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ARITHMETIC PROPERTIES 
 
 
 
ASSOCIATIVE 
COMMUTATIVE 
DISTRIBUTIVE 
ARITHMETIC OPERATIONS EXAMPLES 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
EXPONENT PROPERTIES 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
PROPERTIES OF INEQUALITIES 
 
 
 
 PROPERTIES OF COMPLEX NUMBERS 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ABSOLUTE VALUE 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
LOGARITHM PROPERTIES 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
QUADRATIC EQUATION 
 
For the equation 
 RADICAL PROPERTIES 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
COMMON FACTORING EXAMPLES 
 
 
 
 
 
 
 
 
 
COMPLETING THE SQUARE 
 
1. Divide by the coefficient a. 
2. Move the constant to the other side. 
3. Take half of the coefficient b/a, square 
 it and add it to both sides. 
4. Factor the left side of the equation. 
5. Use the square root property. 
6. Solve for x. 
 
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ALGEBRA 
 
PROPERTIES 
 
 
 
FRUSTUM OF A CONE 
 
 
 
 
 
 
SQUARE RECTANGLE CIRCLE 
TRIANGLE 
CIRCULAR RING SPHERE 
CUBE 
RECTANGULAR BOX 
CYLINDER 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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CIRCULAR SECTOR 
 
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TRAPEZOID 
 
PYTHAGOREAN THEOREM 
 
RIGHT CIRCULAR CONE 
 
GEOMETRY 
 
SHAPES AND SOLIDS 
 
PARALLELOGRAM 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
RIGHT TRIANGLE DEFINITION 
UNIT CIRCLE DEFINITION 
 
 
 
 
 
 
 
 
 
 
 
 
 
TRIG FUNCTIONS DOMAIN 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
TRIG FUNCTIONS RANGE 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
TRIG FUNCTIONS PERIOD 
 
 
 
 
 
 
 
 
 
 
 
 
 
INVERSE TRIG FUNCTION NOTATION 
 
 
 
 
INVERSE TRIG FUNCTION RANGE 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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TRIGONOMETRY 
 
DEFINITION 
 
INVERSE TRIG DOMAIN 
 
 
 
 
 
 
TANGENT IDENTITIES 
 
 
 
 
 
 
 
 
 
RECIPROCAL IDENTITIES 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
PYTHAGOREAN IDENTITIES 
IDENTITIES 
 
 
 
PERIODIC IDENTITIES 
IDENTITIES 
 
 
 
 
 
 
EVEN/ODD IDENTITIES 
IDENTITIES 
 
 
 
 
 
 
DOUBLE ANGLE IDENTITIES 
 
 
 
 
 
 
 
 
 
HALF ANGLE IDENTITIES 
ITIES 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
TRIGONOMETRY 
 
SUM/DIFFERENCES IDENTITIES 
 
 
 
 
 
 
 
PRODUCT TO SUM IDENTITIES 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
SUM TO PRODUCT IDENTITIES 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
COFUNCTION IDENTITIES
 
 
 
RIGHT TRIANGLE DEFINITION 
UNIT CIRCLE DEFINITION 
 
 
 
 
 
 
 
Trig Functions Domain 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
TRIG FUNCTIONS RANGE 
 
 
 
 
 
 
 
TRIG FUNCTIONS PERIOD 
 
 
 
 
INVERSE TRIG FUNCTION NOTATION 
 
 
 
 
INVERSE TRIG FUNCTION RANGE 
 
 
 
 
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TRIGONOMETRY 
 
DEFINITION 
 
 
INVERSE TRIG DOMAIN 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
LAW OF SINES 
 
 
 
 
 
 
 
 
 
 
LAW OF COSINES 
 
 
 
 
LAW OF TANGENTS 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
MOLLWEIDE’S FORMULA 
 
 
 
 
 
 
 
 
 
 
 
 
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LAWS AND IDENTITIES 
 
 
 
 
 
 
 
 
 
where and 
 
INTEGRATION BY SUBSTITUTION 
COMMON INTEGRALS 
 
 
 or 
 
INTEGRATION BY PARTS 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
INTEGRATION PROPERTIES 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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Left-hand and right-hand rectangle approximations 
Midpoint Rule 
Trapezoid Rule 
 
APPROXIMATING DEFINITE INTEGRALS 
 
 
 
 
APPROXIMATION BY SIMPSON RULE FOR EVEN N 
 
CALCULUS 
 
INTEGRALS 
 
 
 
 
 
 
 
 
 
 
 
 
EXPRESSION EVALUATION 
 
SUBSTITUTION 
 
IDENTITY USED 
 
EXPRESSION 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
TRIGNOMETRIC SUBSTITUTION 
DEFINITE INTEGRAL DEFINITION 
 
 
 
 
 
 
 
 
where 
 
 
 and 
FUNDAMENTAL THEOREM OF CALCULUS 
 
 
 
 
 
where f is continuous on [a,b] and 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
DERIVATIVE DEFINITION 
BASIC PROPERTIES 
CHAIN RULE AND OTHER EXAMPLES 
 
 
 
 
 
 
 
MEAN VALUE THEOREM 
 
 
 
 
PRODUCT RULE 
 
 
 
 
 
 
 
 
 
 
QUOTIENT RULE 
 
 
 
 
POWER RULE 
 
 
 
 
CHAIN RULE 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
COMMON DERIVATIVES 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
PROPERTIES OF LIMITS 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
LIMIT EVALUATIONS AT +- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
LIMIT EVALUATION METHOD – FACTOR AND CANCEL 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
L’HOPITAL’S RULE 
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CALCULUS 
 
DERIVATIVES AND LIMITS 
 
	1.algebra
	2.geometry-shapes-solids
	3.trigonometry-definition
	4.trigonometry-laws-and-identities
	5.calculus-integrals
	6.calculus-derivatives-limits