrogen Bond A weak bond between a hydrogen atom and an electronegative atom Positive Ion (cation) Formed when an atom loses one or more electrons Negative Ion (anion) Formed when an atom gains one or more electrons Van der Waals Force A weak force between molecules Matter Substances that have mass and occupy space States of Matter -Solid -Liquid Sound Energy Energy in sound waves Chemical Reactions Reaactions that can be quick or slow Catalysts Accelerate chemical reactions Chemical Equations Describes chemical reactions Unbalanced Equations One that does not follow the law of conservation of mass, which states that matter can only be changed Periodic Table Groups elements with similar chemical properties together Rows on Periodic Table Periods Columns on Periodic Table Groups or familes Suspensions Mixtures of heterogeneous materials Collodial Suspension A mixture of large particles Emulsion A liquid or solid being dispersed Foam A liquid that has gas dispersed through it Base Properties -Conduct electricity -Change red litmus paper to blue -Feel slippery -React with acids to neutralize Salt Properties -Dissociate in water -Ionic compounds of metallic and nonmetallic ions -Comprised of tightly bonded ions Acid Properties -Conduct electricity -Chnge blue litmus paper to red -Sour taste -react with bases to neutralize Water Properties -High Polarity, hydrogen bonding, cohesiveness, adhesiveness, high specific heat, high latent heat, and high heat of vaporization -Room temperature when liquid -Resists heat and motion -Is cohesive Potential of Hydrogen (pH) A measurement of the concentration of hydrogen ions in a substance in terms of the number of moles of H+ per liter of solution Neutral pH pH of 7 Acidic pH pH less than 7 Basic pH pH greater than 7 Kinetic Theory of Gases Assumes that gas molecules are small compared to the distances between them and that they are in constant random motion Inorganic Compounds Compounds that lack carbon Organic Compounds Compounds that include carbon and form covalent bonds Polar Patially positively charged on one end and partially negatively charged on the other Oxidized Number of electorns are reduced Zoology Study of animals Botany Study of plants Biophysics Application of the laws of physics to the process of orginaisms and the application of the facts about living things to human processess and inventions Biochemistry Study of the chemistry of living organisms, including diseases and he pharaceutical drugs used to cure them Cytology Study of cells Histology Study of the tissues of plants and animals Organology Study of tissues organized into organs Physiology -Paraasites Carbon Element founf in all living things Hydrocarbons Composed only of hydrogen and carbon, are the simplest organic molecules Carbohydrates Compounds made of hydrogen, carbon, and oxygen Macromolecules -Sugars -Starches -Cellulose Lipids Cmpounds that are insoluableor only partially soluable in water Protien Complex substances that make up almost half the dry weight of amilam bodies Nucleic Acids Large molecules composed of a large number of simple molecules Cell The basic organizational unit of all living things Membrane A comparable, semi permeable plasitic bag Transport Holes Proteins that help certain molecues and ions move in and out of the cell Cytoplasm Fluid in the cell Organelles Groups of complex molecules that help a cell survive Eukaryotic Cells -Nucleus -Nuclear envelope -Chromatin -Mitochondria Photosynthesis Occurs when the energy from the sun hits a chloroplast and the chlorophyll used that energy to combine carbon dioxide and water to make sugars and oxygen Passive Transport Within a cell and does not require energy and work Active Transport When a cell uses energy to move individual molecules across the cell membrane to maintain a proper balance Mitosis The duplication of a cell and all its parts Mitosis Phases -Prophase (duplicateto prepare for divison) -Metaphase (different pieces align themselves for split up) -Anaphase (half chromosomes on one side and half on the other) -Telophase (cell membrane closes and cells split into 2 pieces -Interphase (resting stage) Microbes The smallest, simplest, and most abundant organism on earth Roots Structures designed to pull water and minerals from soil or water Stems Transport food and water and act as support structures Leaves The site for photosynthesis and are connected to the rest of the plant by a vascular system Gymnosperms Plants with vascular systems and seeds but no flowers Cycads Sturdy plants with bug, waxy fronds that make them lool like ferns or palms Conifers Trees that thrive in northern latitudes and have cones Angiosperms Plants that haveflowers Dicot Has seeds with 2 cotyledons or 2 seed leaves of food Arthropod Characteristics -Have exoskeleton -They molt -Several legs -Advanced nervous system -Develop through metamorphosis Reptile Types -Crocodilla -Squamata -Chelonia The complex and interconnected dynamics of the continents, atmosphere, oceans, ice, and life forms Earth Science Disciplines -Geology (study of the origin and structure of earth and the changes) -Meteorology (study of the atmosphere) -Oceanography (study of the oceans) -Ecology (study of living organisms in realtion to their environment) Units of Time Eons-> eras-> periods-> epchs-> ages Geological Eras Hydrosphere Anything on earth that is related to water Hydrologic Cycle The journey water takes as it assumes different forms Aquifer An underground water reservior formed from groundwater that has infiltrated from the surface by passing through the soil and permeable rock layers Biosphere The living world of trees, bugs, and animals Ecological System The community of all living organisms in a specific area interacting with nonliving factors Biome A general ecosystem tyoe definded by the plants and animals that live there and the local climate patterns Erosion The process that breaks down matter Denudation Erosion or land by weather or breaking waves Mass Wasting The movement of masses of dirt and rock from one place to another Names of Climates -Polar (ice caps) -Polar (tundra) -Subtropical (dry summer) -Subtropical (dry winter) -Subtropical (humid) -Subtropical (marine west coast) -Subtropical (mediterranean) -Subtropical (wet) -Tropical (monsoon) -Tropical (Savannah/grasslands) -Tropucal (wet) Layers of the Earth -Crust (the outermost layer of the earth that is comprised of the continents and the ocean basins) -Mantle (2 sections that are made up with silicates) -Core (seperated into 2 parts) Composition of Earths Atmosphere 79% nitrogen, 20% oxygen, 1% other gases Earths Atmosphere Layers -Troposhphere (closest layer to where the earth takes place) -Stratoshpere (air flow is horizontal) -Mesosphere (cold layer) -Thermosphere (many ionized atoms) Paleontology The study of phrehistoric plant and animal life through the analysis of fossil remains Law of Superposition The bottom layer of a series of sedimentary layers is the oldest Igneous Intrusions Cuts through or fows above other rocks Contact Metamorphism The recrystillization of rocks due to changes in physical and chemical conditions Match Rocks to Events -Types or patterns -Small time periods -Volcanic ash -Meteor impact Mountain A portion of the earth that has been raised above its surroundings by volcanic action or plate movement Volcano Types Comets Celestrial bodies composed of dust, rock, frozen gas, and ice Coma Comets fog like envelope that glows with sunlight Solar Winds Blow a comet away from the sun and give it a tail of dust or particles Asteroids Irregularly shaped boulders that orbit the sun Meteoroids Fragments of asteroids of various sizes Scientific Experimentation -Hypothesis -Theory -Scientific law -Control and constants -Independent variable -Dependent variable Conclusions Based on data analysis and background research Scientific Method -Observation -Theory or hypothesis -Experimental method -Analysis and evaluation -Modification and replication Science Inquiry The impetus and catalyst for all scientific research and experimentation Science A method of acquiring and obtaining knowledge Hypothetico-Deductive Process States that to have an idea and then formulate a hypothesis are essentially creative process, driven by eons of human experience Basic Science Spurred on by scientific inquiry, the human need to explain the observed physical world Applied Science Has specific practical goal or application, it is designed to solve a problem Measuring Data The process of determining variablrd such as time, space, and temperature of objects and processes in precise numbers Data Must Be? -Organized -Classified Scientific Laws Laws that must be true, not just probable Scientific Prediction Stating in advance the outcome from testing a theory or hypothesis in a controlled experiment Verification Establishes once and for all the truth of the statement Confirmation The testing of claims to see how true they are Unit System The basis of quantitative measurements Systeme International (SI) The most commonly used unit system in the world Significant Figures Indicate how precisely a quantity is known Science Accuracy A measure of how close a measurement is to the true value Science Precison A measure of how close repeated measurements are to one another Galaxies Consist of stars, stellar remnants, and dark matter Types of Galaxies -Dwarf galaxies -Giant galaxies -Milky Way galaxy -Andromeda galaxy Intergalactic Space Consists of gas with an average density of less than one atom per cubic meter Dark Matter May account for up to 90% of the mass of galaxies Troposphere Where most weather takes place Meteorology The study of the atmosphere, particularly as it pertains to forecasting the weather and understandding its processes Weather The condition of the atmosphere at any given momement Climate -The Shot Hear Round the World Turning Points of the American Revolution -Second Continental Congress -Common Sense -Declaration of Independence -Alliance with France -Treaty of Paris Declaration of Independence Officially seperated the colonies from British rules Articles of Confederation The original constitution of the USA, outlining how sovereignty would be shared among the states in the new country Confederation Period The period in US history directly following the American Revolution, from 1783-1788 Federalist Era More power was placed on the federal government and the 3 branches of government were established, from 1788-1801 Amendment A change to the Constitution The Bill of Rights The first ten amendments to the Constitution Jeffersonian Era Jefferson was big on activism and American Republicanism, from 1801-1817 Era of Good Feelings Collapse of the Federalist system and Monroe tried partisan political systems, from 1817-1825 Jacksonian Era Voting rights expanded to men over 21 and lots of expansionism, from 1825-1849 Civil War Era Slaavery became an issue with the states and Confederacy was formed, from 1850- 1865 Reconstruction Period South was under control of the US and military occupation began in the Confederacy, from 1865-1877 13th Amendment Declared slavery illegal 14th Amendment Made all persons born or naturalized in the US citizens and forbade any state to interfere with their fundamental civil rights 15th Amendment Made it illegal to deny individuals the right to vote on the grounds of race Major Changes in Late 1800s -Industrialization -Raailroad Expansion -Gold and silver minig -Cattle ranching Gilded Age Enormous wealth aand grossly opulent lifestyle enjoyed by families Robber Barons -Jay Gould (railroads) -Andrew Carnegie (steel) -John D. Rockefeller Sr. (oil) -Philip Danforth Armour (meatpacking) -John Jacob Astor (fur pelts) -Cornelius Vanderbilt (steamboat shipping) Population in Late 1800s The population in the US doubled between 1860-1890, with the arrival of 10 million immigrants Progressive Era American created the Monroe Doctrine and participated in Spanish-American wars, from 1890-1920 Accomplishments of the Progressive Era -Hepburn Act -Sherman Anti-trust Act -Clayton Anti-Trust Act -Forest Service -Pure Food and Drug Act -Federal Reserve System -Fair Trade Commission Wolrd War I American declared neutraility and did not want to go into war but had to and got victory in 1918 Roaring Twenties