Chapter 1: Linear and Quadratic Functions
Objectives:
Section 1-1 "Points and Lines"
Objective: To find the intersection of two lines and to find the length and the coordinates of the midpoint of a segment.
Section 1-2 "Slopes of Lines"
Objective: To find the slope of a line and to determine whether two lines are parallel, perpendicular, or neither.
Section 1-3 "Finding Equations of Lines"
Objective: To find an equation of a line given certain geometric properties of the line.
Section 1-4 "Linear Functions and Models"
Objective: To model real-world situations by means of linear functions.
Section 1-5 "The Complex Numbers"
Objective: To add, subtract, multiply, and divide complex numbers.
Section 1-6 "Solving Quadratic Equations"
Objective: To solve quadratic equations using different methods.
Section 1-7 "Quadratic Functions and Their Graphs"
Objective: To define and graph quadratic functions.
Section 1-8 "Quadratic Models"
Objective: To model real-world situations using quadratic functions.
Here are some videos that may help review some of the concepts discussed in chapter 1:
Section 1-2 VIDEO "Slopes of Lines"
Section 1-3 VIDEO "Finding Equations of Lines"
Section 1-4 VIDEO "Linear Functions and Models"
Section 1-5 VIDEO "Complex Numbers"
Chapter 2: Polynomial Functions
Objectives:
Section 2-1 "Polynomials"
Objective: To identify a polynomial function, to evaluate it using synthetic substitution, and to determine its zeros.
Section 2-2 "Synthetic Division; the Remainder and Factor Theorems"
Objective: To use synthetic division and to apply the remainder and factor theorems.
Section 2-3 "Graphing Polynomial Functions"
Objective: To graph a polynomial function and to determine an equation for a polynomial graph.
Section 2-4 "Finding Maximums and Minimums of Polynomial Functions"
Objective: To write a polynomial function for a given situation and to find the maximum or minimum value of the function.
Section 2-5 "Using Technology to Approximate Roots of Polynomial Functions"
Objective: To use technology to approximate the real roots of a polynomial equation.
Section 2-6 "Solving Polynomial Equations by Factoring"
Objective: To solve polynomial equations by various methods of factoring, including the use of the rational root theorem.
Section 2-7 "General Results for Polynomial Equations"
Objective: To apply general theorems about polynomial equations.
Here are some videos that may help review some of the concepts discussed in chapter 2:
Chapter 3: Inequalities
Objectives:
Section 3-1 "Linear Inequalities; Absolute Value"
Objective: To solve and graph linear inequalities in one variable.
Section 3-2 "Polynomial Inequalities in One Variable"
Objective: To solve and graph polynomial inequalities in one variable.
Section 3-3 "Polynomial Inequalities in Two Variables"
Objective: To graph polynomial inequalities in two variables and to graph the solution set of a system of inequalities.
Section 3-4 "Linear Programming"
Objective: To solve certain applied problems using linear programming.
Here are some videos that may help review some of the concepts discussed in chapter 3:
Section 3-1 VIDEO "Linear Inequalities; Absolute Value"
Section 3-2 VIDEO "Polynomial Inequalities in One Variable"
Section 3-3 VIDEO "Polynomial Inequalities in Two Variables"
Chapter 4: Functions
Objectives:
Section 4-1 "Functions"
Objective: To identify a function, to determine the domain, range, and zeros of a function, and to graph a function.
Section 4-2 "Operations on Functions"
Objective: To perform operations on functions and to determine the domains of the resulting functions.
Section 4-3 "Reflecting Graphs; Symmetry"
Objective: To reflect graphs and to use symmetry to sketch graphs.
Section 4-4 "Periodic Functions; Stretching and Translating Graphs"
Objective: To determine periodicity and amplitude from graphs, to stretch and shrink graphs both vertically and horizontally, and to translate graphs.
Section 4-5 "Inverse Functions"
Objective: To find the inverse of a function, if the inverse exists.
Section 4-7 "Forming Functions from Verbal Descriptions"
Objective: To form a function of one variable from a verbal description and, when appropriate, to determine the minimum or maximum value of the function.
Here are some videos that may help review some of the concepts discussed in chapter 4:
Chapter 5: Exponents and Logarithms
Objectives:
Section 5-1 "Growth and Decay: Integral Exponents"
Objective: To define and apply integral exponents.
Section 5-2 "Growth and Decay: Rational Exponents"
Objective: To define and apply rational exponents.
Section 5-3 "Exponential Functions"
Objective: To define and use exponential functions.
Section 5-4 "The Number e and the Function ex"
Objective: To define and apply the natural exponential function.
Section 5-5 "Logarithmic Functions"
Objective: To define and apply logarithms.
Section 5-6 "Laws of Logarithms"
Objective: To prove and apply laws of logarithms.
Section 5-7 "Exponential Equations; Changing Bases
Objective: To solve exponential equations and to change logarithms from one base to another.
Here are some videos that may help review some of the concepts discussed in chapter 5:
Section 5-2 VIDEO "Growth and Decay: Rational Exponents"
Section 5-3 VIDEO "Exponential Functions"
Section 5-4 VIDEO "The Number e and the Function e to the x"
Section 5-5 VIDEO "Logarithmic Functions"
Chapter 7: Trigonometric Functions
Objectives:
Section 7-1 "Measurement of Angles"
Objective: To find the measure of an angle in either degrees or radians and to find coterminal angles.
