Primitive function 12

• Understanding primitive function
• Primitive function of a given function
• The notation for primitive functions
• "Antiderivative" and "Indefinite integral" as synonyms for primitive function
• Properties of primitive function
• Primitive function and continuity
• Primitive functions of elementary functions
• Methods for computing primitive functions
• Calculate a primitive function using the table of usual antiderivatives
• Calculate antiderivatives of the usual functions
• Antiderivatives rules (sum, difference and constan rule)
• Antiderivative power rule
• Calculate antiderivatives of a subtraction
• Calculate antiderivatives of a rational fraction
• Calculate the antiderivatives of composed functions
• Calculate the antiderivative using integration by parts
• Antiderivative of trig functions
• Antiderivative of exponential function
• Calculate primitive function of function that takes the value y0 at x0
• Graphing the primitive function
• Calculate the antiderivatives of the addition

Integration Calculus 12

• Understanding integration
• Fundamental theorems of integral calculus
• Types of integrals (definite integral and indefinite integral)
• Properties of integral calculus
• Integral calculus formulas
• Methods to find integrals
• Finding integrals by integration by parts
• Finding integrals by substitution method
• Finding integrals by integration by partial fractions
• Interpretation geometries of integration
• Application of integral calculus
• Find accumulation of changes in the function
• Find average change
• Calculate the area
• Calculate the distance
• Calculate the volumes
• Calculate the surface area of revolution
• Calculate the volume of revolution
• Differentiation of Logarithmic Functions

Differentiation 12

• Understanding differential
• Derivative of function as limits
• Differentiation formulas
• Interpretation geometries of differentiation
• Understanding Differentiation Rules
• Product Rule
• Quotient Rule
• Chain Rule
• Differentiation of Elementary Functions
• Differentiation of Trigonometric Functions
• Differentiation of Inverse Trigonometric Functions
• Differentiation of Special Functions
• Higher-Order Differentiation
• The second derivative
• Real-Life Applications of Differentiation
• Understand the relationship between differentiability and continuity
• Distinguish between functions written in implicit form and explicit form
• Use implicit differentiation to find the derivative of a function

Differential Equations 12

• Understanding Differential Equations
• Order Of Differential Equations
• Types Of Differential Equations
• Ordinary Differential Equations
• Linear Differential Equations
• Methods For Solving Differential Equations
• Solve Differential Equations
• Applications Of Differential Equations
• Differential Equations: Word Problems

Complex Numbers 12

• Complex Numbers: Mixed Review
• The Real Part And The Imaginary Part Of A Complex Numbers
• Pure Imaginary Numbers Or Real Numbers
• Simplifying Pure Imaginary Numbers
• Properties Of Complex Numbers
• Complex Conjugates: Mixed Review
• Properties Of Complex Conjugates
• The Reciprocal Of A Complex Number
• Modulus Of A Complex Number
• Properties Of The Modulus Of A Complex Number
• Relationship Between The Complex Conjugate And The Modulus
• Relationship Between Addition And The Modulus Of A Complex Number
• Powers Of Complex Numbers And The Modulus
• Argument Of Complex Numbers
• Finding The Argument Of A Complex Number In Radians
• Properties Of Argument Of Complex Numbers
• Finding The Principal Argument Of A Complex Number
• Finding The Argument Of A Complex Number Using The Inverse Tangent Function
• Finding The Argument Of A Complex Number Using Positive Acute Angles
• The Relationship Between The Complex Conjugate And The Argument
• Finding Argument Of The Conjugate Of A Complex Number
• Finding Arguments Of Products And Quotients
• Finding The Argument Of Powers Of Complex Numbers (In Algebraic Form)
• Finding The Modulus And The Argument Of A Complex Number
• Polar Form Of A Complex Number
• Writing A Complex Number In Polar Form Given Its Modulus And Principal Argument
• Finding The Polar Form Of Complex Numbers Represented On The Argand Diagram
• Finding The Modulus And Principal Argument Of Complex Numbers In Polar Form
• Converting A Complex Number From The Cartesian To The Polar Form
• Converting Complex Numbers From The Polar To The Cartesian Form
• Polar Form Of The Conjugate Of A Complex Number
• Multiplication Of Complex Numbers In Polar Form
• The Quotient Of Complex Numbers In Polar Form
• Relationship Between Sine, Cosine, And The Exponential Function
• Exponential Form Of A Complex Number
• Converting Complex Numbers From Polar To Exponential Form
• Converting Complex Numbers From Cartesian To Exponential Form
• Converting Complex Numbers From Exponential To Cartesian Form
• Converting Complex Numbers Between Exponential And Polar And Cartesian Form
• Multiplication Of Complex Numbers In Exponential Form
• Euler’s Formula
• Division Of Complex Numbers In Exponential Form
• Conjugate Of Complex Numbers In Exponential Form
• Adding Complex Numbers In Exponential Form
• Properties Of Complex Numbers In Exponential Form
• De Moivre’s Theorem Formula
• Using De Moivre’s Theorem To Find The Product Of Complex Powers
• Using De Moivre’s Theorem To Find The Difference Of Complex Powers
• Using De Moivre’s Theorem To Raise To A Power
• Solving Problems With Powers Of Complex Numbers
• Using De Moivre’s Theorem To Find The Roots Of A Complex Number

Law of Sines and Cosines 12

• Use Law Of Sines To Solve Oblique Triangles (AAS)
• Use Law Of Sines To Solve Oblique Triangles (ASA)
• Use Law Of Sines To Solve Oblique Triangle (The Ambiguous Case SSA - Single Solution)
• Use Law Of Sines To Solve Oblique Triangle (The Ambiguous Case SSA - Two Solution)
• Find The Areas Of Oblique Triangles
• Use Law Of Sines To Solve Real Life Problems
• Use The Law Of Cosines To Solve Oblique Triangles (SSS)
• Use The Law Of Cosines To Solve Oblique Triangles (SAS)
• Use Law Of Cosines To Solve Real Life Problems
• Use Heron’s Area Formula To Find Areas Of Triangles

Vectors 12

• Initial point of a vector
• Terminal point of a vector
• Direction of a vector
• Magnitude of vector
• Represent vectors graphically
• Scalar multiplication of a vector
• Represent Vector Operations Algebraically
• Represent Vector Operations Graphically
• Properties Of Vector Addition
• Properties Of Vector Scalar Multiplication
• Unit Vectors
• Write A Linear Combination Of Unit Vectors
• Find Direction Angles Of Vectors
• Component Form Of A Vector
• Transform A Vector Using Matrix Multiplication
• Find The Area Of A Parallelogram Defined By Vectors
• Find The Area Of A Triangle Defined By Vectors
• Use Vectors To Determine Weight
• Use Vectors To Find Speed And Direction
• Finding Dot Products Of Two Vectors
• Properties Of The Dot Product
• Find The Angle Between Two Vectors
• Orthogonal Vectors
• Vector Components
• Determine Work Using Vectors
• Sum Of A Finite Arithmetic Sequence

Sequences and Series 12

• Determine whether a sequence is finite or infinite
• Use Sequence Notation To Write The Terms Of A Sequence
• Recursive Sequences
• Factorial Notation
• Simplify Factorial Notation Rational Expressions
• Write The Terms Of A Sequence Involving Factorials
• Evaluate A Sequence With Summation Notation
• Properties Of Sums
• Defining Series
• Finding The Sum Of A Series
• Using A Recursion Formula
• Partial Sum Of An Arithmetic Sequence
• Sum Of A Finite Geometric Sequence
• Sum Of An Infinite Geometric Series
• Use Sequences And Series To Solve Real World Problems
• Find A Formula For A Finite Sum
• Sums Of Powers Of Integers
• Finite Differences

Conics 12

• Use the center, the radius, and the Pythagorean theorem to derive the equation of a circle.
• Foci Of An Ellipse
• Major And Minor Axis Of An Ellipse
• Co-Vertices Of An Ellipse
• Derive The Equation Of An Ellipse
• Graph Ellipses
• Graph Ellipses Using Translations
• Eccentricity Of An Ellipse
• Foci Of A Hyperbola
• Axes Of A Hyperbola
• Vertices Of A Hyperbola
• Asymptotes Of A Hyperbola
• Use The Distance Formula And Foci To Derive The Equation Of A Hyperbola
• Graph Hyperbolas
• Classify A Second Degree Equation As Either A Parabola, Circle, Ellipse, Or Hyperbola From General Equations.
• Classify A Second Degree Equation As Either A Parabola, Circle, Ellipse, Or Hyperbola Using The Discriminant
• Rotation Of Axes For An Ellipse
• Rotation Of Axes For A Hyperbola
• Rotation Of Axes For A Parabola

