Material Covered
Honors PreCalculus
Chapter PP.1 Real Numbers and Alegbraic Expressions
Numbers: Real, rational, irrational, integers, whole, natural
Number Line
Definition and Properties of Absolute Value
Distance Between Two Points on a Real Number Line
Order of Operations
Understand the rules of Properties of Real Numbers
P.2 Exponents and Scientific Notation
Definition of a Natural Number Exponent
Properties of Exponents, Simplifying Exponential Expressions
Converting from Scientific to Decimal Notation, and the reverse
P.3 Radicals and Rational Exponents
Square Roots of Perfect Squares
Product Rule for Square Roots
Quotient Rule for Square Roots
Combining Radicals that first require simplification
Rationalizing Denominators
Product and Quotient Rule for nth Roots
Definition of Rational Exponents
Simplifying Expressions with Rational Exponents
P.4 PolynomialsAdding , Subtracting, Multiplying Polynomial
FOIL Method
P.5 Factoring PolynomialsGreatest Common Factor
Factoring by Grouping
Factoring Trinomials
Factoring the Difference of Two Squares
Factoring the Sum and Difference of Two Cubes
P.6 Rational ExpressionsMultiplying, Dividing, Adding, Subtracting and Simplifying Rational Expressions
Least Common Denominator
Complex Rational Expressions
Simplifying Fractional Rational Expressions Containing Radicals
Rationalizing a Numerator
P.7 Linear ExpressionsDefinition of a Linear Equation
Solving Linear Equations
Equations Involving Absolute Value
Rewriting and Solving an Absolute Value Equation without Absolute Value Bars
P.8 Quadratic EquationsSolving a Quadratic Equation by Factoring
Completing the Square
The Quadratic Formula
P.9 Linear InequalitiesGraphing Inequalities
Intervals and Inequalities, set-builder notation and interval notation
Solving Linear and Compound Inequalities
Definition of Solving a Absolute Value Inequality
Chapter 1
1.1 Graphs and Utilities
Plotting points in a rectangular coordinate system
Graphs of Equations
Graphing Calculator
Intercepts
Interpreting Graphs
1.2 Lines and SlopeSlope of a line
Point-slope Form of the equation of a line
Slope-intercept Form of the equation of a line
Equations of Horizontal and Vertical Lines
General Form of the Equation of a Line
Finding Slope and y-Intercept
Equations of a Line Parallel to a Given Line
Equations of a Line Perpendicular to a Given Line
Slope as a rate of change
1.3 Distance and Midpoint Formulas
The Distance Formula
The Midpoint Formula
The Standard Form of the Equation of a Circle
The General Form of the Equation of a Circle
1.4 Basics of a Function
Definition of a Relation
Domain and Range of a Relation
Definition of a Function
Evaluating a Function
The Domain of a Function
1.5 Graphs of Functions
Graphing by Plotting Points
Obtaining Information from a Function’s Graph
The Vertical Line Test
Increasing, Decreasing, and Constant Functions
Definitions of Relative Maximum and Relative Minimum
Average Rate of Change of a Function
Average Velocity of an Object
Definition of Even and Odd Functions
Even Functions and y-Axis Symmetry
Odd Functions and Origin Symmetry
Step Functions—Greatest Integer Function
1.6 Transformation of Functions
Graphs of Common Functions—Constant, Identity, Cubic, Square Root, Absolute Value
Vertical Shifts
Horizontal Shifts
Combining Horizontal and Vertical Shifts
Reflection about the x-Axis
Reflection about the y-Axis
Stretching and Shrinking Graphs
1.7 Combinations of Functions; Composite Functions
The Sum, Difference, Product, and Quotient of Functions
The Composition of Functions
Composite Functions and Finding Its Domain
Decomposing Functions
1.8 Inverse Functions
Definition of an Inverse Function
Verifying Inverse Functions
Finding the Inverse of a Function
Horizontal Line Test for Inverse Functions
Graphs of the Function and Its Inverse
Modeling with Functions
Common Formulas for Area, Perimeter, Volume, and Surface Area
Obtaining a Function from a Geometric Formula
1.9 Modeling with Functions
Functions from Verbal Descriptions
Modeling Costs of Long-Distance Carriers
Modeling the Number of Customers and Revenue
Functions from Formulas
Common formulas for Area, Perimeter, and Volume
Obtaining a Function from a Geometric Formula
Modeling the Area of a Rectangle with a Fixed Perimeter
Common Formulas for Surface Area
End of 1st Trimester
Chapter 2