Section 7-2 "Sectors of Circles"
Objective: To find the arc length and area of a sector of a circle and to solve problems involving apparent size.
Section 7-3 "The Sine and Cosine Functions"
Objective: To use the definitions of sine and cosine to find values of these functions and to solve simple trigonometric equations.
Section 7-4 "Evaluating and Graphing Sine and Cosine"
Objective: To use reference angles, calculators, and special angles to find values of the sine and cosine functions and to sketch their graphs.
Section 7-5 "The Other Trigonometric Functions"
Objective: To find values of the tangent, cotangent, secant, and cosecant functions and to sketch the functions' graphs.
Section 7-6 "The Inverse Trigonometric Functions"
Objective: To find values of the inverse trigonometric functions.
Here are some videos that may help review some of the concepts discussed in chapter 7:
Chapter 8: Trigonometric Equations and Applications
Objectives:
Section 8-1 "Simple Trigonometric Equations"
Objective: To solve simple trigonometric equations and to apply them.
Section 8-2 "Sine and Cosine Curves"
Objective: To find equations of different sine and cosine curves and to apply these equations.
Section 8-3 "Modeling Periodic Behavior"
Objective: To use trigonometric functions to model periodic behavior.
Section 8-4 "Relationships Among the Functions"
Objective: To simplify trigonometric expressions and to prove trigonometric identities.
Section 8-5 "Solving More Difficult Trigonometric Equations"
Objective: To use trigonometric identities or technology to solve more difficult trigonometric equations.
Here are some videos that may help review some of the concepts discussed in chapter 8:
Chapter 9: Triangle Trigonometry
Objectives:
Section 9-1 "Solving Right Triangles"
Objective: To use trigonometry to find unknown sides or angles of a right triangle.
Section 9-2 "The Area of a Triangle"
Objective: To find the area of a triangle given the lengths of two sides and the measure of the included angle.
Section 9-3 "The Law of Sines"
Objective: To use the law of sines to find unknown parts of a triangle.
Section 9-4 "The Law of Cosines"
Objective: To use the law of cosines to find unknown parts of a triangle.
Mixed Trigonometry Exercises
Section 9-5 "Applications of Trigonometry to Navigation and Surveying"
Objective: To use trigonometry to solve navigation and surveying problems.
Here are some videos that may help review some of the concepts discussed in chapter 9:
Section 9-1 VIDEO "Solving Right Triangles"
Section 9-2 VIDEO "Area of a Triangle"
Chapter 10: Trigonometric Addition Formulas
Objectives:
Section 10-1 "Formulas for cosine alpha +/- beta and sine alpha +/- beta"
Objective: To derive and apply formulas for cosine alpha +/- beta and sine alpha +/- beta.
Section 10-2 "Formulas for tangent alpha +/- beta"
Objective: To derive and apply formulas for tangent alpha +/- beta.
Section 10-3 "Double-Angle and Half-Angle Formulas"
Objective: To derive and apply double-angle and half-angle formulas.
Section 10-4 "Solving Trigonometric Equations"
Objective: To use identities to solve trigonometric equations.
Here are some videos that may help review some of the concepts discussed in chapter 10:
Section 10-2 VIDEO "Formulas for Tangent of a Sum/Difference"
Section 10-3a VIDEO "Double Angle Formulas"
Chapter 6: Analytic Geometry
Objectives:
Section 6-1 "Coordinate Proofs"
Objective: To prove theorems from geometry by using coordinates.
Section 6-2 "Equations of Circles"
Objective: To find equations of circles and to find the coordinates of any points where circles and lines meet.
Section 6-3 "Ellipses"
Objective: To find equations of ellipses and to graph them.
Section 6-4 "Hyperbolas"
Objective: To find equations of hyperbolas and to graph them.
Section 6-5 "Parabolas"
Objective: To find equations of parabolas and to graph them.
Here are some videos that may help review some of the concepts discussed in chapter 6:
Chapter 15: Combinatorics
Objectives:
Section 15-1 "Venn Diagrams"
Objective: To use Venn diagrams to illustrate intersections and unions of sets and to use the inclusion-exclusion principle to solve counting problems.
Section 15-2 "The Multiplication, Addition, and Complement Principles"
Objective: To use the multiplication, addition, and complement principles to solve counting problems.
Section 15-3 "Permutations and Combinations"
Objective: To solve problems involving permutations and combinations.
Section 15-4 "Permutations with Repetition; Circular Permutations"
Objective: To solve counting problems that involve permutations with repetition and circular permutations.
Mixed Combinatorics Exercises
Here are some videos that may help review some of the concepts discussed in chapter 15:
Chapter 13: Sequences and Series
Objectives:
Section 13-1 "Arithmetic and Geometric Sequences"
Objective: To identify an arithmetic or geometric sequence and find a formula for its nth term.
Section 13-2 "Recursive Definitions"
Objective: To use sequences defined recursively to solve problems.
Section 13-3 "Arithmetic and Geometric Series and Their Sums"
Objective: To find the sum of the first n terms of arithmetic or geometric series.
Section 13-4 "Limits of Infinite Sequences"
Objective: To find or estimate the limit of an infinite sequence or to determine that the limit does not exist.
Section 13-5 "Sums of Infinite Series"
Objective: To find the sum of an infinite geometric series.
Here are some videos that may help review some of the concepts discussed in chapter 13: