# Precalculus Textbook Work

**TEXTBOOK HOMEWORK **

**Learning**how to read and use the examples from a math textbook is a critical skill for any advanced math student--- for any math student.

**ALL**the "Are You Prepared Questions"

**AYP?**

**ALL**the "Concepts and Vocabulary" Questions

**C&V**

**SB, Pencil + 1**. This means they are to do all problems marked with a pencil, which means they have an example in the reading to help, as well as

*AT LEAST*one additional problem from that section. They must do all SB questions until chapter's end unless otherwise stated

**Unit 1-- Functions**

**1.1 Rectangular Coordinates; Graphing Utilities**

Objectives

**1.2 Graphs of Equations in Two Variables**

1.3 Solving Equatiosn in One Variable Using a Graphing Utility

1.3 Solving Equatiosn in One Variable Using a Graphing Utility

**1.4 Lines**

**1.5 Circles**

CHAPTER 2 FUNCTIONS (Unit 7)

CHAPTER 2 FUNCTIONS (Unit 7)

**2.1 Functions**

**2.2 The Graph of a Function**

**2.3 Properties of Functions**

1. Determine Even and Odd Functions From a GRaph

2. Identify Even and Odd Functions from the Equation

3. Use a GRaph to Determine whether a function is increasing, decreasing or constnat

4. Use a graph to locate local maximia and ocal minima

5. Use a graphing utility to approximate local maxima and local minima and to determine where a gunction is increasing or decreasing

6. Find the Average Rate of change of a function

**2.4 Linear Functions and Models**

1 Graph Linear Functions

2. Work with Applications of Linear Functions

3. Draw and interpret scatter diagrams

4. Distinguish between linear and nonlinear relations

5. Use a Grpahing Utility to find line of best fit

6. Construct a Linear Model Using Direct Variation

Read 93-101 Do AYP 1-4, C&V 5-10, 11,19,25,35,39

**2.5 Library of Functions; Piece-Wise Defined Functions**

1. Grpah the functions listed in the library of Functions

2. Graph Piecewise Defined Functions

Project: Create a FAMILY ALBUM Example

**2.6 Graphing Techniques: Transformations**

Objectives

1. Graph Functions Using Veritical and Horizontal Shifts

2. Graph Functions Using Compression and Stretches

3. Graph Functions Using Reflections about the x-Axis or y-Axis

**2.7 Mathematical Models: Constructing Functions**

Read 130-134 Do 3,9,15,27

1. Construct and Analyze Functions

**CHAPTER 3 POLYNOMIALS (Unit 8)**

**3.1 Quadratic Functions and Models**

Objectives

- Graph a quadratic function using transformations
- Identify the vertex and axis of symmetry of a quadratic equation
- Graph a quadratic using its vertex, axis of symmetry and intercepts
- Use the maximum or minimum value of a quadratic to solve applied problems
- Use a graphing utility to find the quadratic of best fit data

**3.2 Polynomial Functions and Models**

Do AYP 1-4, C&V 5-10, 37, 45, 69, 81** tech

Objectives

- Identify the polynomial function and their degree
- Graph polynomial functions using transformations
- Identify the zeroes of a polynomial function and their multiplicity
- Analyze the graph of a polynomial function
- Find the cubic of best fit data

**3.3 Properties of Rational Functions**

Read p 186-195

Do AYP 1-4, C&V 5-10 31,37, 41, 43, 47

Objectives

1. Find the Dopmain of a Rational Function

2. Find the Vertical Asymptotes of a Rational Function

**3.4 The Graph of the Rational Function: Inverse and Joint Variation**

Read p 198-207

Objectives:

1 Analyze the Graph of a Rational Function

2. Solve Applied Problems Involving Rational Functions

3. Construct a Model Using Inverse Variation

4. Construct a Model Using Combined Variation

**3.5 Polynomial and Rational Inequalities**

Objectives

1. Solve Polynomial Inequalities algebraically and Graphically

2. Solve Rational Inequalities Algebraically and Graphically

**3.6 The Real Zeroes of a Complex Function**

Do AYP 1-4, C&V 5-10, 11,21,33, 39, 63, 75, 85

Objectives

1. Use the Remainder and Factor Theorems

2. Use the Rational Zeroes Theorem

3. Find the Real Zeroes of a Polynomial Function

4. Solve Polynomial Equations

5. Use the Theorem for Bounds on Zeros

6. Use the Intermediate Value Theorem

**3.7 Complex Zeros: Fundamental Theorem of Algebra**

Read 233-236 AYP 1-2 C&V 3-6

17, 21, 27, 33,

Objectives:

1. Use the Conjugate Pairs Theorem

2. Find a Polynomial With a Specified Zero

3. Find the complex Zeroes of a Polynomial

10.5 Partial Fraction Decomposition

Read p 785-792 Do AYP 1-4, SB 13,19,21,35

Objectives:

1. Decompose P/Q, Where Q has only nonrepeated linear factors

2.Decompose P/Q, Where Q has repeated linear factors

Decompose P/Q, Where Q has a irreducible quadratic factor

Decompose P/Q, Where Q has repeated irreducible quadratic factor

**Unit 9 Exponential and Logarithmic Functions**

**4.1 Composite Functions**

Read p 248-253

Do AYP 11-3, C&V 3-6, 7,9,11,21,35,53,

Objectives

1. Form a Composite Function

2. Find the Domain of a Composite Function

**4.2 One-to-One Functions; Inverse Functions**

Read 256-266

Do AYP 1-3, C&V 4-8, Skill Building 9-35 odd, 37, 41, 49, 57, 63, 69, 73

Objectives

1 Determine Whether a Function is one to one

2. Determine the inverse of a function defined be a map or an ordered pair

3. Obtain the graph of the inverse function from the graph of the function

4. Find the inverse of a function defined by an equation

**4.3 Exponential Functions**

Read p271-282

DO AYP 1-5, C&V 6-10 11, 21, 29-36, 37, 45, 53,57, 59, 67, 73, 81

Objectives

1. Evaluate exponential functions

2. Graph exponential functions

3. Define the number e

Solve exponential equations

**4.4 Logarithmic Functions**

Read 287-296

Do AYP 1-3, C&V 4-8

SB 9, 21, 33, 53, 63, 67-74

Objectives

1. Change Exponential Expressions to Logarithmic Expressions and Logartithmic Expressions to Exponential Expressions

2. Evaluate Logarithmic Espressions

3. Determine the Domain of a Logarithmic Discussion

4. Graph Logarithmic Functions

5. Solve Logarithmic Equations

KhanAcademy Videos

- Logarithms
- Ex: Converting an exponential to logarithmic statement
- Simplifying logarithms
- Fancier logarithm expressions
- Simplifying logarithms 2
- Graphing Logarithmic Functions

**4.5 Properties of Logarithms**

Read 300-307

Do C&V 1-6

9,13,17,45,51,65

Objectives

1Work with the Properties of Logarithms

2 Write a Logarithmic Expressions as the Sum or Difference of Logarithms

3 Write a Logarithmic Expression as a single logarithm

4 Evaluate Logarithms whose base is neither 10 nor e

5 Graph logarithmic functions whose base is neither 10 nor e

**4.6 Logarithmic and Exponential Equations**

**4.7 Compound Interest**

Read 315-322

Do AY 1-2

SB 3, 11, 13, 23, 25, 31

Objectives

1. Determine the Future Value of a Lump Sum of money

2. Calculate Effective Rates of Return

3. Determine the Present Value of a Lump Sum of Money

4. Determine the Time Required to Double or Triple a Lump Sum of Money

**4.8 Exponential Growth and Decay; Newton's Law; Logistic Growth and Decay**

Read p 324-334

Do 1,3,5,9,13,19

Objectives

1. Find Equations of Populations that Obey the Law of Uninhibited Growth

2. Find Equations that Open the Law of Decay

3. Use Newtons Law of Cooling

4 Use Logistic Models

**4.9 Building Exponential, Logarithmic and Logistic Models from Data**

Read 337-342

Do 342 1, 3, 7, 9

Objectives

1. Use a Graphing Utility to Plot an Exponential Function to Data

2. Use a Graphing Utility to Plot an Logarithmic Function to Data

**3. Use a Graphing Utility to Plot an Logistic Function to Data**

**5.1 Angles and Their Measure**

Objectives

1. Convert between Degrees, Minutes Seconds and Decimal Forms of Angles

Objectives

2.Find the Arc Length of a Circle

3. Convert Degrees to Radians and Radians to Degrees

4. Find the Area of a Sector of a Circle

5. Find the Linear Speed of an Object Travelling in a Circular Motion

Read p 356-366 Suggested Problems- 1-10, 11, 15, 21, 23, 27, 29, 31, 35, 43, 47, 42, 61, 67, 71, 75, 79, 83, 89, 97, 99, 101, 109

