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Mathematics

AP Calculus Cheat Sheet

Subject: 
Calculus
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Calculus
Mathematical analysis
Mathematics
Integral calculus
Differentiation rules
Integration by parts
Differential equation
derivative
Quotient Rule
Integration by substitution
Antiderivative
Product rule

Calculus Cheat Sheet Visit http://tutorial.math.lamar.edu for a complete set of Calculus notes. ? 2005 Paul Dawkins Limits Definitions Precise Definition : We say ( )limx a f x L? = if for every 0e > there is a 0d > such that whenever 0 x a d< - < then ( )f x L e- < . ?Working? Definition : We say ( )limx a f x L? = if we can make ( )f x as close to L as we want by taking x sufficiently close to a (on either side of a) without letting x a= . Right hand limit : ( )limx a f x L+? = . This has the same definition as the limit except it requires x a> . Left hand limit : ( )limx a f x L-? = . This has the same definition as the limit except it requires x a< . Limit at Infinity : We say ( )limx f x L?? = if we

Theorems, Postulates, and Corollaries

Subject: 
Geometry
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Logic
Mathematics
Human development
Computer file formats
geometry
theorem
Axiom
Attachment theory
Portable Document Format
Technology
theorems

Geometry Cheat Sheet of Theorems, Postulates, and Corollaries
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comp sci

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Calculus
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Mathematics
Mathematical logic
Logic
Inductive reasoning
Knowledge
Mathematical proofs
Mathematical induction
Proof theory
Graph theory
Structural induction
Recursive definition
XTR
discrete math

CS 330 : Discrete Computational Structures Fall Semester, 2013 Assignment #5 Due Date: Friday, Oct 11 Suggested Reading: Rosen Section 5.1 - 5.2; Lehman et al. Chapter 5.1 - 5.3 These are the problems that you need to turn in. For more practice, you are encouraged to work on the other problems. Always explain your answers and show your reasoning. 1. Rosen, Section 5.1: Exercise 4 2. Rosen, Section 5.1: Exercise 6 3. Rosen, Section 5.1: Exercise 10 4. Rosen, Section 5.1: Exercise 16 5. Rosen, Section 5.1: Exercise 20 6. Rosen, Section 5.1: Exercise 32 7. Rosen, Section 5.1: Exercise 44 8. Let P (n) be the statement that n-cent postage can be formed using just 3-cent and 8-cent stamps. Prove that P (n) is true for all n ? 14, using the steps below.

Variables Practice

Subject: 
Biology
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Design of experiments
Statistics
Mathematics
scientific method
Dependent and independent variables
Variable
experiment
Internal validity
Manipulation checks
AP
Biology

Independent and Dependent Variables An independent variable is a factor that is manipulated in an experiment.? The experimenter controls whether or not subjects are exposed to the independent variable.?? The dependent variable is measured to determine if the manipulation of the independent variable had any effect.? For example,?? to test a hypothesis that eating carrots improves vision, the experimenter would manipulate whether or not subjects ate carrots.? Thus, eating carrots is the independent variable.? Each subject?s vision would be tested to see if carrot eating had any effect.? Thus, vision is the dependent variable.? The subjects assigned to eat carrots are in the experimental group, whereas subjects not eating carrots are in the control group. ?

Math Algebra

Subject: 
Algebra
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Mathematics
Algebra
Elementary algebra
equations
Quadratic forms
Quadratic
polynomials
Linear equation
Matrix
Completing the square
Factorization
Differential equation
education

CALIFORNIA CONTENT STANDARDS: ALGEBRA I # of Items % Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences. In addition, algebraic skills and concepts are developed and used in a wide variety of problem-solving situations. N/A N/A Algebra I 65 100% Standard Set 1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable: N/A 1.1 Students use properties of numbers to demonstrate whether assertions are true or false. 1/2**

Summary of Trig Inverse Function

Subject: 
Trigonometry
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Mathematics
trigonometry
geometry
Mathematical analysis
Inverse trigonometric functions
Sine
Trigonometric functions
Unit Circle
Cartesian coordinate system
Inverse function

