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AP Environmental Science Biomes Flashcards

8989721917	Temperate Deciduous Forest	-Cool Winters, Warm Summers (Seasonal Variation) -Precipitation is relatively evenly spread throughout the year -Deciduous Trees (Oak, Beech) -Europe, China, Eastern North America -Northern Hemisphere -Good Soils	0
8989721918	Temperate Grassland	-Cool Winters, Warm Summers (seasonal variation is more extreme than temperate deciduous forests) -Limited amount of precipitation -Frequent fires (no trees) -Also called prairie or steppe -Northern Hemisphere -North America, Middle East, Europe, Asia -Very fertile soils (used for agriculture)	1
8989721919	Temperate Rainforest	-Cool Winters, Warm Summers (Seasonal Variation) -Large amount of precipitation (Less rain in winters) -Coniferous Trees -Provide lumber and paper -Northern Hemisphere -East coast of North America and Canada -Fertile soils that are susceptible to land slides and erosion if forests are cleared	2
8989721920	Tropical Rainforest	-Warm all year round -Very high amount of precipitation (300-500 mm per month) -Southern Hemisphere -Central America, Africa, South America, Southeast Asia -Great Biodiversity -Poor, thin soils	3
8989721921	Tropical Dry Forest/Tropical Deciduous Forest	-Warm all year round -Extreme wet and dry seasons -Wet summer (October to April) and dry winter (May, June, July, August, September) -Southern Hemisphere -India, Africa, South America, northern Australia -Erosion-prone soils	4
8989721922	Savanna (Tropical Grasslands)	-Slight seasonal variation (warmer in summer) -Extreme wet and dry seasons -Wet Summer (not as wet as tropical dry forest) -Southern Hemisphere -Isolated Trees -Africa, South America, India, Australia -Zebras, Giraffes, Gazelles	5
8989721923	Desert	-Driest Biome -Barely an rainfall -Slight seasonal variation -Saline soils -Little Vegetation -Temperatures drop at night -Northern Hemisphere -Africa, Mexico, Middle East, Asia	6
8989721924	Tundra	-Coldest Biome -Warmer in summers, but still cold (5 degrees celsius) -Freezing in winters (-20 degrees celsius) -Northern Hemisphere -Dry -Slightly wet summers -Soil is permanently frozen (permafrost) -Also occurs as alpine tundra at the tops of mountains -Northern Europe, Northern Canada, Northern Asia, Greenland	7
8989721925	Boreal Forest/Taiga/Coniferous Forest	-Largest Biome -Northern Hemisphere -Coniferous Trees (Pinecones) -Cold. Cooler in summers (never above 20 degrees Celsius) -Moderate Precipitation -More wet in summer than winter -Poor soils -Moose, Wolves, Lynx, Bears -Northern Europe, Canada, Northern Asia	8
8989721926	Chaparral	-Densely thicketed -Highly seasonal -Cool, wet winters and warm, dry summers -Induced by oceanic influences -Northern Hemisphere -California, Chile, Australia -Frequent fires	9

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AP Biology: Organic Molecules Flashcards

This vocabulary set includes classes of organic molecules as well as examples of each

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5958295722	Macromolecules	Molecules composed of thousands of atoms: the four main classes being carbohydrates, lipids, prteins, and nucleic acids	0
5958295723	Polymer	Chainlike molecules, consisting of many similar or identical building blocks linked by covalent bonds.	1
5958295724	Monomer	The building blocks of polymers polymers: connected by covalent bonds.	2
5958295725	Dehydration Synthesis	Removing water to create a bond.	3
5958295726	Hydrolysis	Adding water to break a bond	4
5958295727	Carbohydrates	A macromolecule made up of C, H and O, with a 2:1 ratio between the hydrogen and oxygen.	5
5958295728	Monosaccharides	Simple sugars with 1 ring: Provides immediate energy, classified by the amount of carbons	6
5958295729	Disaccharides	Double sugars with 2 rings	7
5958295730	Polysaccharides	Polymers, with many rings, joined by glucosidic linkages. Acts as an energy storage macromolecule, building materials for cells or whole organisms	8
5958295731	Maltose	A disaccharide formed by joining the two glucose molecules: found in malt sugar	9
5958295732	Sucrose	A disaccharide formed by joining glucose and fructose, major form of sugars in plants: found in table sugar	10
5958295733	Lactose	A disaccharide formed by joining glucose and galactose. People who lack the enzyme to digest this sugar are "intolerant"	11
5958295734	Glycosidic Linkages	"oxygen bridge" that bonds two monosaccharides	12
5958295735	Starch	storage polymer of glucose in PLANTS, uses alpha linkages	13
