MAC 1147 Topics (Stewart) 6^th ed

The Main Topics list the material/examples required from the e-book.

 The Main Concepts must be study before taking the test. The listed problems must be worked after you have worked the suggested examples below, and you have worked the book homework. To make sure you are prepared for the test, these problems must be worked without referring to your book/ notes.

This book contains more material than is required for this course. The only material/examples required to be read from the book is listed below.

Test #1

Below are the Main Concepts for Test #1

 Section 1.8,  and Chapters 3 and 4

Ch 1 Fundamentals

1.5   Equations     Lecture 1.5     If you do not have word or PowerPoint, please click on to download MS Office Viewer .

Solving Quadratic Equations: Do the tutorialon page 48, and do Ex 6.

1.8      Coordinate Geometry    Lecture 1.8

Distance and Midpoint Formula: Watch the videoon page 84, and do example (Ex) 2-3.

Circles: Do the tutorialon page 88, and do Ex 8,9,10.

Symmetry: Do the tutorialon page 90, and do Ex 11.

Ch 2 Functions

2.1   What is a function?     Lecture 2.1

Evaluating Functions: Do Ex 4 on page 145.

Ch 3 Polynomials and Rational Functions

3.1      Quadratic Functions and Models    Lecture 3.1

Review the definition of a quadratic function, and watch the videoon page 224.

Graphing Quadratic Functions Using the Standard Form: Do Ex 1.

Minimum and Maximum Values of a Quadratic Function: Do the tutorialon page 225, do Ex 2, watch the videoon page 226, and do Ex 3-4.

Modeling with Quadratic Functions: watch the videoson page 228, and do Ex 5-6. Watch the videoon page 229.

3.2      Polynomial Functions and Their Graphs    Lecture 3.2   

Review the definition of a polynomial function, and do the tutorialon page 232, and watch the videoon page 233.

Graphing Basic Polynomial Functions: Do Ex 1.

End Behavior and Leading Term: Do Ex 2-3

Using Zeros to Graph Polynomials: do the tutorial, and watch the video on page 236. Do the tutorial, watch the video on page 237, and do Ex 4-7

Shape of a Graph Near a Zero: Do Ex 8.

Local Maxima and Minima of Polynomials: watch the videoson page 241 and 242. Do Ex 9-10.

3.3      Dividing Polynomials    Lecture 3.3

Long Division of Polynomials: do the tutorial, and watch the video  on page 247. Do Ex 1-2.

Synthetic Division: do the tutorial, on page 248. Do Ex 3, and watch the video  on page 249.

The Remainder and Factor Theorem: Watch the video  on page 249, Do Ex 4. Watch the video on page 250. Do Ex 5.

3.4      Real Zeros of Polynomials     Lecture 3.4

Rational zeros of Polynomials: watch the video  on page 253. Do Ex 1-3.  Do the tutorialon page 256.

Use Algebra and Graphing Devices to Solve Polynomial Equations: Do Ex 7. Do the tutorial, on page 248. Do Ex 3, and watch the video  on page 249.

The Remainder and Factor Theorem: Watch the video  on page 249, Do Ex 4. Watch the video on page 250. Do Ex 5.

3.5      Complex Numbers    Lecture 3.5

Review the definition of Complex Numbers, and do Ex 1.

Arithmetic Operations of Complex Numbers: Watch the videos  on page 265. Do Ex 2. Watch the videos  on page 266. Do Ex 3.

Square Roots of Negative Numbers: Do Ex 4-5.

Quadratic Equations with Complex Solutions: Watch the videos  on page 267. Do Ex 6.

3.6      Complex Zeros and the Fundamental Theorem of Algebra.     Lecture 3.6

Do the tutorial, on page 269.

The Fundamental Theorem of Algebra and Complete Factorization: Watch the videos  on page 270. Do Ex 1-2.

Zeros and Their Multiplicity: Do Ex 3-5

Complex Zeros Come in Conjugate Pairs: Watch the video  on page 274. Do Ex 6.

Linear and Quadratic Factors: Watch the videos  on page 275. Do Ex 7.

3.7      Rational Functions    Lecture 3.7

Rational Functions and Asymptotes: Do Ex 1.  Do the tutorialand watch the video  on page 279. Do Ex 2, and watch the video  on page 280.  

