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Reference sheet for inside cover of INBs
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Reference sheet for Algebra/Geometryx Exponents:
a2 – b2 = (a – b) (a + b)
Copyright © Regents Exam Prep Center http://regentsprep.org
Perimeter: add the distances around the outside. Circumference: 2C r dS S
Pythagorean Theorem: Right Triangles only. 2 2 2c a b � Triples: 3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25
Trig: Right triangles only
sin oA
h ( ; cos a
Ah
( ; tan oA
a (
Angle of elevation: from horizontal line of sight up. Angle of depression: from horizontal line of sight down.
Volume and Surface Area: rectangular solidV l w h < <
rectangular solid 2 2 2SA lh hw lw � � 2
cylinderV r hS 2
closed cylinder 2 2SA rh rS S �
Error in Measurement: Relative error = |measure-actual| actual % of Error = Relative • 100% Permutations: Arrangement in specific order.
!P( )!n r
nn r
�
Data: 5 Statistical Summary: minimum, maximum, median, 1st quartile, 3rd quartile Quartiles divide data into 4 equal parts. Percentiles divide data into 100 equal parts.
Percentile rank of score x 100number of scores below xn
< , where n is
the number of scores. Mean = average. Mode = most often (may be more than one answer). Median = middle. Outliers = values that are far away from the rest of the data. Median best describes data if outliers exist. Range = difference between the maximum and minimum values.
Area: 12triangleA bh
2
3
4equilateral triangles
A
rectangleA bh 2
squareA bh s
parallelogramA bh
1 2rhombus 2
d dA bh
<
trapezoid 1 21 ( )2
A h b b � 2
circleA rS 2
sector of circle 360n
A rS
2semicircle
12
A rS
2quarter circle
14
A rS
Probability: P(A’) = 1 – P(A) complement P(A and B) = P(A)•P(B) independent P(A and B) = P(A)•P(B/A) dependent P(A or B) = P(A) + P(B) mutually exclusive P(A or B) = P(A) + P(B) – P(A and B) not exclusive P(B/A) = P(A and B)/P(A) conditional probability P(B/A) means probability of B given A has occurred.
Box and Whisker Plot: 1st and 3rd quartiles are at the ends of the box, median is a vertical line in the box, and the max/min are at the ends of the whiskers. Helpful in interpreting the distribution of data.
Literal equations: a = b + cd, solve for c. a – b = cd a – b = c d Use same strategies as for solving equations.
Sets: Union - all elements in both sets. Intersection - elements where sets overlap.
' Complement - elements not in the set.
A BA BA
*�
{ } or � means null set.
Exponential Growth and Decay: Decay: where 0 and 0 1xy ab a b ! � �
Growth: where 0 and 1xy ab a b ! !
Copyright © Regents Exam Prep Center http://regentsprep.org
Algebra – Things to Remember! Scientific Notation: 3.2 x 1013
The first number must be 1 < n < 10 Factorial: 5! = 5•4•3•2•1 1! = 1 FYI: 0!=1
Absolute Value: | -5 | = 5 | 5 | = 5 Represents distance
Exponents: 2 2( 3) 3� z � •m n m nx x x �
02 1 •( )n m n mx x
33
144
� m
m nn
xx
x�
( ) •n n nxy x y
Properties of Real Numbers: Commutative Property: a + b = b + a ab = ba Associative Property: a+(b+c) = (a+b)+c a(bc) = (ab)c Distributive Property: a(b+c) = ab + ac Identity: a + 0 = a a • 1 = a Inverse: a + (-a) = 0 a • (1/a) = 1 Zero Property: a • 0 = 0
Undefined: 6
7 x� is undefined when x = 7 since
the denominator = 0.
Degree: Degree of monomial = sum of exponents 4x3 is of degree 3 x2y3 is of degree 5
Polygons and sides: triangle – 3 quadrilateral – 4 pentagon – 5 hexagon – 6 septagon – 7
octagon – 8 nonagon – 9 decagon – 10 dodecagon - 12
Multiply: (distribute or FOIL) ( 3)( 2) • • 2 3• 3• 2x x x x x x� � � � � = 2 5 6x x� �
2 2 2( ) 2a b a ab b� � � 2 2 2( ) 2a b a ab b� � �
Direct Variation: y = kx where k = constant of variation k = y/x
Solving Equations: 1. Deal with any parentheses in the problem. 2. Combine similar terms on same side of = sign. 3. Get the needed variables on the same side of = sign. 4. Isolate the needed variable by add or subtract. 5. Find the needed variable by divide or multiply.
Add Fractions: Get the common denominator: 5 3 5 9 14 76 2 6 6 6 3x x x x x x� �
Factor: Look for a GCF (greatest common factor) Factor binomial or trinomial.
2 2 ( )( )a b a b a b� � �
Quadratic Equation:
2 5 6 0 Set = 0.( 3)( 2) 0 Factor.
3; 2 Find roots
x xx x
x x
� � � �
Interval Notation: (1,5) 1 5[1,5] 1 5
xx
l � �l d d
Inequalities: 5 3 13 Remember to
3 8 change direction4 8 of inequality when
2 mult/div by a negative.
x xx xx
x
� d �� d �� dt �
Function: Passes the vertical line test.A set of ordered pairs in which each x element has only one y element associated with it. f (x) = 3x + 4 f (3) = 3•3 + 4 = 13
Systems: y – 2x = 1 y + 2x = 9
Linear: substitute; add to eliminate one variable or graph.
y = x2 –x-6 y = 2x – 2
Linear Quadratic: substitute or graph
For inequality systems, graph. x = abscissa, y = ordinate Slope:
2 1
2 1
= = .
y yvertical change risem
horizontal change run x x�
�
Equations of Lines: m = slope
1 1
slope-intercept( ) point-slope
y mx by y m x x �� �
Parallel and Perpendicular: Parallel: slopes are equal. Perpendicular: slopes are negative reciprocals (flip over and negate)
Parabola: 2y ax bx c � �
Axis of symmetry:
2
bx
a�
Roots: where the graph crosses the x-axis.