5958295736	Cellulose	Made up cell walls of plants, using beta linkages	14
5958295737	Glycogen	Branched polysaccharide of glucose, used for storage in animals	15
5958295738	Chitin	Makes up the exoskeleton of pill bugs; extremely strong, contains nitrogen-containing appendage on each glucose. Structural support for the cell walls of many fungi.	16
5958295739	Lipids	nonpolar class of molecules. Have C, H and O, but not in a 2:1 ratio.	17
5958295740	Triacylglycerols	(Fats): Store large amounts of energy, made up of 1 glycerol + 3 fatty acids -> 1 fat + 3 water molecules. Functions as energy storage, to cushion vital organs, and insulation.	18
5958295741	Glycerol	3-C alcohol that is building block of triglycerides	19
5958295742	Fatty Acid	Carboxyl group attached to long hydrocarbon chain.	20
5958295743	Ester Linkage	Joins 3 fatty acids to a glycerol, creating a triacylglycerol	21
5958295744	Saturated fatty acids	Fatty acids with single bonds, hydrogen at every possible position, a straight shape, from an animal source. Solid at room temperature.	22
5958295745	Unsaturated fatty acids	Fatty acids with double and single bonds, without hydrogens at every possible position, a kinked/bent shape, from a plant source. Liquid at room temperature.	23
5958295746	Phospholipid	2 fatty acids attached to a glycerol, with a phosphate group in the 3rd position. Have both hydrophobic and hydrophilic bonds	24
5958295747	Steroid	A type of lipid: A carbon skeleton with 4 fused carbon rings, which are closely interlocked. ex., cholesterol	25
5958295748	Proteins	Polymer of one or more chains of amino acids with diverse	26
5958295749	Antibodies	Bind to particular foreign substances that fit their binding sites	27
5958295750	Neurotransmitters	Pass signals from one cell to another by binding to receptror sites on proteins in the membrane of the recieving cell	28
5958295751	Enzymes	Recognize and bind to specific substrates, facilitating a chemical reaction	29
5958295752	Primary Structure	The unique sequence of amino acids, determined by DNA. Changing this affects a protein's conformation and ability to function.	30
5958295753	Secondary Structure	Results from hydrogen bonds at regular intervals doing the polypeptide backbone, typically developed as an alpha helix or a beta pleated sheet.	31
5958295754	Tertiary Structure	The protein has folded up upon itself, held together by hydrogen bonds, ionic bonds, Van der Waals reactions, or disulfide bridges	32
5958295755	Quarternary structure	Union of 2+ polypeptide subunits	33
5958295756	Enzymes	Speeds up the rate of reactions, but are not consumed by the reaction. Lowers the activation energy of a reaction, and makes it easier to perform these reactions.	34
5958295757	Substrate	A reactant that binds to an enzyme	35
5958295758	Active Site	A pocket/groove on the surface of a protein on the surface of the protein into which the substrate fits. The substrate is held to this area through weak interactions, such as hydrogen bonds or Van der Waals.	36
5958295759	Lock and Key Hypothesis	Substrates fit into enzymes like a key fits into a lock	37
5958295760	Induced Fit Hypothesis	As the substrate binds, the enzyme changes shape leading to a tighter induced fit, bringing chemical groups into position to catalyze the reaction.	38
5958295761	Cofactors	Non-protein factors, helping the enzyme fit substrates. ex: zinc, iron, copper	39
5958295762	Competitive Inhibitors	Blocks the active site from having a substrate meet. Acts as a feedback mechanism	40
5958295763	Noncompetitive inhibitors	Blocks the substrates at a place away from the active site.	41
5958295764	Allosteric Enzymes	Enzymes that can change their shape: one shape is active (reaction occurs) and one is inactive (reaction doesn't occur)	42
5958295765	Nucleic Acids	An organic compound made up of a pentose sugar, phosphate, and nitrogen base. The three types are DNA, RNA and ATP	43
5958295766	Ribonucleic acid (RNA)	Many types of instructional nucleic acid, which is directed by DNA and contributes to protein production	44
5958295767	Deoxyribonucleic acid (DNA)	Provides the genetic coding for organisms and directs RNA synthesis: synthesized through dehydration synthesis, connecting the sugar of one nucleotide to another with a strong phosphodiester.	45
5958295768	Nucleotide	The building blocks of nucleic acids	46
5958295769	Pentose sugar	Deoxyribose and ribose; a building block of nucleic acids	47
5958295770	Phosphate	Makes DNA and RNA charged; a building block of nucleic acids	48