2.1 Complex Numbers
The Imaginary Unit i
Adding and Subtracting Complex Numbers
Multiplying Complex Numbers
Complex Conjugates and Division
Quadratic Equations with Complex Imaginary Solutions
2.2 Quadratic Functions
Graphs of Quadratic Functions
Parabola vertex
Graphing Quadratic Functions with Equations in Standard Form
Graphing Quadratic Functions in the Form f(x) = ax^2 + bx + c
Minimum and Maximum: Quadratic Functions
Problem solving strategies for maximizing or minimizing
Solving a Number Problem
Maximizing Area
2.3 Polynomial Functions and Their Graphs
Smooth, Continuous Graphs
End Behavior of Polynomial Functions
The Leading Coefficient Test
Zeros of Polynomial Functions
Multiplicity and x-Intercepts
The Intermediate Value Theorem for Polynomials
A Strategy for Graphing Polynomial Functions
2.4 Dividing Polynomials; Remainder and Factor Theorems
Long Division of Polynomials and the Division Algorithm
Dividing Polynomials Using Synthetic Division
2.5 Zeros of Polynomial Functions
The Rational Zero Theorem
Solving Polynomial Equations
Properties of Polynomial Equations
Fundamental Theorem of Algebra
Linear Factorization Theorem
Finding Polynomial Functions when the Zeros Are Given
Descarte’s Rule of Signs
2.6 Rational Functions and Their Graphs
Rational Functions
Finding the Domain
Vertical Asymptotes
Horizontal Asymptotes
Strategy for Graphing a Rational Function
Slant Asymptotes
Applications – Cost function, Uniform Motion
2.7 Polynomial and Rational Inequalities
Definitiion of a polynomial inequality
Solving Polynomial Inequalities
Solving Rational Inequalities
Position Function for a Free-Falling Object Near Earth’s Surface
Direct Variation
Direct Variation with Powers
Inverse Variation
Definition of the Exponential Function
Evaluation an Exponential Function
Graphing Exponential Functions
Compound Interest
n compoundings per year
Continuous compounding
Definition of the Logarithmic Function
Location of Base and Exponent in Exponential and Logarithmic Forms
Evaluating Logarithms
Basic Logarithmic Properties Involving One
Inverse Properties of Logarithms
Characteristics of the Graphs of Logarithmic Functions
Transformations Involving Logarithmic Functions
Finding the Domain of a Logarithmic Function
Properties of Common Logarithms
Finding the Domain of Natural Logarithmic Functions
Properties of Natural Logarithmis
The Product Rule
The Quotient Rule
The Power Rule
Properties for Expanding Logarithmic Expressions
Change-of-Base Property
3.4 Exponential and Logarithmic Equations
Using Natural Logarithms to Solve Exponential Equations
Exponentiating both sides of an equation
Exponential Growth and Decay Models
Logistic Growth Models
Angles
Measuring Angles Using Degrees
Coterminal Angles
Finding Complements and Supplements
Definition of a Radian
Radian Measure
Conversion Between Degrees and Radians
Length of a Circular Arc
Definitions of Linear and Angular Speed
4.2 Trigonometric Functions: The
Unit Circle
Definitions of the Trigonometric Functions in Terms of a
Finding Values of the Trigonometric Functions
The Domain and Range of the Sine and Cosine Functions
Even and Odd Trigonometric Functions
Trigonometric Identities
Reciprocal Identities, Quotient Identities
Pythagorean Identities
Definition of a Periodic Function
Periodic Properties of the Sine, Cosine, Tangent, and Cotangent Functions
Using a Calculator to Evaluate Trigonometric Functions
4.3 Right Triangle Trigonometry
Right Triangle Definitions of Trigonometric Functions
Evaluating Trigonometric Functions
Sines, Cosines, Tangents of Special Angels
Cofunction Identities
Problem Solving
Definitions
Evaluating Trigonometric Functions
Signs of Trigonometric Functions in each of the four quadrants
Definition of Reference Angle
Using Reference Angles to Evaluate Trig. Functions
4.5 Graphs of Sine and Cosine Functions
Graphing variations of Sine
Determining Amplitudes and Periods
Graphing variations of Cosine
Graphing variations of Tangent, Cotangent, cosecant, and secant
4.7 Inverse Trigonometric Functions
Review important points from Section 1.8
Inverse Sine Function and finding exact values
Inverse Cosine Function and finding exact values
Inverse Tangent Function and finding exact values
Using the calculator to evaluate
Inverse Properties
Evaluating Composite Trigonometric Expressions