Copyright © Regents Exam Prep Center http://regentsprep.org
Algebra – Things to Remember! Scientific Notation: 3.2 x 1013
The first number must be 1 < n < 10 Factorial: 5! = 5•4•3•2•1 1! = 1 FYI: 0!=1
Absolute Value: | -5 | = 5 | 5 | = 5 Represents distance
Exponents: 2 2( 3) 3� z � •m n m nx x x �
02 1 •( )n m n mx x
33
144
� m
m nn
xx
x�
( ) •n n nxy x y
Properties of Real Numbers: Commutative Property: a + b = b + a ab = ba Associative Property: a+(b+c) = (a+b)+c a(bc) = (ab)c Distributive Property: a(b+c) = ab + ac Identity: a + 0 = a a • 1 = a Inverse: a + (-a) = 0 a • (1/a) = 1 Zero Property: a • 0 = 0
Undefined: 6
7 x� is undefined when x = 7 since
the denominator = 0.
Degree: Degree of monomial = sum of exponents 4x3 is of degree 3 x2y3 is of degree 5
Polygons and sides: triangle – 3 quadrilateral – 4 pentagon – 5 hexagon – 6 septagon – 7
octagon – 8 nonagon – 9 decagon – 10 dodecagon - 12
Multiply: (distribute or FOIL) ( 3)( 2) • • 2 3• 3• 2x x x x x x� � � � � = 2 5 6x x� �
2 2 2( ) 2a b a ab b� � � 2 2 2( ) 2a b a ab b� � �
Direct Variation: y = kx where k = constant of variation k = y/x
Solving Equations: 1. Deal with any parentheses in the problem. 2. Combine similar terms on same side of = sign. 3. Get the needed variables on the same side of = sign. 4. Isolate the needed variable by add or subtract. 5. Find the needed variable by divide or multiply.
Add Fractions: Get the common denominator: 5 3 5 9 14 76 2 6 6 6 3x x x x x x� �
Factor: Look for a GCF (greatest common factor) Factor binomial or trinomial.
2 2 ( )( )a b a b a b� � �
Quadratic Equation:
2 5 6 0 Set = 0.( 3)( 2) 0 Factor.
3; 2 Find roots
x xx x
x x
� � � �
Interval Notation: (1,5) 1 5[1,5] 1 5
xx
l � �l d d
Inequalities: 5 3 13 Remember to
3 8 change direction4 8 of inequality when
2 mult/div by a negative.
x xx xx
x
� d �� d �� dt �
Function: Passes the vertical line test.A set of ordered pairs in which each x element has only one y element associated with it. f (x) = 3x + 4 f (3) = 3•3 + 4 = 13
Systems: y – 2x = 1 y + 2x = 9
Linear: substitute; add to eliminate one variable or graph.
y = x2 –x-6 y = 2x – 2
Linear Quadratic: substitute or graph
For inequality systems, graph. x = abscissa, y = ordinate Slope:
2 1
2 1
= = .
y yvertical change risem
horizontal change run x x�
�
Equations of Lines: m = slope
1 1
slope-intercept( ) point-slope
y mx by y m x x �� �
Parallel and Perpendicular: Parallel: slopes are equal. Perpendicular: slopes are negative reciprocals (flip over and negate)
Parabola: 2y ax bx c � �
Axis of symmetry:
2
bx
a�
Roots: where the graph crosses the x-axis.
Copyright © Regents Exam Prep Center http://regentsprep.org
Algebra – Things to Remember! Scientific Notation: 3.2 x 1013
The first number must be 1 < n < 10 Factorial: 5! = 5•4•3•2•1 1! = 1 FYI: 0!=1
Absolute Value: | -5 | = 5 | 5 | = 5 Represents distance
Exponents: 2 2( 3) 3� z � •m n m nx x x �
02 1 •( )n m n mx x
33
144
� m
m nn
xx
x�
( ) •n n nxy x y
Properties of Real Numbers: Commutative Property: a + b = b + a ab = ba Associative Property: a+(b+c) = (a+b)+c a(bc) = (ab)c Distributive Property: a(b+c) = ab + ac Identity: a + 0 = a a • 1 = a Inverse: a + (-a) = 0 a • (1/a) = 1 Zero Property: a • 0 = 0
Undefined: 6
7 x� is undefined when x = 7 since
the denominator = 0.
Degree: Degree of monomial = sum of exponents 4x3 is of degree 3 x2y3 is of degree 5
Polygons and sides: triangle – 3 quadrilateral – 4 pentagon – 5 hexagon – 6 septagon – 7
octagon – 8 nonagon – 9 decagon – 10 dodecagon - 12
Multiply: (distribute or FOIL) ( 3)( 2) • • 2 3• 3• 2x x x x x x� � � � � = 2 5 6x x� �
2 2 2( ) 2a b a ab b� � � 2 2 2( ) 2a b a ab b� � �
Direct Variation: y = kx where k = constant of variation k = y/x
Solving Equations: 1. Deal with any parentheses in the problem. 2. Combine similar terms on same side of = sign. 3. Get the needed variables on the same side of = sign. 4. Isolate the needed variable by add or subtract. 5. Find the needed variable by divide or multiply.
Add Fractions: Get the common denominator: 5 3 5 9 14 76 2 6 6 6 3x x x x x x� �
Factor: Look for a GCF (greatest common factor) Factor binomial or trinomial.
2 2 ( )( )a b a b a b� � �
Quadratic Equation:
2 5 6 0 Set = 0.( 3)( 2) 0 Factor.
3; 2 Find roots
x xx x
x x
� � � �
Interval Notation: (1,5) 1 5[1,5] 1 5
xx
l � �l d d
Inequalities: 5 3 13 Remember to
3 8 change direction4 8 of inequality when
2 mult/div by a negative.
x xx xx
x
� d �� d �� dt �
Function: Passes the vertical line test.A set of ordered pairs in which each x element has only one y element associated with it. f (x) = 3x + 4 f (3) = 3•3 + 4 = 13
Systems: y – 2x = 1 y + 2x = 9
Linear: substitute; add to eliminate one variable or graph.
y = x2 –x-6 y = 2x – 2
Linear Quadratic: substitute or graph
For inequality systems, graph. x = abscissa, y = ordinate Slope:
2 1
2 1
= = .
y yvertical change risem
horizontal change run x x�
�
Equations of Lines: m = slope
1 1
slope-intercept( ) point-slope
y mx by y m x x �� �
Parallel and Perpendicular: Parallel: slopes are equal. Perpendicular: slopes are negative reciprocals (flip over and negate)
Parabola: 2y ax bx c � �
Axis of symmetry:
2
bx
a�
Roots: where the graph crosses the x-axis.