5958295771	Nitrogen base	Adenosine, Thymine, Guanine, Cytosine, Uracil (RNA); building blocks of DNA. A+T are always together, and G+C are always together based on their properties. U is only found in RNA.	49
5958295772	Purines	Adenosine, Guanine; have a double ring, where 1 6-membered ring joined to 1 5-membered ring	50
5958295773	Pyrimidines	Thymine, Cytosine, Uracil; 1 6-membered ring	51
5958295774	Phosphodiester Link	The bond between a sugar and a phosphate.	52
5958295775	glucose	A sugar that is the major source of energy for the body's cells, monosaccharide example	53
5958295776	fructose	Sugar that is naturally found in fruit and honey. It's also added to sweeten drinks, monosaccharide example	54
5958295777	ribose	A five-carbon sugar present in RNA	55
5958295778	deoxyribose	A five-carbon sugar that is a component of DNA nucleotides	56
5958295779	functional group	A specific configuration of atoms commonly attached to the carbon skeletons of organic molecules and involved in chemical reactions.	57
5958295780	hydroxyl group	A functional group consisting of a hydrogen atom joined to an oxygen atom by a polar covalent bond. Molecules possessing this group are soluble in water and are called alcohols.	58
5958295781	carbonyl	C=O carbon double bonded to an oxygen	59
5958295782	carboxyl	A functional group present in organic acids and consisting of a single carbon atom double-bonded to an oxygen atom and also bonded to a hydroxyl group.	60
5958295783	amino	functional group containing Nitrogen and two hydrogens	61
5958295784	phosphate group	A functional group consisting of a phosphorus atom covalently bonded to four oxygen atoms	62
5958295785	sulfhydryl	A functional group consisting of a sulfur atom bonded to a hydrogen atom (—SH).	63

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Vocabulaire 9 (Pre-AP) Flashcards

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9202596566	Ma maison a ...	My house has ...	0
9202596567	Il y a ...	There is/are ...	1
9202596568	Il n'y a pas ...	There is not/There are not ...	2
9202596569	une fenêtre	a window	3
9202596570	un jardin	a garden, yard	4
9202596571	une porte	a door	5
9202596572	un arbre	a tree	6
9202596573	un garage	a garage	7
9202596574	une cheminée	a chimney	8
9202596575	un escalier	a staircase	9
9202596576	étage	floor, storey	10
9202596577	pièce	room	11
9202596578	la cuisine	the kitchen	12
9202596579	la salle de bain	the bathroom	13
9202596580	la salle à manger	the dining room	14
9202596581	le salon	the living room	15
9202596582	la chambre	the bedroom	16
9202596583	Dans ma chambre, il y a ...	In my room, there is/are ...	17
9202596584	une télévision	a television	18
9202596585	un lit	a bed	19
9202596586	une table de nuit	a nightstand	20
9202596587	une bibliothèque	a bookcase	21
9202596588	un bureau	a desk	22
9202596589	une chaise	a chair	23
9202596590	un placard	a closet	24
9202596591	un réveil	an alarm clock	25
9211892787	une commode	a chest of drawers	26
9202596592	un canapé	a couch	27
9202596593	une table	a table	28
9202596594	une console de jeu vidéo	a game console	29
9202596595	Ma maison est ...	My house is ...	30
9202596596	devant	in front	31
9202596597	derrière	behind	32
9202596598	ici	here	33
9202596599	là-bas	over there	34
9202596600	à gauche	to the left	35
9202596601	à droite	to the right	36
9202596602	dans	in	37
9202596603	à côté	next to	38
9202596604	chez	at the house of	39
9202596605	sur	on	40
9202596606	sous	under	41

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AP Biology Evolution Flashcards

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6458821897	homologous structures	structures in different species that are similar because of common ancestry	0
6458821898	vestigial structures	remnants of features that served important functions in the the organism's ancestors	1
6458821899	convergent evolution	the independent evolution of similar features in different lineages	2
6458821900	Hardy-Weinberg	the frequencies of alleles and genotypes in a population will remain constant from generation to generation, provided that only Mendelian segregation and recombination of alleles are at work	3
6458821901	gene pool	the aggregate of all of the alleles for all of the loci in individuals in a population	4
6458821902	population	a group of individuals of the same species that live in the same area and interbreed, producing fertile offspring	5
6458821903	natural selection	a process in which organisms with certain inherited characteristics are more likely to survive and reproduce than are organisms with other characteristics	6
6458821904	genetic drift	changes in the gene pool due to random events	7
6458821905	founder effect	when a individuals become isolated from a larger population, this smaller group may establish a new population whose gene pool differs from the source population	8
6458821906	bottleneck effect	when there is a severe drop in population size, certain alleles may be overrepresented among the survivors, others may be underrepresented, and some may be absent altogether	9
6458821907	gene flow	the transfer of alleles into or out of a population due to the movement of fertile individuals or their gametes	10
6458821908	directional selection	when conditions favor individuals exhibiting one extreme of a phenotypic range, thereby shifting the frequency curve for the phenotypic character in one direction or the other	11
6458821909	disruptive selection	when conditions favor individuals at both extremes of a phenotypic range over individuals with intermediate phenotypes	12
6458821910	stabilizing selection	acts against both extreme phenotypes and favors intermediate variants	13
6458821911	sexual selection	a form of natural selection in which individuals with certain inherited characteristics are more likely than other individuals to obtain mates	14
6458821912	sexual dimorphism	marked differences between the two sexes in secondary sexual characteristics, which are not directly associated with reproduction or survival (differences in size, color, ornamentation, and behavior)	15
6458821913	diploidy	the state of being diploid, that is having two sets of chromosomes	16
6458821914	heterozygote advantage	when individuals who are heterozygous at a particular locus have greater fitness than do both kind of homozygous	17
6458821915	frequency-dependent selection	fitness of a phenotype declines if it becomes too common in the population	18
6458821916	speciation	the process by which one species splits into two or more species	19
6458821917	microevolution	changes over time in allele frequencies in a population	20
6458821918	macroevolution	the broad pattern of evolution over long time spans	21
6458821919	species	a group of populations whose members have the potential to interbreed in nature and produce viable, fertile offspring- but do not produce viable, fertile offspring with members of other such groups	22
6458821920	reproductive isolation	the existance of biological barriers that impede members of two species from producing viable offspring	23
6458821921	hybrids	offspring that result from interspecific mating	24
6458821922	prezygotic barriers	impede mating or hinder fertilization if mating occurs (five types: habitat, temporal, behavioral, mechanical, gametic)	25
6458821923	post zygotic barriers	prevents hybrid zygote from developing into a viable fertile adult through reducing hybrid viability, reducing hybrid fertility, or hybrid breakdown	26
6458821924	allopatric speciation	gene flow is interrupted when a population is divided into geographically isolated subpopulations	27
6458821925	sympatric speciation	speciation occurs in populations that live in the same geographic area (usually occurs due to polyploidy, habitat differentiation, and sexual selection)	28
6458821929	punctuated equilibrium	the theory that in the evolution there are long periods of little morphological change punctuated by relatively short periods of significant change	29
6458821930	ribozyme	RNA that can also carry out a number of enzyme-like catalytic functions	30
6458821931	protobionts	collections of abiotically produced molecules surrounded by a membrane-like structure with simple chemical reactions (precursor of prokaryotic cells)	31
6458821932	endosymbiosis	mitochondria and chloroplasts were formally small prokaryotes that began living within larger cells	32
6458821933	adaptive radiation	Period of evolutionary change in which groups of organisms form many new species whose adaptations allow them to fill vacant ecological roles in their communities	33
6458821934	homeotic genes	master regulatory genes that determine such basic features as where a pair of wings and a pair of legs will develop on a bird or how a plant's flower parts are arranged	34
6458821935	phylogeny	the evolutionary history of a species or group of species	35
6458821936	systematics	study and classification of biodiversity and determining their evolutionary relationships	36
6458821937	phylogenetic tree	evolutionary history of a group of organisms represented in a branching diagram	37
6458821938	analogy	similarity due to convergent evolution	38
6458821939	homology	similarity due to shared ancestry	39