**5.2 Trigonometric Functions Unit Circle Approach**

Objectives

1. Find the Exact Values of the Trigonometric Functions Using a Point on the Unit Circle

Objectives

2. Find the Exact Values of the Trigonometric Functions of Quadrantal Angles

3. Find the Exact Values of Trigonometric functions of pi/4 = 45

4. Find the Exact Values of Trigonometric functions of pi/6 = 30 and pi/3=60

5. Find the Exact Values for Integer Multiples of pi/6 = 30, pi4=45 and pi/3=60

6. Use a Calculator to Approximate the Value of a Trigonometric Function

7. Use a Circle of Radius r to Evaluate the Trigonometric Functions

Read 370-383 Suggested Problems- 1-10, 11, 13, 17, 19, 21, 27, 33, 39, 41, 49, 53, 57, 63, 67, 73, 83, 89, 97, 103

**5.3 Properties of the Trigonometric Functions**

Objectives

1. Determine the Domain and Range of the Trigonometric Functions

2. Determine the Period of the Trigonometric Functions

3. Determine the Signs of the Trigonometric Functions in a Given Quadrant

4. Find the Values of the Trigonometric Functions Using Fundamental Identities

5. Find the Exact Values of the Trigonometric Functions of an Angle Given One of the Functions and the Quadrant of the Angles

6. Use Even-Odd Properties to Find the Exact Values of the Trigonometric Functions

**Objectives**

5.4 Graphs of the Sine and Cosine Function

5.4 Graphs of the Sine and Cosine Function

- Graph transformations of the sine function
- Graph transformations of the cosine function
- Determine the amplitude and period of sinusoidal functions
- Graph sinusoidal functions using key points
- Find and equation for a sinusoidal graph

Read p 402-414

Do AYP 1-2. C&V 3-6, SB 9. 11, 13, 25, 33, 41 (47-56), 61, 71, 75

**5.5 Graphs of the Tangent, Cotangent Cosecant and Secant Functions**

Read p 419-423

Objectives:

1. Graph Transformations of the Tangent and Cotangent Functions

2. Graph Transformations of the Secant and Cosecant Function

Do p 423 AYP 1-2, C&V 3-6, SB 7, 15, 17-20, 25, 31, 37

**5.6 Phase Shift; Sinusoidal Curve Fitting**

Objectives

- Graph sinusoid functions in the form Asin(Bx-c)
- Find a sinusoidal function from data

Do C&V 1-2, SB 3, 15, 21, 27 MInimum- do more if you can

**CHAPTER 6/ UNIT 5 Analytical Trig**

**6.1 The Inverse Sine, Cosine and Tangent Function**** ** READ 448-457

AYP 1-6 C&V 7-12 SB PENCIL 13,17,19,23,25,37,39 + 1 (15,21,31,33,43,49,53)

**6.2 The Inverse Trig Functions Continued **** ** READ 460-464

AYP 1-3 C&V SB (9,23,27,39,45) +1 (15,25,35,43,49)

**6.3 Trigonometric Identities **** ** READ 475-470

AYP 1-2 C&V 3-8 SB (9,11,13,19,27,53,69,99) +1 (15,17,31,37,55,71,77,91,101)

**6.4 Sum and Difference Formulas** READ p 473-481

AYP 1-3, C&V 4-8, SB 11, 17, 23, 27, 31, 39, 51,67,77 +1 ( 15,19,29,35,55,69)

**6.5 Double and Half Angle Formulas**** ** READ 483-490

C&V 1-6, SB 7, 19, 29, 51 +1 (11,27,39,51)

**6.6 Product to Sum Formulas** READ 493-495

Extra Credit 5 points for sum to product/product to sum work

**6.7 Trigonometric Equations (I)** READ 496-500

AYP 1-2, C&V 3-6, SP Pencil + 1 7, 13, 31, 41, ** 59 Recommend (9, 17, 25, 33, 43, 47)