Asymptotes of Rational Functions: Do Ex 3-4.

Graphing Rational Functions: Do Ex 5-7.

Slant Asymptotes and End Behavior: Do Ex 8-9.

Ch 4 Exponential and Logarithmic Functions

4.1      Exponential  Functions        Lecture 4.1

Exponential Functions: Do the tutorial  on page 302, do Ex 1-4 on pages 303-304 and watch the videos.

Compound Interest: Do the tutorialon page 306, and do Ex 6.

4.2      The Natural Exponential Function        Lecture 4.2

The Number e: Do the tutorial  on page 310

The Natural Exponential Function: watch the videoon page 311, and do Ex 2-3.

Continuous Compounded Interest: Do the tutorial  on page 312, watch the video, and do Ex 4.

4.3      The Logarithmic Function        Lecture 4.3

Logarithmic Function: Watch the videoon page 315, do the tutorial  on page 316, and do Ex 1-3.

Graphs of Logarithmic Functions: watch the videoon page 317, and do Ex 4. Do the tutorial  on page 318, and do Ex 5-6.

Common Logarithms: Watch the videoon page 319, and do Ex 7-8.

Natural Logarithms: Watch the videoon pages 320, Watch the videoon page 321 and do Ex 9-10.

4.4      Laws of Logarithms        Lecture 4.4

Laws of Logarithms: Watch the videoson page 325 and do Ex 1.

Expanding and Combining Logarithmic Expressions: Watch the videoson page 326 and do Ex 2-5.

Change of Base Formula: Watch the videoson page 328 and do Ex 6-7.

4.5      Exponential and Logarithmic Equations        Lecture 4.5

Exponential Equations: Do the tutorialon page 331, and do Ex 1. Watch the videoon page 332, and do Ex 2-3. Watch the videoon page 333, and do Ex 4-5.

Logarithmic Equations: Watch the videoon page 334, and do Ex 6. Watch the videoon page 335, and do Ex 7-8. Do Ex 9-10 on page 336.

Compound Interest: Do the tutorialon page 337, and do Ex 11-12.

4.6      Modeling with Exponential and Logarithmic Functions        Lecture 4.6

Exponential Growth (Doubling Time): Do the tutorialon page 340. Do Ex 1-2 on page 341.

Exponential Growth (Relative Growth rate): Watch the videoon page 343, and do Ex3. Watch the videoon page 344, and do Ex5.

Radioactive Decay: Watch the videoon page 345, and do Ex 6.

Newton's Law of Cooling: Do the tutorialon page 346, and do Ex 7. Watch the videoon page 347.

Logarithmic Scales: Do Ex 8 on page 348, watch the videoon page 349, and do Ex 9-10. Do Ex 11 on page 350.

Test #2

Below are the Main Concepts for Test #2

Chapters 5 and 6

Ch 5 Trigonometric Functions: Unit Circle Approach

5.1      The Unit Circle        Lecture 5.1

The Unit Circle: Do the tutorial  on page 370, do Ex 1,2.

Terminal Points on The Unit Circle: Do Ex 3, and watch the videoon page 371.  Do Ex 3,4.

The Reference Number: Do Ex 5,6.

5.2      The Trigonometric Functions of Real Numbers          Lecture 5.2

The Trigonometric Function: Do the tutorial , watch the video, and  on page 377. Watch the video, and  on page 378 and do Ex 1. Make sure you memorize the table at the margin on page 378 (see the pattern). With this table, you can generate table 1

Values of the Trigonometric Function: Do Ex 2,3,4 starting on page 380.   

Fundamental Identities: Do Ex 5,6 on page 383.  

Ch 6 Trigonometric Functions: Right Triangle Approach

6.1      Angle Measure         Lecture 6.1

Angle Measure: Do the tutorial  on page 434, watch the video  on page 435, and do Ex 1.

Angles in Standard Position: Watch the videoon page 435, and do Ex2,3.

Length of a Circular Arc: Watch the videoon page 437, and do Ex 4.

Area of a Circular Sector: Do Ex 5 on page 438.

Circular Motion: : Watch the video, do the tutorial  on page 439, , and do Ex 6,7.

6.2      Trigonometry of Right Triangles          Lecture 6.2

Trigonometric Ratios: Do the tutorial on page 443. Watch the videoon page 444, and do Ex 1,2.

Special Triangles: Watch the videoon page 445.

Applications of Trigonometry of Right Triangles: Do Ex 3 on page 445. Watch the videoon page 446, and do Ex 4,5.

6.3      Trigonometric Functions of Angles        Lecture 6.3

Trigonometric Functions of Angles: Do the tutorial on page 452.

Evaluating Trigonometric Functions of Angles: Watch the videoson page 454, and do Ex 1,2,3. Watch the videoon page 456, and do Ex 4.

Trigonometric Identities: Do the tutorial on page 457, do Ex 5. Watch the videoson page 456, and do Ex 6,7.     

 Areas of Triangles: Do Ex8.

Ch 5 Trigonometric Functions: Unit Circle Approach

5.3      Trigonometric Graphs     Lecture 5.3

Graphs of Sine and Cosine: Do the tutorial  on page 386. Watch the videoson page 387.

Graphs of Transformations of Sine and Cosine: Do Ex 1,2,3,4,5 starting on page 388.

Using Graphing Devices to Graph Trigonometric Functions: Do Ex 6,7,8 starting on page 393.

5.4      More Trigonometric Graphs        Lecture 5.4

Graphs of tangent, Cotangent, Secant and Cosecant: Do the tutorial , watch the videosand on pages 399 and 400.

Graphs of Transformations of Tangent and Cotangent: Do Ex 1,2,3 starting on page 401.   

Graphs of Transformations of Cosecant and Secant: Do Ex 4,5  starting on page 403. 

5.5      Inverse Trigonometric Functions and Their Graphs     Lecture 5.5

The Inverse Sine Function: Do the tutorial  on page 406. Watch the videoon page 407, and do Ex 1,2,3.

The Inverse Cosine Function: Do Ex 4,5 starting on page 408.

The Inverse Tangent Function: Do Ex 6 on page 410. 

The Inverse Secant, Cosecant and Cotangent Functions:  Read pages 410-411.

5.6      Modeling Harmonic Motion        Lecture 5.6

Simple Harmonic: Do the tutorial  on page 412. Watch the videosand  on page 413 and do Ex 1,2,3.

Ch 6 Trigonometric Functions: Right Triangle Approach

6.4      Inverse Trigonometric Functions and Right Angles        Lecture 6.4

The Inverse Sine, Inverse Cosine and Inverse Tangent Functions: Do the tutorial  on page 462, and do Ex 1. Watch the videoon page 463, and do Ex2.

Solving for Angles In Right Triangles: Watch the videoon page 464, and do Ex 3,4,5,6 starting on page 464.

Evaluating Expressions Involving Inverse Trigonometric Functions: Do Ex 7,8 on page 466.

6.5      The Law of Sines         Lecture 6.5

Law of Sines: Do the tutorial on page 469. Watch the videoson page 477, and do Ex 2,3.

6.6      The law of Cosines         Lecture 6.6

Law Of Cosines: Do the tutorial on page 476, and do Ex 1. Watch the videoson page 470, and do Ex 1,2.

Navigation Heading and Bearing: Do Ex 4 on page 478.

Area of a Triangle: Watch the videoon page 479, and do Ex 5.

Test #3

Below are the Main Concepts for Test #3

Chapters 7, 8,9

  Ch 7 Analytic Trigonometry

7.2      Addition and Subtraction Formulas        Lecture 7.2

Addition and Subtraction Formulas: Watch the videoon page 500.  Do not need to do the proof of the addition formula for cosine. Do Ex 1 on page 501. Do the tutorial  on page 501, and do Ex 2. Watch the videoon page 502, and do Ex 3.

Evaluating expressions Involving Inverse Trigonometric Functions: Do Ex 6,7 on page 503

Expressions of the form A sin x + B cos x: Do Ex 8,9 on page 505.

7.3      Double-Angle, Half-Angle and Product-Sum Formulas        Lecture 7.3

Double-Angle Formulas: Do the tutorial , watch the videoon page 508, and do Ex 1,2

Half-Angle Formulas: watch the videoon page 509, and do Ex 4. Do Ex 5,6 on page 511

Evaluating expressions Involving Inverse Trigonometric Functions: Do Ex 7,8 on page 512

7.4      Basic Trigonometric Equations        Lecture 7.4

Basic Trigonometric Equations: Do the tutorial  on page 517, and do Ex 1. Watch the videoon page 518, and do Ex 2,3,4 starting on page 517. Watch the videoon page 520, and do Ex 5.

Solving Trigonometric Equations by Factoring: Watch the videoon page 521, and do Ex 6.

7.5      More Trigonometric Equations         Lecture 7.5

Solving Trigonometric Equations by using Identities: Do the tutorial  on page 524, and do Ex 1,2. Watch the video  on page 525, and do Ex 3,4.

Equations with Trigonometric Functions of Multiple Angles by Factoring: Do Ex 5,6 starting on page 526.         

Ch 8 Polar Coordinates and Parametric Equations

8.1      Polar Coordinates        Lecture 8.1

Definition of Polar Coordinates: Do the tutorial, watch the videoon page 542, and do Ex 1. Watch the videoon page 543, and do Ex 2. 

Relationship Between Polar and Rectangular Coordinates: Watch the videoon page 544, and do Ex 3,4. 

Polar Equations: Do Ex 5 on page 144, watch the videoon page 545, and do Ex 6.  

8.2      Graphs of Polar Equations        Lecture 8.2

Graphing Polar Equations: Do the tutorialon page 547. Watch the videos on page 548, and do Ex 1,2,3. Do Ex 4 on page 549. Watch the videos on page 550, and do Ex 5. 

Symmetry:  Do Ex 6 on page 551 

Graphing Polar Equations with Graphing Devices: Do Ex 67,8 starting on on page 551. 

8.4      Plane Curves and Parametric Equations        Lecture 8.4

Plane Curves and Parametric Equations: Do the tutorialon page 564, and do Ex 1.  

Eliminating the Parameter:  Do Ex 2 on page 556. Watch the videoon page 556, and do Ex 3,4.  

Finding Parametric Equations for a Curve:  Watch the videoon page 566, and do Ex 5.

Using Graphing Devices Parametric Equations for a Curve:  Watch the videoon page 567, and do Ex 7.  

Ch 9 Vectors in Two and Three Dimensions

9.1      Vectors in Two Dimensions         Lecture 9.1

Geometric Description of Vectors: Watch the videoon page 580.

Vectors in the Coordinate Plane: Watch the videoon page 581 and do Ex 1. Do Ex 2 on page 582. Watch the videoon page 583, and do Ex 3,4,5. 

Using Vectors to Model Velocity and Force: Do Ex 6 on page 585. Watch the videoon page 585, and do Ex 7. Watch the videoon page 586, and do Ex 8.

9.2      The Dot Product            Lecture 9.2

           The Dot Products of Vectors: Do the tutorial, watch the videoon page 590, and do Ex 1. Watch the videos on page 591,

           and do Ex 2,3.

The Component of u along v:  Do the tutorial on page 592, and do Ex 4,5.

Projection of u into v: Watch the videoon page 593, videos on page 594, and do Ex 6.

Work: Watch the videoon page 594, and do Ex 7,8.

Test #4

Below are the Main Concepts for Test #4

Chapters 10, 11 and 13

Ch 10 Systems of Equations and Inequalities

10.1      Systems of Linear Equations in Two Variables        Lecture 10.1

Review the concept, and do the tutorialon page 630.

Substitution Method: Watch the videoon page 631 and, do Ex 1.

Elimination Method: Watch the videoon page 632 and, do Ex 2.

Graphical Method: Watch the videoon page 633 and, do Ex 3.

The Number of Solutions of a Linear System in Two Variables: Watch the videoon page 633 and, do Ex 4,5,6.

Modeling with Linear Systems: do Ex 7 on page 635. Watch the videoon page 637, and do Ex 8.

10.3      Matrices and Systems of Linear Equations         Lecture 10.3

Matrices: Do the tutorialon page 649

The Augmented Matrix of a Linear System: Do Ex 1

Gaussian Elimination:  Use the calculator and the Row Echelon Form (ref) command to solve systems of Equations.  Do Ex 3. You only need to do the back substitution step. See the Calculator Basics Handout found in the Calculator Link in BB.   