6458821940	clade	a group of species which includes an ancestral species and all of its descendants	40
6458821941	outgroup	a species or group of species from an evolutionary lineage that is known to have diverged before the lineage that includes the species we are studying	41
6458821944	horizontal gene transfer	a process in which genes are transferred from one genome to another through mechanisms such as exchange of transposable elements and plasmids, viral infection and perhaps fusion of organisms	42
6458821945	Darwin's Theory (five parts)	1. Variation 2. Overproduction 3. Competition 4. Survival of the fittest 5. Overtime, emergence of new species (new alleles)	43

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AP Biology: Ecology Flashcards

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6449507008	ecology	study of the distribution and abundance of organisms and their interactions with other organisms and with their physical environment	0
6449507009	population	group of individuals of the same species living in the same area	1
6449507010	community	group of populations of different species living in the same area	2
6449507011	ecosystem	interrelationships between organisms in a community and their physical environment	3
6449507012	biosphere	composed of all the regions of the earth that contain living things (hydrosphere, geosphere, and atmosphere)	4
6449507013	habitat	type of place where an organism usually lives	5
6449507014	niche	role of an organism in its environment	6
6449507015	biotic	living	7
6449507016	abiotic	nonliving	8
6449507017	climate	long-term / average weather conditions in a given area; major components include temperature, precipitation, sunlight, and wind	9
6449507037	population size	total number of individuals in the population	10
6449507038	population density	total number of individuals per area or volume occupied	11
6449507039	population dispersion	pattern of organism grouping: clumped, random, uniform	12
6449507040	clumped dispersion	most common pattern of distribution, like humans in cities or schools of fish	13
6449507041	uniform dispersion	distribution pattern like trees in an human-made orchard, or bird nests	14
6449507042	random dispersion	distribution pattern like trees in a forest or weeds in a field	15
6449507043	age structure diagram	describes the abundance of individuals of each age	16
6449507044	survivorship curves	describe how mortality of individuals in a species varies during their lifetimes	17
6449507045	type I survivorship curve	describe a species in which most individuals survive to middle age; after that age, mortality is high.example: humans	18
6449507046	type II survivorship curve	describe organisms in which the length of survivorship is random, that is, the likelihood of death is the same at any ageexample: rodents, invertebrates	19
6449507047	type III survivorship curve	describe species in which most individuals die young, with only a relative few surviving to reproductive age and beyondexample: oysters, species with free-swimming larvae	20
6449507048	biotic potential	maximum growth rate of a population under ideal conditions with unlimited resources and without any growth restrictions	21
6449507050	carrying capacity	maximum number of individuals of a population that can be sustained by a particular habitat	22
6449507051	limiting factors	factors that prevent a population from attaining its biotic potential	23
6449507053	density-dependent limiting factors	limiting effect becomes more intense as the population density increases examples: parasites and disease, competition, toxic effect of waste products, predation, stress	24
6449507054	density-independent limiting factors	occur independently of the density of a population examples: natural disasters and climate extremes	25
6449507057	exponential growth	occurs when reproductive rate is greater than zero; forms a J-shaped curve on a graph	26
6449507058	logistic growth	occurs when limiting factors restrict the size of a population to the carrying capacity of the habitat; forms an S-shaped curve on a graph	27
6449507060	reproductive success	measure of fitness - how well an organism survives and reproduces	28
6449507063	interspecific competition	competition between two different species	29
6449507065	resource partitioning	some species coexist in spite of apparent competition for the same resources. they actually occupy slightly different niches.	30
6449507073	herbivore	animal that eats plants	31
6449507074	symbiosis	two species that live together in close contact during a portion or all of their lives	32