Copyright © Regents Exam Prep Center http://regentsprep.org
Algebra – Things to Remember! Scientific Notation: 3.2 x 1013
The first number must be 1 < n < 10 Factorial: 5! = 5•4•3•2•1 1! = 1 FYI: 0!=1
Absolute Value: | -5 | = 5 | 5 | = 5 Represents distance
Exponents: 2 2( 3) 3� z � •m n m nx x x �
02 1 •( )n m n mx x
33
144
� m
m nn
xx
x�
( ) •n n nxy x y
Properties of Real Numbers: Commutative Property: a + b = b + a ab = ba Associative Property: a+(b+c) = (a+b)+c a(bc) = (ab)c Distributive Property: a(b+c) = ab + ac Identity: a + 0 = a a • 1 = a Inverse: a + (-a) = 0 a • (1/a) = 1 Zero Property: a • 0 = 0
Undefined: 6
7 x� is undefined when x = 7 since
the denominator = 0.
Degree: Degree of monomial = sum of exponents 4x3 is of degree 3 x2y3 is of degree 5
Polygons and sides: triangle – 3 quadrilateral – 4 pentagon – 5 hexagon – 6 septagon – 7
octagon – 8 nonagon – 9 decagon – 10 dodecagon - 12
Multiply: (distribute or FOIL) ( 3)( 2) • • 2 3• 3• 2x x x x x x� � � � � = 2 5 6x x� �
2 2 2( ) 2a b a ab b� � � 2 2 2( ) 2a b a ab b� � �
Direct Variation: y = kx where k = constant of variation k = y/x
Solving Equations: 1. Deal with any parentheses in the problem. 2. Combine similar terms on same side of = sign. 3. Get the needed variables on the same side of = sign. 4. Isolate the needed variable by add or subtract. 5. Find the needed variable by divide or multiply.
Add Fractions: Get the common denominator: 5 3 5 9 14 76 2 6 6 6 3x x x x x x� �
Factor: Look for a GCF (greatest common factor) Factor binomial or trinomial.
2 2 ( )( )a b a b a b� � �
Quadratic Equation:
2 5 6 0 Set = 0.( 3)( 2) 0 Factor.
3; 2 Find roots
x xx x
x x
� � � �
Interval Notation: (1,5) 1 5[1,5] 1 5
xx
l � �l d d
Inequalities: 5 3 13 Remember to
3 8 change direction4 8 of inequality when
2 mult/div by a negative.
x xx xx
x
� d �� d �� dt �
Function: Passes the vertical line test.A set of ordered pairs in which each x element has only one y element associated with it. f (x) = 3x + 4 f (3) = 3•3 + 4 = 13
Systems: y – 2x = 1 y + 2x = 9
Linear: substitute; add to eliminate one variable or graph.
y = x2 –x-6 y = 2x – 2
Linear Quadratic: substitute or graph
For inequality systems, graph. x = abscissa, y = ordinate Slope:
2 1
2 1
= = .
y yvertical change risem
horizontal change run x x�
�
Equations of Lines: m = slope
1 1
slope-intercept( ) point-slope
y mx by y m x x �� �
Parallel and Perpendicular: Parallel: slopes are equal. Perpendicular: slopes are negative reciprocals (flip over and negate)
Parabola: 2y ax bx c � �
Axis of symmetry:
2
bx
a�
Roots: where the graph crosses the x-axis.
Copyright © Regents Exam Prep Center http://regentsprep.org
Algebra – Things to Remember! Scientific Notation: 3.2 x 1013
The first number must be 1 < n < 10 Factorial: 5! = 5•4•3•2•1 1! = 1 FYI: 0!=1
Absolute Value: | -5 | = 5 | 5 | = 5 Represents distance
Exponents: 2 2( 3) 3� z � •m n m nx x x �
02 1 •( )n m n mx x
33
144
� m
m nn
xx
x�
( ) •n n nxy x y
Properties of Real Numbers: Commutative Property: a + b = b + a ab = ba Associative Property: a+(b+c) = (a+b)+c a(bc) = (ab)c Distributive Property: a(b+c) = ab + ac Identity: a + 0 = a a • 1 = a Inverse: a + (-a) = 0 a • (1/a) = 1 Zero Property: a • 0 = 0
Undefined: 6
7 x� is undefined when x = 7 since
the denominator = 0.
Degree: Degree of monomial = sum of exponents 4x3 is of degree 3 x2y3 is of degree 5
Polygons and sides: triangle – 3 quadrilateral – 4 pentagon – 5 hexagon – 6 septagon – 7
octagon – 8 nonagon – 9 decagon – 10 dodecagon - 12
Multiply: (distribute or FOIL) ( 3)( 2) • • 2 3• 3• 2x x x x x x� � � � � = 2 5 6x x� �
2 2 2( ) 2a b a ab b� � � 2 2 2( ) 2a b a ab b� � �
Direct Variation: y = kx where k = constant of variation k = y/x
Solving Equations: 1. Deal with any parentheses in the problem. 2. Combine similar terms on same side of = sign. 3. Get the needed variables on the same side of = sign. 4. Isolate the needed variable by add or subtract. 5. Find the needed variable by divide or multiply.
Add Fractions: Get the common denominator: 5 3 5 9 14 76 2 6 6 6 3x x x x x x� �
Factor: Look for a GCF (greatest common factor) Factor binomial or trinomial.
2 2 ( )( )a b a b a b� � �
Quadratic Equation:
2 5 6 0 Set = 0.( 3)( 2) 0 Factor.
3; 2 Find roots
x xx x
x x
� � � �
Interval Notation: (1,5) 1 5[1,5] 1 5
xx
l � �l d d
Inequalities: 5 3 13 Remember to
3 8 change direction4 8 of inequality when
2 mult/div by a negative.
x xx xx
x
� d �� d �� dt �
Function: Passes the vertical line test.A set of ordered pairs in which each x element has only one y element associated with it. f (x) = 3x + 4 f (3) = 3•3 + 4 = 13
Systems: y – 2x = 1 y + 2x = 9
Linear: substitute; add to eliminate one variable or graph.
y = x2 –x-6 y = 2x – 2
Linear Quadratic: substitute or graph
For inequality systems, graph. x = abscissa, y = ordinate Slope:
2 1
2 1
= = .
y yvertical change risem
horizontal change run x x�
�
Equations of Lines: m = slope
1 1
slope-intercept( ) point-slope
y mx by y m x x �� �
Parallel and Perpendicular: Parallel: slopes are equal. Perpendicular: slopes are negative reciprocals (flip over and negate)
Parabola: 2y ax bx c � �
Axis of symmetry:
2
bx
a�
Roots: where the graph crosses the x-axis.