Trig Inverse Function Summary Function Meaning Domain Range Quadrants of Found on the (i.e., possible (i.e., possible the Unit Circle calculator by values for x) values for y) from Which Range Values Come j=sin!x y is the angle in the first or [-1, 1] [-nI2, n12] I and IV sin" (X) j=arcsin x fourth quadrant whose sine value is x j=cosir Y is the angle in the first or [-1, 1] [0, n] I and II cos-I(X) y=arccos x second quadrant whose cosine value is x j=tanix y is the angle in the first or (-00, (0) (-nl2, n12) I and IV tan" (X) y=arctanx fourth quadrant whose , tangent value is x

Trig formula sheet

Subject: 
Trigonometry
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Mathematics
Mathematical analysis
Special functions
trigonometry
Analytic functions
logarithms
Exponentials
Natural logarithm
Inverse function
Trigonometric functions
Sine
Inverse trigonometric functions
education

All Rights Reserved: http://regentsprep.org Algebra 2 ? Things to Remember! Exponents: 0 1x ? 1m m x x ? ? ?m n m nx x x ?? ?( )n m n mx x? m m n n x x x ?? n n n x x y y ? ? ?? ?? ? ( ) ?n n nxy x y? Complex Numbers: 1 i? ? ; 0a i a a? ? ? 2 1i ? ? 14 2 1i i? ? ? divide exponent by 4, use remainder, solve. ( ) conjugate ( )a bi a bi? ? 2 2( )( )a bi a bi a b? ? ? ? 2 2a bi a b? ? ? absolute value=magnitude Logarithms log yby x x b? ? ? ln logex x? natural log e = 2.71828? 10log logx x? common log Change of base formula: log log logb a a b

Physics Knight 2E Ch 1 Test Bank

Subject: 
Physics
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Actuarial science
Financial risk
Mathematical finance
Value at risk
Var
Static single assignment form
Numerical linear algebra
Mathematics
Applied mathematics
Sedenion

College Physics, 2e (Knight) Chapter 1 Representing Motion 1.1 Quantitative 1) The following conversion equivalents are given: 1 gal = 231 in3 1 ft = 12 in 1 min = 60 s A pipe delivers water at the rate of 95 gal/min. The rate, in in3/s, is closest to: A) 0.21 B) 0.19 C) 0.17 D) 0.15 E) 0.14 Answer: A Var: 50+ 2) The following conversion equivalents are given: 1 m = 100 cm 1 in = 2.54 cm 1 ft = 12 in A bin has a volume of 1.5 m3. The volume of the bin, in ft3, is closest to: A) 35 B) 41 C) 47 D) 53 E) 59 Answer: D Var: 1 3) The following conversion equivalents are given: 1 mile = 5280 ft 1 ft = 12 in 1 m = 39.37 in 1 hour = 60 min 1 min = 60 s

Algebra 1

Subject: 
Algebra
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Mathematics
Abstract algebra
Algebra
Elementary arithmetic
Binary operations
Elementary algebra
Negative number
Addition
multiplication
Number
Inequality
Distributive Property
education

Curriculum Map Staff Name: Mr. Kurth Course: Algebra 1 Month/Unit: Sept 6 ? Sep 17 UNIT 1 ? Tools of Algebra C O N T E N T Using Variables Exponents and Order of Operations Addition and Subtraction of Real Numbers Multiplication and Division of Real Numbers Distributive Property Various Properties of Real Numbers Graphing Data on a Coordinate Plane S K I L L S Add, Subtract, Multiply and Divide Variables Solve for variables Correct processing real numbers through the order of operations Use the distributive property Compare integers and real numbers

Rational Functions

Subject: 
Algebra
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Mathematics
Abstract algebra
Algebra
Division
Polynomial
Fraction
Rational function
Number
Partial fraction
Algebraic number
education

Extending function arithmetic to division results in the family of "rational" functions (Quotients of polynomials) with the property that Let be the degree of the numerator and be the degree of the denominator A rational function is said to be: Strictly proper if Proper if Improper if Any rational function which is not strictly proper can be expressed as the sum of a polynomial and a strictly proper rational function Given with Let be the result of the quotient and be the remainder of the same quotient, then EXAMPLE: Any strictly proper rational function can be expressed as the sum of simpler rational functions whose denominators are quadratic or linear polynomials Display Mode:

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