6449507076	mutualism	a relationship in which both species benefit	33
6449507077	commensalism	a relationship in which one species benefits while the second is neither helped nor harmed	34
6449507078	parasitism	a relationship in which one benefits while the another is harmed	35
6449507083	mimicry	two or more species resemble one another in appearance or behavior	36
6449507086	ecological succession	change in the composition of species over time; one community is gradually and predictably replaced by another community	37
6449507087	climax community	final successional stage of constant species composition; persists relatively unchanged until destroyed by a catastrophic event, like fire	38
6449507089	pioneer species	species that are the first to colonize a newly exposed habitat; work to break down rock into smaller rock, then into sand, and finally into soil as succession progresses	39
6449507090	primary succession	occurs where no soil was previously present; begins on rock. pioneer species and other plants break down rock into pebbles, then sand, then soil. as organisms die and decompose, it nourishes the soil allowing for more and larger organisms to grow or live in that area	40
6449507091	secondary succession	occurs as primary succession, except soil is already present	41
6449507093	food web	expanded, more complete version of a food chain that shows all major plants in the ecosystem, various animals that eat them, and the animals that eat the animals	42
6449507094	autotrophs	perform photosynthesis	43
6449507095	heterotrophs	consumer other organisms for organic material and/or a source of energy	44
6449507096	ecological pyramids	show relationships between trophic levels	45
6449507103	detritivores / decomposers	heterotrophs that obtain their energy by consuming dead plants and animals	46
6449507104	10 % rule	90% of the energy in a trophic pyramid is used, stored, or lost	47
6449507105	primary productivity	amount of organic matter produced through photosynthetic activity per unit of time	48
6449507107	keystone species	one that has a strong influence on the health of a community or ecosystem; removal of this species results in dramatic changes in the makeup of species that comprise other trophic levels	49
6449507108	invasive species	introduced species that has no competition or natural predators; disrupts a community	50
6449507111	biodiversity	function of the number of species, niches, and trophic levels in the ecosystem and the complexity of its food web	51
6449507128	global climate change	Burning of fossil fuels releases greenhouse gases such as carbon dioxide into the atmosphere. These greenhouse gases trap infrared radiation, raising the temperature of the earth's atmosphere and resulting in large scale climate change.	52

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BC Calculus AP Review Flashcards

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9584854110	Double Angle Formula for cos²(θ)		0
9584854111	Double Angle Formula for sin²(θ)		1
9584854112	sin(0)=		2
9584854113	sin(π/4)		3
9584854114	sin⁻¹(-1)		4
9584854115	tan⁻¹(-1)		5
9584854116	1+cot²(θ)		6
9584854117	1+tan²(θ)		7
9584854118	sin(2θ)		8
9584854119	cos(2θ)		9
9584854120	log(AB)		10
9584854121	log(A / B)		11
9584854122	log(A) ^ x		12
9584854123	e^(ln(x))		13
9584854124	ln(x) / ln(a)		14
9584854125	Simplify the expression into one log: 2 ln(x) + ln(x+1) - ln(x-1)		15
9584854126	For what value of x is there a hole, and for what value of x is there a vertical asymptote? f(x) = ((x - a)(x - b))/ ((x - a)(x - c))		16
9584854127	Definition of the Derivative (Using the limit as h→0)		17
9584854128	lim x→₀ sin(x)/x		18
9584854129	lim x→∞ tan⁻¹(x)		19
9584854130	First derivative test for a local max of f at x = a		20
9584854131	First derivative test for a local min of f at x = a		21
9584854132	Second derivative test for a local max of f at x = a		22
9584854133	Second derivative test for a local min of f at x = a		23
9584854134	Test for max and mins of f on [a, b]		24
9584854135	Inflection Points		25
9584854136	ƒ'(x) < 0		26
9584854137	ƒ''(x) < 0 or ƒ'(x) is decreasing		27
9584854138	ƒ'(x) > 0		28
9584854139	ƒ''(x) > 0 or ƒ'(x) is increasing		29
9584854140	Intermediate Value Theorem (IVT)		30
9584854141	Mean Value Theorem (MVT)		31
9584854142	Rolle's Theorem		32
9584854143	Squeeze Theorem		33
9584854144	ƒ(x) is continuous at x = a if...		34
9584854145	Extreme Value Theorem		35
9584854146	Critical Points		36
9584854147	Three types of discontinuities.		37
