Читать книгу Pre-Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice) - Mary Jane Sterling, Mary Sterling Jane - Страница 3

1  Cover

2  Title Page

3  Copyright

4  Introduction What You’ll Find How This Workbook Is Organized Beyond the Book Where to Go for Additional Help

5  Part 1: The Questions Chapter 1: Getting Started with Algebra Basics The Problems You’ll Work On What to Watch Out For Identifying Which System or Systems a Number Belongs To Recognizing Properties of Number Systems Simplifying Expressions with the Order of Operations Graphing Inequalities Using Graphing Formulas Applying Graphing Formulas Chapter 2: Solving Some Equations and Inequalities The Problems You’ll Work On What to Watch Out For Using Interval and Inequality Notation Solving Linear Inequalities Solving Quadratic Inequalities Solving Absolute Value Inequalities Working with Radicals and Fractional Notation Performing Operations Using Fractional Exponents Factoring Using Fractional Notation Solving Radical Equations Rationalizing Denominators Chapter 3: Function Basics The Problems You’ll Work On What to Watch Out For Using Function Notation to Evaluate Function Values Determining the Domain and Range of a Function Recognizing Even Functions Identifying Odd Functions Ruling Out Even and Odd Functions Recognizing One-to-One Functions from Given Relations Identifying One-to-One Functions from Equations Recognizing a Function’s Inverse Determining a Function’s Inverse Executing Operations on Functions Performing Function Composition Doing More Function Composition Using the Difference Quotient Chapter 4: Graphing and Transforming Functions The Problems You’ll Work On What to Watch Out For Functions and Their Inverses Sketching Quadratic Functions from Their Equations Writing Equations from Graphs of Parabolas Investigating and Graphing Radical Functions Investigating Absolute Value Functions Investigating the Graphs of Polynomial Functions Investigating Rational Functions Transformation of Functions Transforming Selected Points Using Functions Sketching Graphs Using Basic Functions and Transformations Sketching More Graphs Using Basic Functions and Transformations Chapter 5: Polynomials The Problems You’ll Work On What to Watch Out For Using Factoring to Solve Quadratic Equations Solving Quadratic Equations by Using the Quadratic Formula Using Completing the Square to Solve Quadratic Equations Solving Polynomial Equations for Intercepts Using Factoring by Grouping to Solve Polynomial Equations Applying Descartes’s Rule of Signs Listing Possible Roots of a Polynomial Equation Dividing Polynomials Using Synthetic Division to Divide Polynomials Checking for Roots of a Polynomial by Using Synthetic Division Writing Polynomial Expressions from Given Roots Writing Polynomial Expressions When Given Roots and a Point Graphing Polynomials Writing Equations from Graphs of Polynomials Chapter 6: Exponential and Logarithmic Functions The Problems You’ll Work On What to Watch Out For Understanding Function Notation Graphing Exponential Functions Solving Exponential Equations Using the Equivalence to Rewrite Expressions Using the Equivalence to Rewrite Expressions Rewriting Logarithmic Expressions Rewriting Logs of Products and Quotients as Sums and Differences Solving Logarithmic Equations Applying Function Transformations to Log Functions Applying Logarithms to Everyday Life Chapter 7: Trigonometry Basics The Problems You’ll Work On What to Watch Out For Using Right Triangles to Determine Trig Functions Solving Problems by Using Right Triangles and Their Functions Working with Special Right Triangles Changing Radians to Degrees Changing Degrees to Radians Finding Angle Measures (in Degrees) in Standard Position Determining Angle Measures (in Radians) in Standard Position Identifying Reference Angles Determining Trig Functions by Using the Unit Circle Calculating Trig Functions by Using Other Functions and Terminal Side Positions Using the Arc Length Formula Evaluating Inverse Functions Solving Trig Equations for x in Degrees Calculating Trig Equations for x in Radians Chapter 8: Graphing Trig Functions The Problems You’ll Work On What to Watch Out For Recognizing Basic Trig Graphs Graphing Sine and Cosine Applying Function Transformations to Graphs of Trig Functions Writing New Trig Functions Using Transformations Graphing Tangent and Cotangent Interpreting Transformations of Trig Functions Graphing Secant and Cosecant Interpreting Transformations from Function Rules Chapter 9: Getting Started with Trig Identities The Problems You’ll Work On What to Watch Out For Proving Basic Trig Identities Returning to Basic