Polar Form 12

• Find The Modulus Of A Complex Number
• Represent A Complex Number In Polar Form
• Use Polar Form To Multiply Complex Numbers
• Use Polar Form To Raise A Number To A Power
• Plot Points In The Polar Coordinate System
• Convert Points From Polar To Rectangular From
• Convert Points From Rectangular To Polar Form
• Convert Polar Equations To Rectangular Form
• Graph Polar Equations By Plotting Points
• Test For Symmetry In Polar Coordinates
• Use Symmetry To Graph A Polar Equation
• Special Polar Graphs: Limacons
• Identify Special Polar Graphs: Rose Curves
• Identify Special Polar Graphs: Lemniscates
• Identify Special Polar Graphs: Circles
• Graph A Rose Curve
• Graph A Lemniscate
• Identify The Type Of Conic From A Polar Equation
• Graph A Conic From Its Polar Equation
• Find The Polar Equation Of A Conic

Trigonometry And The Unit Circle 12

• Measure Angles Using Degree Measure
• Measure Angles Using Radian Measure
• Find Coterminal Angles In Degree Measure
• Find Coterminal Angles In Radian Measure
• Complementary Angles In Radian Measure
• Supplementary Angles In Radian Measure
• Convert An Angle Measure From Degrees To Radians
• Convert An Angle Measure From Radians To Degrees
• Find Arc Length
• Find Linear Speed
• Find Angular And Linear Speed
• Find Area Of A Sector Of A Circle
• Graph The Unit Circle
• Use The Properties Of 30-60-90 Triangles To Find The Coordinate Points At The 〖30〗^° (π/6 radian) Angle Measure On The Unit Circle
• Use The Properties Of 45-45-90 Triangles To Find The Coordinate Points At The 〖45〗^° (π/4 radian) Angle Measure On The Unit Circle
• Use The Properties Of 30-60-90 Triangles To Find The Coordinate Points At The 〖60〗^° (π/3 radian) Angle Measure On The Unit Circle
• Extend Your Knowledge Of The Coordinates At 〖30〗^°,〖45〗^° ,〖60〗^° Angles To Find Coordinates In The Other Three Quadrants Of The Unit Circle
• Understand That For Any Angle θ On The Unit Circle With Points (x,y), □sin sin θ =y
• Understand That For Any Angle θ On The Unit Circle With Points (x,y), □cos cos θ =x
• Understand That For Any Angle θ On The Unit Circle With Points (x,y), □tan tan θ =y/x
• Understand That For Any Angle θ On The Unit Circle With Points (x,y), □csc csc θ =1/y
• Understand That For Any Angle θ On The Unit Circle With Points (x,y), □sec sec θ =1/x
• Understand That For Any Angle θ On The Unit Circle With Points (x,y), □cot cot θ =x/y
• Evaluate Trig Functions From Angle Measures On The Unit Circle
• Evaluate Trigonometric Functions Of Acute Angles

Tangent Functions 12

• Identify Tangent Functions From The Equation
• Identify Tangent Functions From The Graph
• Identify Tangent Functions From The Table
• Identify Tangent Functions From A Set Of Ordered Pairs
• Domain Of Tangent Functions
• Range Of Tangent Functions
• Complete A Function Table From The Graph Of A Tangent Function
• Write Tangent Functions To Solve Word Problems
• Solve Problems Involving Tangent Functions
• Evaluate Tangent Functions
• Identify Increasing, Decreasing And Constant Intervals Of Tangent Functions

Graphing Trig Functions 12

• Determine the period from a sine or cosine function in equation form
• Determine The Amplitude From A Sine Or Cosine Function In Equation Form
• Determine The Period From A Sine Or Cosine Function In Graph Form
• Determine The Amplitude From A Sine Or Cosine Function In Graph Form
• Identify Minimum And Maximum Points Of Sine And Cosine Equations
• Identify Symmetry In The Graphs Of Sine And Cosine
• Graph Sine And Cosine Functions Using Transformations
• Determine The Asymptotes From A Tangent Function In Equation Form
• Determine The Asymptotes From A Tangent Function In Graph Form
• Graph A Tangent Function
• Identify Symmetry In Tangent Graphs
• Graph A Tangent Function Using Transformations
• Determine If Trig Functions Are Odd, Even, Or Neither