9584854148	ƒ(x) is differentiable at x = a if...		38
9584854149	Three conditions where ƒ(x) is not differentiable		39
9584854150	Average rate of change of ƒ(x) over [a, b]		40
9584854151	Instantaneous rate of change of ƒ(a)		41
9584854152	d/dx ( tan⁻¹ ( x ) )		42
9584854153	d/dx ( sin⁻¹ ( x ) )		43
9584854154	d/dx ( e ^ x )		44
9584854155	d/dx ( ln x )		45
9584854156	d/dx ( a ^ x )		46
9584854157	d/dx ( sin x )		47
9584854158	d/dx ( cos x )		48
9584854159	d/dx ( tan x )		49
9584854160	d/dx ( sec x )		50
9584854161	d/dx ( csc x )		51
9584854162	d/dx ( cot x )		52
9584854163	Product Rule		53
9584854164	Quotient Rule		54
9584854165	Chain Rule		55
9584854166	d/dx (ƒ(x)³)		56
9584854167	d/dx ( ln ƒ(x) )		57
9584854168	d/dx (e ^ ƒ(x) )		58
9584854169	Derivative of the Inverse of ƒ(x)		59
9584854170	Implicit Differentiation Find dy/dx: x²/9+y²/4=1		60
9584854171	Equation of a line in point-slope form		61
9584854172	Equation of the tangent line to y = ƒ(x) at x = a		62
9584854173	A normal line to a curve is...		63
9584854174	Velocity of a point moving along a line with position at time t given by d(t)		64
9584854175	Speed of a point moving along a line		65
9584854176	Average velocity of s over [a, b]		66
9584854177	Average speed of s over [a, b]		67
9584854178	Average acceleration given v over [a, b]		68
9584854179	An object in motion is at rest when...		69
9584854180	An object in motion reverses direction when...		70
9584854181	Acceleration of a point moving along a line with position at time t given by d(t)		71
9584854182	How to tell if a point moving along the x-axis with velocity v(t) is speeding up or slowing down at some time t?		72
9584854183	Position at time t = b of a particle moving along a line given velocity v(t) and position s(t) at time t = a		73
9584854184	Displacement of a particle moving along a line with velocity v(t) for a ≤ t ≤ b.		74
9584854313	Total distance traveled by a particle moving along a line with velocity v(t) for a ≤ t ≤ b	...	75
9584854185	The total change in ƒ(x) over [a, b] in terms of the rate of change, ƒ'(x)		76
9584854186	Graph of y = 1/x		77
9584854187	Graph of y = e ^ (kx)		78
9584854188	Graph of y = ln x		79
9584854189	Graph of y = sin x		80
9584854190	Graph of y = cos x		81
9584854191	Graph of y = tan x		82
9584854192	Graph of y = tan⁻¹ x		83
9584854193	Graph of y = √(1 - x²)		84
9584854194	Graph of x²/a² + y²/b² = 1		85
9584854195	L'Hopital's Rule		86
9584854196	To find the limits of indeterminate forms: ∞ × 0		87
9584854197	To find the limits of indeterminate forms: 0 ^ 0, 1 ^ ∞, ∞ ^ 0		88
9584854198	If ƒ(x) is increasing, then a left Riemann sum ...		89
9584854199	If ƒ(x) is decreasing, then a left Riemann sum ...		90
9584854200	If ƒ(x) is increasing, then a right Riemann sum ...		91
9584854201	If ƒ(x) is decreasing, then a right Riemann sum ...		92
9584854202	If ƒ(x) is concave up, then the trapezoidal approximation of the integral...		93
9584854203	If ƒ(x) is concave down, then the trapezoidal approximation of the integral...		94
9584854204	If ƒ(x) is concave up, then a midpoint Riemann sum...		95
9584854205	If ƒ(x) is concave down, then a midpoint Riemann sum...		96
9584854206	Area of a trapezoid		97
9584854207	If ƒ(x) is concave down then the linear approximation...		98
9584854208	If ƒ(x) is concave up then the linear approximation...		99
9584854209	The Fundamental Theorem of Calculus (Part I)		100
9584854210	The Fundamental Theorem of Calculus (Part II)		101
9584854211	∫ x ^ n dx =		102
9584854212	∫ e ^ x dx =		103
9584854213	∫ 1/x dx =		104
9584854214	∫ sin x dx =		105
9584854215	∫ cos x dx =		106
9584854216	∫ sec² x dx =		107
9584854217	∫ a ^ x dx =		108
9584854218	∫ tan x dx =		109
9584854219	∫ 1 / (x² + 1) dx =		110
9584854220	∫ 1 / √(1 - x² ) dx =		111
9584854221	The average value of f from x = a to x = b (Mean Value Theorem for Integrals)		112
9584854222	Integral equation for a horizontal shift of 1 unit to the right.		113
9584854223	Adding adjacent integrals		114
9584854224	Swapping the bounds of an integral		115
9584854225	Exponential Growth Solution of dy/dt = kP P(0) = P₀		116
9584854226	lim n→∞ (1 + 1/n) ^ n		117
9584854227	Steps to solve a differential equation		118
9584854228	To find the area between 2 curves using vertical rectangles (dx)		119
9584854229	To find the area between 2 curves using horizontal rectangles (dy)		120
9584854230	Volume of a disc; rotated about a horizontal line		121
9584854231	Volume of a washer; rotated about a horizontal line		122
9584854232	Volume of a disc; rotated about a vertical line		123