Sine and Cosine to Solve Identities Using Multiplication by a Conjugate to Solve Identities Solving Identities After Raising a Binomial to a Power Solving Identities After Factoring out a Common Function Solving Identities After Combining Fractions Performing Algebraic Processes to Make Identities More Solvable Chapter 10: Continuing with Trig Identities The Problems You’ll Work On What to Watch Out For Using Identities That Add or Subtract Angle Measures Confirming Double-Angle Identities Using Identities That Double the Size of the Angle Confirming the Statements of Multiple-Angle Identities Creating Half-Angle Identities from Double-Angle Identities Creating a Half-Angle Identity for Tangent Using Half-Angle Identities to Simplify Expressions Creating Products of Trig Functions from Sums and Differences Using Product-to-Sum Identities to Evaluate Expressions Using Sum-to-Product Identities to Evaluate Expressions Applying Power-Reducing Identities Using Identities to Determine Values of Functions at Various Angles Working through Identities Using Multiple Methods Chapter 11: Working with Triangles and Trigonometry The Problems You’ll Work On What to Watch Out For Applying the Law of Sines to Find Sides Utilizing the Law of Sines to Find Angles Using the Law of Sines for Practical Applications Investigating the Ambiguous Case of the Law of Sines Determining All Angles and Sides of a Triangle Finding Side Measures by Using the Law of Cosines Using the Law of Cosines to Determine an Angle Applying the Law of Cosines to Real-World Situations Finding Areas of Triangles by Using the Sine Applying the Trig Formula for Area of a Triangle Using the Trig Formula for Area in Various Situations Solving Area Problems Needing Additional Computations Finding Areas of Triangles by Using Heron’s Formula Applying Heron’s Formula Practical Applications Using Heron’s Formula Tackling Practical Applications by Using Triangular Formulas Chapter 12: Complex Numbers and Polar Coordinates The Problems You’ll Work On What to Watch Out For Writing Powers of i in Their Simplest Form Adding and Subtracting Complex Numbers Multiplying Complex Numbers Using Multiplication to Divide Complex Numbers Solving Quadratic Equations with Complex Solutions Graphing Complex Numbers Identifying Points with Polar Coordinates Identifying Points Whose Angles Have Negative Measures Converting Polar to Rectangular Coordinates Converting Rectangular to Polar Coordinates Recognizing Polar Curves Chapter 13: Conic Sections The Problems You’ll Work On What to Watch Out For Identifying Conics from Their Equations Rewriting Conic Equations in Standard Form Writing Equations for Circles Determining Foci and Axes of Symmetry of Parabolas Finding the Vertices and Directrixes of Parabolas Writing Equations of Parabolas Determining Centers and Foci of Ellipses Writing Equations of Ellipses Determining Asymptotes of Hyperbolas Writing Equations of Hyperbolas Changing Equation Format from Trig Functions to Algebraic Changing Equation Format from Algebraic to Trig Chapter 14: Systems of Equations and Inequalities The Problems You’ll Work On What to Watch Out For Using Substitution to Solve Systems of Linear Equations with Two Variables Using Elimination to Solve Systems of Linear Equations with Two Variables Solving Systems of Equations Involving Nonlinear Functions Solving Systems of Linear Equations Solving Systems of Linear Equations with Four Variables Graphing Systems of Inequalities Decomposition of Fractions Operating on Matrices Changing Matrices to the Echelon Form Solving Systems of Equations Using Augmented Matrices Solving Systems of Equations Using the Inverse of the Coefficient Matrix Applying Cramer’s Rule to Solve Systems of Equations Chapter 15: Sequences and Series The Problems You’ll Work On What to Watch Out For Finding Terms of Sequences Determining Rules for Sequences Working with Recursively Defined Sequences Adding Terms in an Arithmetic Series Summing Terms of a Series Finding Rules and Summing Terms of a Series Calculating the Sum of a Geometric Series Determining Formulas and Finding Sums Counting Items by Using Combinations Constructing Pascal’s Triangle Applying Pascal’s Triangle Utilizing the Binomial Theorem Chapter 16: Introducing Limits and Continuity The Problems You’ll Work On What to Watch Out For Determining Limits from Graphs Determining One-Sided Limits Determining Limits from Function Values Determining Limits from Function Rules Applying Laws of Limits Investigating Continuity

6  Part 2: The Answers Chapter 17: Answers

7  Index

8  About the Author

9  Connect with Dummies

10  End User License Agreement