Cosecant Functions 12

• Identify Cosecant Functions From The Equation
• Identify Cosecant Functions From The Graph
• Identify Cosecant Functions From A Set Of Ordered Pairs
• Domain Of Cosecant Functions
• Range Of Cosecant Functions

Secant Functions 12

• Identify Secant Functions From The Equation
• Identify Secant Functions From The Graph
• Identify Secant Functions From A Set Of Ordered Pairs
• Domain Of Secant Functions
• Range Of Secant Functions

Cotangent Functions 12

• Identify Cotangent Functions From The Equation
• Identify Cotangent Functions From The Graph
• Identify Cotangent Functions From A Set Of Ordered Pairs
• Domain Of Cotangent Functions
• Range Of Cotangent Functions

Graphing Reciprocal Trig Functions 12

• Graph A Cosecant Function
• Graph A Secant Function
• Determine The Period From A Cosecant Or Secant Function In Equation Form
• Determine The Period From A Cosecant Or Secant Function In Graph Form
• Determine The Asymptotes For A Cosecant Function In Equation Form
• Determine The Asymptotes For Secant Function In Equation Form
• Determine The Asymptotes For A Cosecant Function In Graph Form
• Determine The Asymptotes For Secant Function In Graph Form
• Identify Symmetry In Cosecant Graphs
• Identify Symmetry In Secant Graphs
• Graph A Cotangent Function
• Determine The Period From A Cotangent Function In Equation Form
• Determine The Period From A Cotangent Function In Graph Form
• Determine The Asymptotes From A Cotangent Function In Equation Form
• Determine The Asymptotes From A Cotangent Function In Graph Form
• Identify Symmetry Of Cotangent Graphs
• Determine If Reciprocal Trig Functions Are Odd, Even, Or Neither

Inverse Trig Functions 12

• Understand That Arcsine, Arccosine, And Arctangent Represent The Inverse Of A Sine, Cosine, And Tangent Function Respectively
• Evaluate Arcsine Functions Using Unit Circle Knowledge
• Evaluate Arcsine Functions Using A Calculator
• Graph The Arcsine Functions
• Evaluate Arccosine Functions Using Unit Circle Knowledge
• Evaluate Arccosine Functions Using A Calculator
• Graph Arccosine Functions
• Domain Of Arcsine And Arccosine Functions
• Range Of Arcsine Functions
• Range Of Arccosine Functions
• Evaluate Arctangent Functions Using Unit Circle Knowledge
• Evaluate Arctangent Functions Using A Calculator
• Graph Arctangent Functions
• Domain Of Arctangent Functions
• Range Of Arctangent Functions
• Properties Of Inverse Trig Functions

Trig Identities 12

• Use Reciprocal Identities To Evaluate Trig Functions
• Use Quotient Identities To Evaluate Trig Functions
• Use Pythagorean Identities To Evaluate Trig Functions
• Use Cofunction Identities To Evaluate Trig Functions
• Use Even/Odd Identities To Evaluate Trig Functions
• Simplify A Trigonometric Expression Using Trig Identities
• Add And Subtract Trigonometric Expressions Using Trig Identities
• Trigonometric Substitution
• Rewrite A Logarithmic Expression Using Trig Identities
• Verify Trigonometric Identities

Trig Formulas 12

• Use The Sum And Difference Formulas For Sine To Evaluate A Trigonometric Function
• Use The Sum And Difference Formulas For Tangent To Evaluate A Trigonometric Function
• Use Sum And Difference Formulas To Verify Identities
• Use Sum And Difference Formulas To Solve A Trigonometric Equation
• Use Multiple-Angle Formulas To Rewrite Trigonometric Functions
• Use Multiple-Angle Formulas To Evaluate Trigonometric Functions
• Use Double-Angle Formulas To Rewrite Trigonometric Functions
• Use Double-Angle Formulas To Evaluate Trigonometric Functions
• Use Power-Reducing Formulas To Rewrite Trigonometric Functions
• Use Half-Angle Formulas To Rewrite Trigonometric Functions
• Use Half-Angle Formulas To Evaluate Trigonometric Functions
• Use Product-To-Sum Formulas To Rewrite Trigonometric Functions
• Use Product-To-Sum Formulas To Evaluate Trigonometric Functions
• Use Sum-To-Product Formulas To Rewrite Trigonometric Functions
• Use Sum-To-Product Formulas To Evaluate Trigonometric Functions
• Use Trigonometric Formulas To Rewrite Real Life Models