Gauss-Jordan Elimination: Use the calculator and the Reduced Row Echelon Form (rref) command to solve systems of Equations.  Do Ex 4. You only need to interpret the last matrix. See the Calculator Basics Handout found in the Calculator Link in BB.  

Inconsistent and Dependent Systems: Do Examples 5,6,7 on page 655 by using your calculator.

Modeling with Linear Systems: Do Examples 8 on page 658 by using your calculator.

10.6      Determinants and Cramer’s Rule            Lecture 10.6

Determinants of a 2 X 2 Matrix: do the tutorial, and watch the video  on page 682. Do Ex 1.

Determinants of a n X n Matrix: Do Ex 2,3 using the calculator. See the Calculator Basics Handout in the Calculator link in BB.

Cramer’s Rule: do the tutorialon page 687. Watch the video on page 288, and do Ex 6,7. You must know how to do Cramer’s rule of 2X2 systems by hand. Higher systems are done using the calculator.

Areas of Triangles Using Determinants: do the tutorial, and watch the video  on page 682. Do Ex 8.

10.7    Partial Fractions        Lecture 10.7

Distinct Linear Factors: Do the tutorialon page 693.Watch the videos  on page 694. Do Ex 1.

Repeated Factors:  Do Ex 2 on page 695.

Irreducible Quadratic Factors: Watch the video  on page 693. Do Ex 3.

10.8      Systems of Nonlinear Equations        Lecture 10.8

Substitution and Elimination Method: Do the tutorialon page 698.

Watch the videos  on page 699. Do Ex 1,2.

Graphical Methods: Watch the video  on page 700. Do Ex 3.

Ch 11 Conic Sections

11.1      Parabolas            Lecture 11.1

Geometric Definition of a Parabola: Do the tutorial  on page 724.

Equations and Graphs of Parabolas: Watch the video   on page 725. Do Ex 1. Do the tutorialon page 726, and do Ex 2,3,4

Applications: Watch the videos, do the tutorialon page 729, and do Ex 6.

11.2      Ellipses        Lecture 11.2

Geometric Definition of an Ellipse: Watch the video   on page 732.

Equations and Graphs of Ellipses: Do the tutorial, watch the videoon page 734. Watch the videoon page 735 and do Ex 1,2. Watch the videoon page 736, and do Ex 3.

Eccentricity of an Ellipse: Do the tutorial  on page 736. Watch the videoon page 737, and do Ex 4.

11.3      Hyperbolas            Lecture 11.3

Geometric Definition of a Hyperbola: Watch the videoon page 741.

Equations and Graphs of Hyperbolas: Do the tutorial  on page 742. Watch the videoon page 743, and do Ex 1. Do the tutorial  on page 744, and do Ex 2. Watch the videoon page 745, and do Ex 3.

11.4      Shifted Conics            Lecture 11.4

Shifted Ellipses: Do the tutorial  on page 750. Watch the videoon page 751, and do Ex 1.

Shifted Parabolas: Do the tutorial  on page 751. Watch the videoon page 752, and do Ex 2.

Shifted Hyperbolas: Watch the videoson page 752, and do Ex 3.

The General Equation of a Shifted Conic: Do Ex 4.

Ch 13 Limits: A Preview of Calculus

13.1      Finding Limits Numerically and Graphically            Lecture 13.1

Definition of a Limit: Watch the video   on page 840.

Estimating Limits Numerically and Graphically: Watch the video   on page 841, and do Ex 1.

Limits That Fail to Exist: Watch the videoon page 843, and do Ex 3,4,5.

One Sided: Watch the videoon page 844, and do Ex 6,7 starting on page 845.

13.2      Finding Limits Algebraically            Lecture 13.2

The Limits Laws: Do the tutorial , and watch the videoon page 848, and do Ex 1 on page 849.

Applying the Limits Laws: Do Ex 2 on page 850. Watch the videoon page 851, an do Ex 3.

Finding Limits Using Algebra and the Limits Laws: Do Ex 4 on page 852. Watch the videoon page 853, and do Ex 5,6.

Using Left - and Right - Hand Limits: Do Ex 7 on page 853. Watch the videoon page 854, and do Ex 8,9.