9584854233	Volume of a washer; rotated about a vertical line		124
9584854234	Volume of solid if cross sections perpendicular to the x-axis are squares		125
9584854235	Volume of solid if cross sections perpendicular to the x-axis are isosceles right triangles		126
9584854236	Volume of solid if cross sections perpendicular to the x-axis are equilateral triangles		127
9584854237	Volume of solid if cross sections perpendicular to the x-axis are semicircles		128
9584854238	Volume of a prism		129
9584854239	Volume of a cylinder		130
9584854240	Volume of a pyramid		131
9584854241	Volume of a cone		132
9584854242	Volume of a sphere		133
9584854243	Surface Area of a cylinder		134
9584854244	Surface Area of a sphere		135
9584854245	Area of a Sector (in radians)		136
9584854246	Slope of a parametric curve x = x(t) and y = y(t)		137
9584854247	Horizontal Tangent of a parametric curve		138
9584854248	Vertical Tangent of a parametric curve		139
9584854249	Second Derivative of a parametric curve		140
9584854250	Velocity vector of a particle moving in the plane x = x(t) and y = y(t)		141
9584854251	Acceleration vector of a particle moving in the plane x = x(t) and y = y(t)		142
9584854252	Speed of a particle moving in the plane x = x(t) and y = y(t)		143
9584854253	Distance traveled (Arc Length) by a particle moving in the plane with a ≤ t ≤ b x = x(t) and y = y(t)		144
9584854254	Position at time t = b of a particle moving in the plane given x(a), y(a), x′(t), and y′(t).		145
9584854255	Magnitude of a vector in terms of the x and y components		146
9584854256	Graph of θ = c (c is a constant)		147
9584854257	Graph of r = θ		148
9584854258	Graphs of: r = c r = c sin(θ) r = c cos(θ) (c is a constant)		149
9584854259	Graphs of: r = sin(k θ) r = cos(k θ) (k is a constant)		150
9584854260	Graph of: r = 1 + cos(θ)		151
9584854261	Graph of: r = 1 + 2 cos(θ)		152
9584854262	Slope of polar graph r (θ)		153
9584854263	Area enclosed by r = f(θ), α ≤ θ ≤ β		154
9584854264	Double Angle Formula for cos²θ		155
9584854265	Double Angle Formula for sin²θ		156
9584854266	dx/dθ < 0		157
9584854267	dx/dθ > 0		158
9584854268	dy/dθ < 0		159
9584854269	dy/dθ > 0		160
9584854270	Convert from polar (r,θ) to rectangular (x,y)		161
9584854271	Convert from rectangular (x,y) to polar (r,θ)		162
9584854272	Horizontal Tangent of a Polar Graph		163
9584854273	Vertical Tangent of a Polar Graph		164
9584854274	Integration by Parts Formula		165
9584854275	∫ lnx dx = ?		166
9584854276	Improper Integral: ∫ 1/x² dx bounds: [0,1]		167
9584854277	Improper Integral: ∫ f(x) dx bounds: [0,∞]		168
9584854278	Arc length of a function f(x) from x = a to x = b		169
9584854279	Arc length of a polar graph r 0 ≤ θ ≤ π		170
9584854280	Arc Length of a graph defined parametrically with a ≤ t ≤ b x = x(t) and y = y(t)		171
9584854281	Differential equation for exponential growth dP/dt = ?		172
9584854282	Solution of a differential equation for exponential growth		173
9584854283	Differential equation for decay dP/dt = ?		174
9584854284	Solution of a differential equation for decay		175
9584854285	Logistic differential equation dP/dt = ?		176
9584854286	Solution of a logistic differential equation		177
9584854287	Graph of a Logistic Function (include inflection pt.)		178
9584854288	Euler's Method for solving y' = F (x,y) with initial point (x₀ , y₀)		179
9584854289	Power Series for f(x) = 1 / (1 - x) (include IOC)		180
9584854290	Power Series for f(x) = tan⁻¹ x (include IOC)		181
9584854291	Power Series for f(x) = ln (1 + x) (include IOC)		182
9584854292	Taylor Series for f(x) about x = 0 (Maclaurin Series)		183
9584854293	Taylor Series for f(x) about x = c		184
9584854294	Maclaurin Series for f (x) = e∧x (include IOC)		185
9584854295	Maclaurin Series for f (x) = sin x (include IOC)		186
9584854296	Maclaurin Series for f (x) = cos x (include IOC)		187
9584854297	Error for the partial sum, Sn, of an infinite series S		188
9584854298	Error bound of an alternating series		189
9584854299	Lagrange error bound		190
9584854300	Geometric sequence (def. and conv. property)		191
9584854301	Harmonic Series (def. and conv. property)		192
9584854302	p-series (def. and conv. property)		193
9584854303	Divergence Test		194
9584854304	If lim n→∞ a(sub n) = 0, then ∑ a(sub n) for n from 1 to ∞ ...		195
9584854305	Integral Test		196
9584854306	Alternating Series Test		197
9584854307	Direct Comparison Test		198
9584854308	Limit Comparison Test		199
9584854309	Ratio Test		200
9584854310	n-th Root Test		201
9584854311	Interval of Convergence (IOC)		202
9584854312	Radius of Convergence		203