Copyright © Regents Exam Prep Center http://regentsprep.org
Algebra – Things to Remember! Scientific Notation: 3.2 x 1013
The first number must be 1 < n < 10 Factorial: 5! = 5•4•3•2•1 1! = 1 FYI: 0!=1
Absolute Value: | -5 | = 5 | 5 | = 5 Represents distance
Exponents: 2 2( 3) 3� z � •m n m nx x x �
02 1 •( )n m n mx x
33
144
� m
m nn
xx
x�
( ) •n n nxy x y
Properties of Real Numbers: Commutative Property: a + b = b + a ab = ba Associative Property: a+(b+c) = (a+b)+c a(bc) = (ab)c Distributive Property: a(b+c) = ab + ac Identity: a + 0 = a a • 1 = a Inverse: a + (-a) = 0 a • (1/a) = 1 Zero Property: a • 0 = 0
Undefined: 6
7 x� is undefined when x = 7 since
the denominator = 0.
Degree: Degree of monomial = sum of exponents 4x3 is of degree 3 x2y3 is of degree 5
Polygons and sides: triangle – 3 quadrilateral – 4 pentagon – 5 hexagon – 6 septagon – 7
octagon – 8 nonagon – 9 decagon – 10 dodecagon - 12
Multiply: (distribute or FOIL) ( 3)( 2) • • 2 3• 3• 2x x x x x x� � � � � = 2 5 6x x� �
2 2 2( ) 2a b a ab b� � � 2 2 2( ) 2a b a ab b� � �
Direct Variation: y = kx where k = constant of variation k = y/x
Solving Equations: 1. Deal with any parentheses in the problem. 2. Combine similar terms on same side of = sign. 3. Get the needed variables on the same side of = sign. 4. Isolate the needed variable by add or subtract. 5. Find the needed variable by divide or multiply.
Add Fractions: Get the common denominator: 5 3 5 9 14 76 2 6 6 6 3x x x x x x� �
Factor: Look for a GCF (greatest common factor) Factor binomial or trinomial.
2 2 ( )( )a b a b a b� � �
Quadratic Equation:
2 5 6 0 Set = 0.( 3)( 2) 0 Factor.
3; 2 Find roots
x xx x
x x
� � � �
Interval Notation: (1,5) 1 5[1,5] 1 5
xx
l � �l d d
Inequalities: 5 3 13 Remember to
3 8 change direction4 8 of inequality when
2 mult/div by a negative.
x xx xx
x
� d �� d �� dt �
Function: Passes the vertical line test.A set of ordered pairs in which each x element has only one y element associated with it. f (x) = 3x + 4 f (3) = 3•3 + 4 = 13
Systems: y – 2x = 1 y + 2x = 9
Linear: substitute; add to eliminate one variable or graph.
y = x2 –x-6 y = 2x – 2
Linear Quadratic: substitute or graph
For inequality systems, graph. x = abscissa, y = ordinate Slope:
2 1
2 1
= = .
y yvertical change risem
horizontal change run x x�
�
Equations of Lines: m = slope
1 1
slope-intercept( ) point-slope
y mx by y m x x �� �
Parallel and Perpendicular: Parallel: slopes are equal. Perpendicular: slopes are negative reciprocals (flip over and negate)
Parabola: 2y ax bx c � �
Axis of symmetry:
2
bx
a�
Roots: where the graph crosses the x-axis.
Copyright © Regents Exam Prep Center http://regentsprep.org
Algebra – Things to Remember! Scientific Notation: 3.2 x 1013
The first number must be 1 < n < 10 Factorial: 5! = 5•4•3•2•1 1! = 1 FYI: 0!=1
Absolute Value: | -5 | = 5 | 5 | = 5 Represents distance
Exponents: 2 2( 3) 3� z � •m n m nx x x �
02 1 •( )n m n mx x
33
144
� m
m nn
xx
x�
( ) •n n nxy x y
Properties of Real Numbers: Commutative Property: a + b = b + a ab = ba Associative Property: a+(b+c) = (a+b)+c a(bc) = (ab)c Distributive Property: a(b+c) = ab + ac Identity: a + 0 = a a • 1 = a Inverse: a + (-a) = 0 a • (1/a) = 1 Zero Property: a • 0 = 0
Undefined: 6
7 x� is undefined when x = 7 since
the denominator = 0.
Degree: Degree of monomial = sum of exponents 4x3 is of degree 3 x2y3 is of degree 5
Polygons and sides: triangle – 3 quadrilateral – 4 pentagon – 5 hexagon – 6 septagon – 7
octagon – 8 nonagon – 9 decagon – 10 dodecagon - 12
Multiply: (distribute or FOIL) ( 3)( 2) • • 2 3• 3• 2x x x x x x� � � � � = 2 5 6x x� �
2 2 2( ) 2a b a ab b� � � 2 2 2( ) 2a b a ab b� � �
Direct Variation: y = kx where k = constant of variation k = y/x
Solving Equations: 1. Deal with any parentheses in the problem. 2. Combine similar terms on same side of = sign. 3. Get the needed variables on the same side of = sign. 4. Isolate the needed variable by add or subtract. 5. Find the needed variable by divide or multiply.
Add Fractions: Get the common denominator: 5 3 5 9 14 76 2 6 6 6 3x x x x x x� �
Factor: Look for a GCF (greatest common factor) Factor binomial or trinomial.
2 2 ( )( )a b a b a b� � �
Quadratic Equation:
2 5 6 0 Set = 0.( 3)( 2) 0 Factor.
3; 2 Find roots
x xx x
x x
� � � �
Interval Notation: (1,5) 1 5[1,5] 1 5
xx
l � �l d d
Inequalities: 5 3 13 Remember to
3 8 change direction4 8 of inequality when
2 mult/div by a negative.
x xx xx
x
� d �� d �� dt �
Function: Passes the vertical line test.A set of ordered pairs in which each x element has only one y element associated with it. f (x) = 3x + 4 f (3) = 3•3 + 4 = 13
Systems: y – 2x = 1 y + 2x = 9
Linear: substitute; add to eliminate one variable or graph.
y = x2 –x-6 y = 2x – 2
Linear Quadratic: substitute or graph
For inequality systems, graph. x = abscissa, y = ordinate Slope:
2 1
2 1
= = .
y yvertical change risem
horizontal change run x x�
�
Equations of Lines: m = slope
1 1
slope-intercept( ) point-slope
y mx by y m x x �� �
Parallel and Perpendicular: Parallel: slopes are equal. Perpendicular: slopes are negative reciprocals (flip over and negate)
Parabola: 2y ax bx c � �
Axis of symmetry:
2
bx
a�
Roots: where the graph crosses the x-axis.
Copyright © Regents Exam Prep Center http://regentsprep.org
Algebra – Things to Remember! Scientific Notation: 3.2 x 1013
The first number must be 1 < n < 10 Factorial: 5! = 5•4•3•2•1 1! = 1 FYI: 0!=1
Absolute Value: | -5 | = 5 | 5 | = 5 Represents distance
Exponents: 2 2( 3) 3� z � •m n m nx x x �
02 1 •( )n m n mx x
33
144
� m
m nn
xx
x�
( ) •n n nxy x y
Properties of Real Numbers: Commutative Property: a + b = b + a ab = ba Associative Property: a+(b+c) = (a+b)+c a(bc) = (ab)c Distributive Property: a(b+c) = ab + ac Identity: a + 0 = a a • 1 = a Inverse: a + (-a) = 0 a • (1/a) = 1 Zero Property: a • 0 = 0
Undefined: 6
7 x� is undefined when x = 7 since
the denominator = 0.
Degree: Degree of monomial = sum of exponents 4x3 is of degree 3 x2y3 is of degree 5
Polygons and sides: triangle – 3 quadrilateral – 4 pentagon – 5 hexagon – 6 septagon – 7
octagon – 8 nonagon – 9 decagon – 10 dodecagon - 12
Multiply: (distribute or FOIL) ( 3)( 2) • • 2 3• 3• 2x x x x x x� � � � � = 2 5 6x x� �
2 2 2( ) 2a b a ab b� � � 2 2 2( ) 2a b a ab b� � �
Direct Variation: y = kx where k = constant of variation k = y/x
Solving Equations: 1. Deal with any parentheses in the problem. 2. Combine similar terms on same side of = sign. 3. Get the needed variables on the same side of = sign. 4. Isolate the needed variable by add or subtract. 5. Find the needed variable by divide or multiply.
Add Fractions: Get the common denominator: 5 3 5 9 14 76 2 6 6 6 3x x x x x x� �
Factor: Look for a GCF (greatest common factor) Factor binomial or trinomial.
2 2 ( )( )a b a b a b� � �
Quadratic Equation:
2 5 6 0 Set = 0.( 3)( 2) 0 Factor.
3; 2 Find roots
x xx x
x x
� � � �
Interval Notation: (1,5) 1 5[1,5] 1 5
xx
l � �l d d
Inequalities: 5 3 13 Remember to
3 8 change direction4 8 of inequality when
2 mult/div by a negative.
x xx xx
x
� d �� d �� dt �
Function: Passes the vertical line test.A set of ordered pairs in which each x element has only one y element associated with it. f (x) = 3x + 4 f (3) = 3•3 + 4 = 13
Systems: y – 2x = 1 y + 2x = 9
Linear: substitute; add to eliminate one variable or graph.
y = x2 –x-6 y = 2x – 2
Linear Quadratic: substitute or graph
For inequality systems, graph. x = abscissa, y = ordinate Slope:
2 1
2 1
= = .
y yvertical change risem
horizontal change run x x�
�
Equations of Lines: m = slope
1 1
slope-intercept( ) point-slope
y mx by y m x x �� �
Parallel and Perpendicular: Parallel: slopes are equal. Perpendicular: slopes are negative reciprocals (flip over and negate)
Parabola: 2y ax bx c � �
Axis of symmetry:
2
bx
a�
Roots: where the graph crosses the x-axis.
Copyright © Regents Exam Prep Center http://regentsprep.org
Algebra – Things to Remember! Scientific Notation: 3.2 x 1013
The first number must be 1 < n < 10 Factorial: 5! = 5•4•3•2•1 1! = 1 FYI: 0!=1
Absolute Value: | -5 | = 5 | 5 | = 5 Represents distance
Exponents: 2 2( 3) 3� z � •m n m nx x x �
02 1 •( )n m n mx x
33
144
� m
m nn
xx
x�
( ) •n n nxy x y
Properties of Real Numbers: Commutative Property: a + b = b + a ab = ba Associative Property: a+(b+c) = (a+b)+c a(bc) = (ab)c Distributive Property: a(b+c) = ab + ac Identity: a + 0 = a a • 1 = a Inverse: a + (-a) = 0 a • (1/a) = 1 Zero Property: a • 0 = 0
Undefined: 6
7 x� is undefined when x = 7 since
the denominator = 0.
Degree: Degree of monomial = sum of exponents 4x3 is of degree 3 x2y3 is of degree 5
Polygons and sides: triangle – 3 quadrilateral – 4 pentagon – 5 hexagon – 6 septagon – 7
octagon – 8 nonagon – 9 decagon – 10 dodecagon - 12
Multiply: (distribute or FOIL) ( 3)( 2) • • 2 3• 3• 2x x x x x x� � � � � = 2 5 6x x� �
2 2 2( ) 2a b a ab b� � � 2 2 2( ) 2a b a ab b� � �
Direct Variation: y = kx where k = constant of variation k = y/x
Solving Equations: 1. Deal with any parentheses in the problem. 2. Combine similar terms on same side of = sign. 3. Get the needed variables on the same side of = sign. 4. Isolate the needed variable by add or subtract. 5. Find the needed variable by divide or multiply.
Add Fractions: Get the common denominator: 5 3 5 9 14 76 2 6 6 6 3x x x x x x� �
Factor: Look for a GCF (greatest common factor) Factor binomial or trinomial.
2 2 ( )( )a b a b a b� � �
Quadratic Equation:
2 5 6 0 Set = 0.( 3)( 2) 0 Factor.
3; 2 Find roots
x xx x
x x
� � � �
Interval Notation: (1,5) 1 5[1,5] 1 5
xx
l � �l d d
Inequalities: 5 3 13 Remember to
3 8 change direction4 8 of inequality when
2 mult/div by a negative.
x xx xx
x
� d �� d �� dt �
Function: Passes the vertical line test.A set of ordered pairs in which each x element has only one y element associated with it. f (x) = 3x + 4 f (3) = 3•3 + 4 = 13
Systems: y – 2x = 1 y + 2x = 9
Linear: substitute; add to eliminate one variable or graph.
y = x2 –x-6 y = 2x – 2
Linear Quadratic: substitute or graph
For inequality systems, graph. x = abscissa, y = ordinate Slope:
2 1
2 1
= = .
y yvertical change risem
horizontal change run x x�
�
Equations of Lines: m = slope
1 1
slope-intercept( ) point-slope
y mx by y m x x �� �
Parallel and Perpendicular: Parallel: slopes are equal. Perpendicular: slopes are negative reciprocals (flip over and negate)
Parabola: 2y ax bx c � �
Axis of symmetry:
2
bx
a�
Roots: where the graph crosses the x-axis.
Copyright © Regents Exam Prep Center http://regentsprep.org
Algebra – Things to Remember! Scientific Notation: 3.2 x 1013
The first number must be 1 < n < 10 Factorial: 5! = 5•4•3•2•1 1! = 1 FYI: 0!=1
Absolute Value: | -5 | = 5 | 5 | = 5 Represents distance
Exponents: 2 2( 3) 3� z � •m n m nx x x �
02 1 •( )n m n mx x
33
144
� m
m nn
xx
x�
( ) •n n nxy x y
Properties of Real Numbers: Commutative Property: a + b = b + a ab = ba Associative Property: a+(b+c) = (a+b)+c a(bc) = (ab)c Distributive Property: a(b+c) = ab + ac Identity: a + 0 = a a • 1 = a Inverse: a + (-a) = 0 a • (1/a) = 1 Zero Property: a • 0 = 0
Undefined: 6
7 x� is undefined when x = 7 since
the denominator = 0.
Degree: Degree of monomial = sum of exponents 4x3 is of degree 3 x2y3 is of degree 5
Polygons and sides: triangle – 3 quadrilateral – 4 pentagon – 5 hexagon – 6 septagon – 7
octagon – 8 nonagon – 9 decagon – 10 dodecagon - 12
Multiply: (distribute or FOIL) ( 3)( 2) • • 2 3• 3• 2x x x x x x� � � � � = 2 5 6x x� �
2 2 2( ) 2a b a ab b� � � 2 2 2( ) 2a b a ab b� � �
Direct Variation: y = kx where k = constant of variation k = y/x
Solving Equations: 1. Deal with any parentheses in the problem. 2. Combine similar terms on same side of = sign. 3. Get the needed variables on the same side of = sign. 4. Isolate the needed variable by add or subtract. 5. Find the needed variable by divide or multiply.
Add Fractions: Get the common denominator: 5 3 5 9 14 76 2 6 6 6 3x x x x x x� �
Factor: Look for a GCF (greatest common factor) Factor binomial or trinomial.
2 2 ( )( )a b a b a b� � �
Quadratic Equation:
2 5 6 0 Set = 0.( 3)( 2) 0 Factor.
3; 2 Find roots
x xx x
x x
� � � �
Interval Notation: (1,5) 1 5[1,5] 1 5
xx
l � �l d d
Inequalities: 5 3 13 Remember to
3 8 change direction4 8 of inequality when
2 mult/div by a negative.
x xx xx
x
� d �� d �� dt �
Function: Passes the vertical line test.A set of ordered pairs in which each x element has only one y element associated with it. f (x) = 3x + 4 f (3) = 3•3 + 4 = 13
Systems: y – 2x = 1 y + 2x = 9
Linear: substitute; add to eliminate one variable or graph.
y = x2 –x-6 y = 2x – 2
Linear Quadratic: substitute or graph
For inequality systems, graph. x = abscissa, y = ordinate Slope:
2 1
2 1
= = .
y yvertical change risem
horizontal change run x x�
�
Equations of Lines: m = slope
1 1
slope-intercept( ) point-slope
y mx by y m x x �� �
Parallel and Perpendicular: Parallel: slopes are equal. Perpendicular: slopes are negative reciprocals (flip over and negate)
Parabola: 2y ax bx c � �
Axis of symmetry:
2
bx
a�
Roots: where the graph crosses the x-axis.
Copyright © Regents Exam Prep Center http://regentsprep.org
Algebra – Things to Remember! Scientific Notation: 3.2 x 1013
The first number must be 1 < n < 10 Factorial: 5! = 5•4•3•2•1 1! = 1 FYI: 0!=1
Absolute Value: | -5 | = 5 | 5 | = 5 Represents distance
Exponents: 2 2( 3) 3� z � •m n m nx x x �
02 1 •( )n m n mx x
33
144
� m
m nn
xx
x�
( ) •n n nxy x y
Properties of Real Numbers: Commutative Property: a + b = b + a ab = ba Associative Property: a+(b+c) = (a+b)+c a(bc) = (ab)c Distributive Property: a(b+c) = ab + ac Identity: a + 0 = a a • 1 = a Inverse: a + (-a) = 0 a • (1/a) = 1 Zero Property: a • 0 = 0
Undefined: 6
7 x� is undefined when x = 7 since
the denominator = 0.
Degree: Degree of monomial = sum of exponents 4x3 is of degree 3 x2y3 is of degree 5
Polygons and sides: triangle – 3 quadrilateral – 4 pentagon – 5 hexagon – 6 septagon – 7
octagon – 8 nonagon – 9 decagon – 10 dodecagon - 12
Multiply: (distribute or FOIL) ( 3)( 2) • • 2 3• 3• 2x x x x x x� � � � � = 2 5 6x x� �
2 2 2( ) 2a b a ab b� � � 2 2 2( ) 2a b a ab b� � �
Direct Variation: y = kx where k = constant of variation k = y/x
Solving Equations: 1. Deal with any parentheses in the problem. 2. Combine similar terms on same side of = sign. 3. Get the needed variables on the same side of = sign. 4. Isolate the needed variable by add or subtract. 5. Find the needed variable by divide or multiply.
Add Fractions: Get the common denominator: 5 3 5 9 14 76 2 6 6 6 3x x x x x x� �
Factor: Look for a GCF (greatest common factor) Factor binomial or trinomial.
2 2 ( )( )a b a b a b� � �
Quadratic Equation:
2 5 6 0 Set = 0.( 3)( 2) 0 Factor.
3; 2 Find roots
x xx x
x x
� � � �
Interval Notation: (1,5) 1 5[1,5] 1 5
xx
l � �l d d
Inequalities: 5 3 13 Remember to
3 8 change direction4 8 of inequality when
2 mult/div by a negative.
x xx xx
x
� d �� d �� dt �
Function: Passes the vertical line test.A set of ordered pairs in which each x element has only one y element associated with it. f (x) = 3x + 4 f (3) = 3•3 + 4 = 13
Systems: y – 2x = 1 y + 2x = 9
Linear: substitute; add to eliminate one variable or graph.
y = x2 –x-6 y = 2x – 2
Linear Quadratic: substitute or graph
For inequality systems, graph. x = abscissa, y = ordinate Slope:
2 1
2 1
= = .
y yvertical change risem
horizontal change run x x�
�
Equations of Lines: m = slope
1 1
slope-intercept( ) point-slope
y mx by y m x x �� �
Parallel and Perpendicular: Parallel: slopes are equal. Perpendicular: slopes are negative reciprocals (flip over and negate)
Parabola: 2y ax bx c � �
Axis of symmetry:
2
bx
a�
Roots: where the graph crosses the x-axis.