Trigonometric Applications 12

• Solve A Right Triangle For Any Missing Angles Using Trigonometry
• Simple Harmonic Motion
• Combining Like Terms Using Trigonometric Functions
• Extract Square Roots From Trigonometric Equation
• Solve A Right Triangle For Any Missing Sides Using Trigonometry
• Find An Angle Of Depression
• Find Directions In Terms Of Bearings
• Solve Trigonometric Equations Of Quadratic Type
• Squaring And Converting To Quadratic Types
• Use The Quadratic Formula To Solve Trigonometric Equations Of Quadratic Type
• Use Inverse Functions To Solve Trigonometric Equations Of Quadratic Type
• Solving A Multiple-Angle Equation

Probability And Statistics 12

• Identify Whether A Question Is A Statistical Question Or Not
• Identify The Statistical Variable
• Determine Whether A Statistical Variable Is Qualitative Or Quantitative
• Identify The Difference Between A Sample And A Population
• Identify Whether A Quantity Is A Statistic Or A Parameter
• Identify A Statistical Study As A Sample Survey
• Identify A Statistical Study As An Experiment
• Determine If A Study Has Bias
• Identify Skewed Distributions
• Use Z-Scores To Compare Data Points From Different Scales
• Evaluate Reports By Estimating Population Parameters
• Use Margin Of Error Formula For Quantitative Data

Limits And Their Properties 12

• Estimate A Limit Using A Numerical Approach
• Estimate A Limit Using A Graphical Approach
• Estimate A Limit Using An Analytic Approach
• Learn That A Limit Can Fail To Exist When Behavior Differs From The Right And From The Left
• Learn That A Limit Can Fail To Exist Because Of Unbounded Behavior
• Limits And Oscillating Behavior
• Use A Formal Definition Of Limit
• Evaluate Basic Limits
• Limit Of A Polynomial
• Limit Of A Rational Function
• Limit Of A Composite Function
• Limits Of Trigonometric Functions
• Evaluate A Limit Using The Dividing Out Technique
• Determine Infinite Limits From The Right
• Use Vertical Asymptotes To Help In Determining Limits

Differentiation 12

• Find The Slope Of The Tangent Line To A Curve At A Point
• Use The Limit Definition To Find The Derivative Of A Function
• Understand The Relationship Between Differentiability And Continuity
• Find The Derivative Of A Function Using The Constant Rule
• Find The Derivative Of A Function Using The Power Rule
• Find The Derivative Of A Function Using The Constant Multiple Rule
• Find The Derivative Of A Function Using The Sum Rule
• Find The Derivative Of A Function Using The Difference Rule
• Find The Derivative Of The Sine Function
• Find The Derivative Of The Cosine Function
• Use Derivatives To Find Rates Of Change
• Find The Derivative Of A Function Using The Product Rule
• Find The Derivative Of A Function Using The Quotient Rule
• Find The Derivative Of A Trigonometric Function
• Find A Higher-Order Derivative Of A Function
• Find The Derivative Of A Composite Function Using The Chain Rule
• Find The Derivative Of A Function Using The General Power Rule
• Simplify Derivatives By Factoring Out The Least Powers
• Simplify Derivatives Of A Quotient
• Simplify Derivatives Of A Power
• Find The Derivative Of A Trigonometric Function Using The Chain Rule
• Distinguish Between Functions Written In Implicit Form And Explicit Form
• Use Implicit Differentiation To Find The Derivative Of A Function

Complex Numbers And Complex Plane 12

• Write Trigonometric Forms Of Complex Numbers
• Multiply Complex Numbers Written In Trigonometric Form
• Divide Complex Numbers Written In Trigonometric Form
• Use Demoivre’s Theorem To Find Powers Of Complex Numbers
• Find Nth Roots Of Complex Numbers
• Multiplying In The Complex Plane
• Dividing In The Complex Plane