**6.8 p Trigonometric Equations (II) **** ** READ 503-508

Do AYP -4, SB Pencil +1 7, 23, 41, 53 +1 (9, 27, 29, 45, 57) Need calc/wolfram

**7.1 Solving Right Triangles**

Read 518-526

Do 526 AYP 1-2, C&V3-8, 9, 19, 29, 39, 49, 51, 67

Objectives

1. Find the Value 0f Trigonometric Functions of Acute Angles

2. Use the Complimentary Angle Theorem

3. Solve Right Triangles

4. Solve Applied Problems

7.2 The Law of Sines

Read p 531 to 538

do p 538 AYP 1-3, C&V4-8, 9,23,25,31,37,39

Objectives:

1: Solve SSA or ASA Triangles

2. Solve SSA Triangles

3. Solve Applied Problems

7.3 The Law of Cosines

Read 543-546

Do AYP 1-2, C&V 3-8, 9, 15, 35 Minimum

Objectives

1. Solve SAS Triangles

2. Solve SSS Triangles

3. Solve Applied Problems

**7.4 Area Formulas**

Read 549-552

Do 552 AYP 1, C&V2-4, SB 5, 11, 23, 37

Objectives

1. Find the Area of SAS Triangles using 1/2bh

2. Find the Area of SSS Triangles using Heron's formula

**7.5 Simple Harmonic Motion: Combining Waves**

**UNIT 10 Parametric and Polar Equations**

**9.7 Plane Curves and Parametrics**

Read 705-716 DO ATP 1, C&V2-6 SB 7, 19, 35, 37, 39, 49

Objectives

1 Graph Parametric Equations by Hand

2. Graph Parametric Equations Using a Graphing Utility

3. Find a Rectangular Equation for a Curve Defined Parametrically

4. Use Time as a Parameter in parametric Equations

5. Find Parametric Equations for a Curve Defined by Rectangular Equations

**8.1 Polar Coordinates**Read 572-579

Do AYP 1-7, C&V 5-10, SB 11, 19, 27, 2`, 39, 51, 55, 59, 75

Objectives

1. Plot Points Using Polar Coordinates

2. Convert from Polar to Rectangular Coordinates

3. Convert from Rectangular to Polar Coordinates

**8.2 Polar Equations and Graphs**

Read p 581-597

Do 597 AYP 1-6, C&V 7-12, SB 13, 15,19, 29-36, 43, 49,51,55,59

Objectives:

1. Graph and Identif Polar Equations by Converting to Rectangular

2. Graph Polar Equations Using A Grpahing Utility

3. Test Polar Equations for Symmetry

4. Graph Polar Equations by Plotting Points

Unit 11Vectors and DeMoivre's

8.4 Vectors

Read 608-617

Do 618, C&V 1-6, SB 7, 9, 27, 33, 39, 49, 61

- Graph Vectors
- Find a Position Vector
- Add and Subtract Vectors
- Find a Scalar Product and the Magnitude of Vector
- Find a Unit Vector
- Find a Vector from Its Direction and Magnitude
- Work with Objects in Static Equilibrium

8.5 The Dot Product

Read 620-626

AYP 1, C&V2-6 SB 7, 19, 25, ,33 35

- Find the Dot Product of Two Cectors
- Find the Angle Between Two Vectors
- Determine Whether Two Vectors are Parallel
- Determine Whether two vectors are Orthogonal
- Decompose a Vector into Two Orthogonal Vectos
- Compute Work

8.6 Vectors in Space [EXTRA CREDIT]

Read 628-636

- Find the Distance Between Two points in Space
- Find Position Vectors in Space
- Perform Operations on Vectores
- Find the Dot Product
- fnd the Angle Bewtween Two Vectors
- find the Direction Angles of a Vector

637 AYP 1, C&V 2-6, 15, 29, 33, 39, 47, 51,59

Read 600-607

AYP 1-4, C&V5-10, SB 11, 23, 33, 41, 53,

- Convert a Complex Number from Rectangular Form to Polar Form
- Plot Points in a Complex Plane
- Find Products and Quotients of Complex Nuimbers in Polar Form
- Use DeMoivre's Theorem
- Find Complex Roots