Copyright © Regents Exam Prep Center http://regentsprep.org
Perimeter: add the distances around the outside. Circumference: 2C r dS S
Pythagorean Theorem: Right Triangles only. 2 2 2c a b � Triples: 3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25
Trig: Right triangles only
sin oA
h ( ; cos a
Ah
( ; tan oA
a (
Angle of elevation: from horizontal line of sight up. Angle of depression: from horizontal line of sight down.
Volume and Surface Area: rectangular solidV l w h < <
rectangular solid 2 2 2SA lh hw lw � � 2
cylinderV r hS 2
closed cylinder 2 2SA rh rS S �
Error in Measurement: Relative error = |measure-actual| actual % of Error = Relative • 100% Permutations: Arrangement in specific order.
!P( )!n r
nn r
�
Data: 5 Statistical Summary: minimum, maximum, median, 1st quartile, 3rd quartile Quartiles divide data into 4 equal parts. Percentiles divide data into 100 equal parts.
Percentile rank of score x 100number of scores below xn
< , where n is
the number of scores. Mean = average. Mode = most often (may be more than one answer). Median = middle. Outliers = values that are far away from the rest of the data. Median best describes data if outliers exist. Range = difference between the maximum and minimum values.
Area: 12triangleA bh
2
3
4equilateral triangles
A
rectangleA bh 2
squareA bh s
parallelogramA bh
1 2rhombus 2
d dA bh
<
trapezoid 1 21 ( )2
A h b b � 2
circleA rS 2
sector of circle 360n
A rS
2semicircle
12
A rS
2quarter circle
14
A rS
Probability: P(A’) = 1 – P(A) complement P(A and B) = P(A)•P(B) independent P(A and B) = P(A)•P(B/A) dependent P(A or B) = P(A) + P(B) mutually exclusive P(A or B) = P(A) + P(B) – P(A and B) not exclusive P(B/A) = P(A and B)/P(A) conditional probability P(B/A) means probability of B given A has occurred.
Box and Whisker Plot: 1st and 3rd quartiles are at the ends of the box, median is a vertical line in the box, and the max/min are at the ends of the whiskers. Helpful in interpreting the distribution of data.
Literal equations: a = b + cd, solve for c. a – b = cd a – b = c d Use same strategies as for solving equations.
Sets: Union - all elements in both sets. Intersection - elements where sets overlap.
' Complement - elements not in the set.
A BA BA
*�
{ } or � means null set.
Exponential Growth and Decay: Decay: where 0 and 0 1xy ab a b ! � �
Growth: where 0 and 1xy ab a b ! !
Copyright © Regents Exam Prep Center http://regentsprep.org
Perimeter: add the distances around the outside. Circumference: 2C r dS S
Pythagorean Theorem: Right Triangles only. 2 2 2c a b � Triples: 3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25
Trig: Right triangles only
sin oA
h ( ; cos a
Ah
( ; tan oA
a (
Angle of elevation: from horizontal line of sight up. Angle of depression: from horizontal line of sight down.
Volume and Surface Area: rectangular solidV l w h < <
rectangular solid 2 2 2SA lh hw lw � � 2
cylinderV r hS 2
closed cylinder 2 2SA rh rS S �
Error in Measurement: Relative error = |measure-actual| actual % of Error = Relative • 100% Permutations: Arrangement in specific order.
!P( )!n r
nn r
�
Data: 5 Statistical Summary: minimum, maximum, median, 1st quartile, 3rd quartile Quartiles divide data into 4 equal parts. Percentiles divide data into 100 equal parts.
Percentile rank of score x 100number of scores below xn
< , where n is
the number of scores. Mean = average. Mode = most often (may be more than one answer). Median = middle. Outliers = values that are far away from the rest of the data. Median best describes data if outliers exist. Range = difference between the maximum and minimum values.
Area: 12triangleA bh
2
3
4equilateral triangles
A
rectangleA bh 2
squareA bh s
parallelogramA bh
1 2rhombus 2
d dA bh
<
trapezoid 1 21 ( )2
A h b b � 2
circleA rS 2
sector of circle 360n
A rS
2semicircle
12
A rS
2quarter circle
14
A rS
Probability: P(A’) = 1 – P(A) complement P(A and B) = P(A)•P(B) independent P(A and B) = P(A)•P(B/A) dependent P(A or B) = P(A) + P(B) mutually exclusive P(A or B) = P(A) + P(B) – P(A and B) not exclusive P(B/A) = P(A and B)/P(A) conditional probability P(B/A) means probability of B given A has occurred.
Box and Whisker Plot: 1st and 3rd quartiles are at the ends of the box, median is a vertical line in the box, and the max/min are at the ends of the whiskers. Helpful in interpreting the distribution of data.
Literal equations: a = b + cd, solve for c. a – b = cd a – b = c d Use same strategies as for solving equations.
Sets: Union - all elements in both sets. Intersection - elements where sets overlap.
' Complement - elements not in the set.
A BA BA
*�
{ } or � means null set.
Exponential Growth and Decay: Decay: where 0 and 0 1xy ab a b ! � �
Growth: where 0 and 1xy ab a b ! !
Copyright © Regents Exam Prep Center http://regentsprep.org
Perimeter: add the distances around the outside. Circumference: 2C r dS S
Pythagorean Theorem: Right Triangles only. 2 2 2c a b � Triples: 3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25
Trig: Right triangles only
sin oA
h ( ; cos a
Ah
( ; tan oA
a (
Angle of elevation: from horizontal line of sight up. Angle of depression: from horizontal line of sight down.
Volume and Surface Area: rectangular solidV l w h < <
rectangular solid 2 2 2SA lh hw lw � � 2
cylinderV r hS 2
closed cylinder 2 2SA rh rS S �
Error in Measurement: Relative error = |measure-actual| actual % of Error = Relative • 100% Permutations: Arrangement in specific order.
!P( )!n r
nn r
�
Data: 5 Statistical Summary: minimum, maximum, median, 1st quartile, 3rd quartile Quartiles divide data into 4 equal parts. Percentiles divide data into 100 equal parts.
Percentile rank of score x 100number of scores below xn
< , where n is
the number of scores. Mean = average. Mode = most often (may be more than one answer). Median = middle. Outliers = values that are far away from the rest of the data. Median best describes data if outliers exist. Range = difference between the maximum and minimum values.
Area: 12triangleA bh
2
3
4equilateral triangles
A
rectangleA bh 2
squareA bh s
parallelogramA bh
1 2rhombus 2
d dA bh
<
trapezoid 1 21 ( )2
A h b b � 2
circleA rS 2
sector of circle 360n
A rS
2semicircle
12
A rS
2quarter circle
14
A rS
Probability: P(A’) = 1 – P(A) complement P(A and B) = P(A)•P(B) independent P(A and B) = P(A)•P(B/A) dependent P(A or B) = P(A) + P(B) mutually exclusive P(A or B) = P(A) + P(B) – P(A and B) not exclusive P(B/A) = P(A and B)/P(A) conditional probability P(B/A) means probability of B given A has occurred.
Box and Whisker Plot: 1st and 3rd quartiles are at the ends of the box, median is a vertical line in the box, and the max/min are at the ends of the whiskers. Helpful in interpreting the distribution of data.
Literal equations: a = b + cd, solve for c. a – b = cd a – b = c d Use same strategies as for solving equations.
Sets: Union - all elements in both sets. Intersection - elements where sets overlap.
' Complement - elements not in the set.
A BA BA
*�
{ } or � means null set.
Exponential Growth and Decay: Decay: where 0 and 0 1xy ab a b ! � �
Growth: where 0 and 1xy ab a b ! !
Copyright © Regents Exam Prep Center
Geometry – Things to Remember! Regular Solids: Tetrahedron – 4 faces Cube – 6 faces Octahedron – 8 faces Dodecahedron – 12 faces Icosahedron – 20 faces
3-D Figures: Prism: V = Bh
Pyramid: 13
V Bh
Cylinder: 2V r hS ; 22 2SA rh rS S �
Cone: 213
V r hS ; 2SA s r rS S �
Sphere: 343
V rS ; 2 24SA r dS S
Locus Theorems: Fixed distance from point.
Fixed distance from a line.
Equidistant from 2 points.
Equidistant 2 parallel lines.
Equidistant from 2 intersecting lines
Polygon Interior/Exterior Angles: Sum of int. angles = 180( 2)n �
Each int. angle (regular) = 180( 2)nn�
Sum of ext. angles = 360
Each ext. angle (regular) = 360n
Congruent Triangles SSS SAS ASA AAS HL (right triangles only)
NO donkey theorem (SSA or ASS)
CPCTC (use after the triangles are congruent)
Related Conditionals: Converse: switch if and then Inverse: negate if and then Contrapositive: inverse of the converse (contrapositive has the same truth value as the original statement)
Triangles: By Sides: Scalene – no congruent sides Isosceles – 2 congruent sides Equilateral – 3 congruent sides By Angles: Acute – all acute angles Right – one right angle Obtuse – one obtuse angle Equiangular – 3 congruent angles(60º) Equilateral l Equiangular Exterior angle of a triangle equals the sum of the 2 non-adjacent interior angles. Mid-segment of a triangle is parallel to the third side and half the length of the third side.
Inequalities: --Sum of the lengths of any two sides of a triangle is greater than the length of the third side. --Longest side of a triangle is opposite the largest angle. --Exterior angle of a triangle is greater than either of the two non-adjacent interior angles.
Pythagorean Theorem: 2 2 2c a b �
Converse: If the sides of a triangle satisfy 2 2 2c a b � then the triangle is a right triangle.
Similar Triangles: AA SSS for similarity SAS for similarity Corresponding sides of similar triangles are in proportion.
Mean Proportional in Right Triangle: Altitude Rule: Leg Rule:
altitupart hyp =other
deal partitude t hyp
hyp =
projele
cg
leg tion
Copyright © Regents Exam Prep Center http://regentsprep.org
Perimeter: add the distances around the outside. Circumference: 2C r dS S
Pythagorean Theorem: Right Triangles only. 2 2 2c a b � Triples: 3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25
Trig: Right triangles only
sin oA
h ( ; cos a
Ah
( ; tan oA
a (
Angle of elevation: from horizontal line of sight up. Angle of depression: from horizontal line of sight down.
Volume and Surface Area: rectangular solidV l w h < <
rectangular solid 2 2 2SA lh hw lw � � 2
cylinderV r hS 2
closed cylinder 2 2SA rh rS S �
Error in Measurement: Relative error = |measure-actual| actual % of Error = Relative • 100% Permutations: Arrangement in specific order.
!P( )!n r
nn r
�
Data: 5 Statistical Summary: minimum, maximum, median, 1st quartile, 3rd quartile Quartiles divide data into 4 equal parts. Percentiles divide data into 100 equal parts.
Percentile rank of score x 100number of scores below xn
< , where n is
the number of scores. Mean = average. Mode = most often (may be more than one answer). Median = middle. Outliers = values that are far away from the rest of the data. Median best describes data if outliers exist. Range = difference between the maximum and minimum values.
Area: 12triangleA bh
2
3
4equilateral triangles
A
rectangleA bh 2
squareA bh s
parallelogramA bh
1 2rhombus 2
d dA bh
<
trapezoid 1 21 ( )2
A h b b � 2
circleA rS 2
sector of circle 360n
A rS
2semicircle
12
A rS
2quarter circle
14
A rS
Probability: P(A’) = 1 – P(A) complement P(A and B) = P(A)•P(B) independent P(A and B) = P(A)•P(B/A) dependent P(A or B) = P(A) + P(B) mutually exclusive P(A or B) = P(A) + P(B) – P(A and B) not exclusive P(B/A) = P(A and B)/P(A) conditional probability P(B/A) means probability of B given A has occurred.
Box and Whisker Plot: 1st and 3rd quartiles are at the ends of the box, median is a vertical line in the box, and the max/min are at the ends of the whiskers. Helpful in interpreting the distribution of data.
Literal equations: a = b + cd, solve for c. a – b = cd a – b = c d Use same strategies as for solving equations.
Sets: Union - all elements in both sets. Intersection - elements where sets overlap.
' Complement - elements not in the set.
A BA BA
*�
{ } or � means null set.
Exponential Growth and Decay: Decay: where 0 and 0 1xy ab a b ! � �
Growth: where 0 and 1xy ab a b ! !