Prentice Hall Mathematics: Algebra Correlated to: Utah Core Curriculum for Math, Intermediate Algebra (Secondary)

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1 Core Standards of the Course Standard 1 Students will acquire number sense and perform operations with real and complex numbers. Objective 1.1 Compute fluently and make reasonable estimates. 1. Simplify numerical expressions with rational exponents. SE/TE: 7-4: Rational Exponents: ; Application, Practice, and Review: , 404, 424, 426, 452 Lesson 7-4 TECH: Graphing Calculator Hint: 386; 2. Add, subtract, and multiply complex numbers. SE/TE: 5-6: Complex Numbers: ; Application, Practice, and Review: 287, 290, 301, 302, 326 Lesson 5-6 TECH: Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive 3. Add, subtract, and multiply matrices using paper and pencil for simple cases and technology for more complicated cases. SE/TE: 4-2: Adding and Subtracting Matrices: ; 4-3: Matrix Multiplication: ; Application, Practice, and Review: 181, , , , 215, 219, 220, 230, 232, 233, 295, 595 1

2 4. Find the multiplicative inverse of a matrix using paper and pencil for a 2 x 2 and technology for larger matrices. Lessons 4-2, 4-3 TECH: Activity: Working With Matrices: 181; Graphing Calculator Hint: 184; Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive Textbook Online; for Homework Help, Lesson and Vocabulary Quizzes, SE/TE: 4-5: 2x2 Matrices, Determinants, and Inverses: ; 4-6: 3x3 Matrices, Determinants, and Inverses: ; Application, Practice, and Review: , 220, 227, 231, 232 Lessons 4-5, 4-6 Objective 1.2 Represent complex numbers in a variety of ways. TECH: Activities: Exercises and Examples: , , 231, 232; Graphing Calculator Hint: 208; Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive 1. Extend the number system to include complex numbers in the form a + bi. SE/TE: 5-6: Complex Numbers: ; Application, Practice, and Review: , 287, 290, 295, 301, 302, 351 Lesson 5-6 2

3 TECH: Activities: Exercises and Examples: 2. Identify the need for the square root of a SE/TE: 5-6: Complex Numbers: ; negative number and define the imaginary number Application, Practice, and Review: , 287, 290, 295, 301, 302, 351 Lesson 5-6 TECH: Activities: Exercises and Examples: 3. Simplify expressions involving radical expressions including square roots of negative numbers. SE/TE: Algebra 1 Review: Square Roots and Radicals: 266; 5-6:Complex Numbers: , ; 5-8: The Quadratic Formula: 7-1: , 295; Roots and Radical Expressions: ; 7-2: Multiplying and Dividing Radical Expressions: ; 7-3: Binomial Radical Expressions: ; Application, Practice, and Review: 113, , 301, 302, 337, , 361, 362, , , , 397, 404, , 419, , 422, , 426, 459, 493 Lessons 5-6, 5-8, 7-1, 7-2, 7-3 TECH: Graphing Calculator Hint: 371; 3

4 1. Identify matrices that can be added, subtracted, or multiplied. Objective 1.3 Identify relationships among real numbers and operations involving these numbers. 2. Demonstrate that matrix multiplication is not commutative. SE/TE: 4-2: Adding and Subtracting Matrices: ; 4-3: Matrix Multiplication: ; Application, Practice, and Review: 181, , , , 215, 219, 220, 230, 232, 233, 295, 595 Lessons 4-2, 4-3 TECH: Activity: Working With Matrices: 181; Graphing Calculator Hint: 184; Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive Textbook Online; for Homework Help, Lesson and Vocabulary Quizzes, SE/TE: 4-3: Matrix Multiplication: ;Application, Practice, and Review: 230, 295 Lesson 4-3 TECH: Graphing Calculator Hint: 184; 3. Identify additive and multiplicative identities and inverses of a matrix when they exist. SE/TE: 4-5: 2x2 Matrices, Determinants, and Inverses: ; 4-6: 3x3 Matrices, Determinants, and Inverses: ; 4-7: Inverse Matrices and Systems: ; Application, Practice, and Review: , 178, 180, 194, 220, 227, 231, 232, 326 4

5 Lessons 4-5, 4-6 TECH: Exercises and Examples: , ; Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive 5

6 Standard 2 Students will represent and analyze mathematical situations and properties using patterns, relations, functions, and algebraic symbols. Objective 2.1 Use patterns, relations, and functions to represent mathematical situations. 1. Compare and contrast relations and functions. SE/TE: 2-1: Relations and Functions: 55-61; 2-2: Linear Equations: 62-70; Extension: Piecewise Functions: 71; 2-3: Direct Variation: 72-77; 2-4: Linear Models: 78-84; Finding a Line of Best Fit: 86-87; 2-5: Absolute Value Functions and Graphs: 88-92; 2-6: Families of Functions: ; 5-1: Modeling Data with Quadratic Functions: ; 5-2: Properties of Parabolas: ; 6-1: Polynomial Functions: ; Extension: End Behavior: 312; 7-6: Function Operations: ; 7-7: Inverse Relations and Functions: ; Graphing Inverses: 413; 7-8: Graphing Square Root and Other Radical Functions: ; 8-1: Exploring Exponential Models: ; Fitting Exponential Curves to Data: 438; 8-2: Properties of Exponential Functions: ; 8-3: Logarithmic Functions as Inverses: ; 9-1: Inverse Variation: ; Graphing Rational Functions: 494; 9-2: The Reciprocal Function Family: ; 9-3: Rational Functions and Their Graphs: ; 13-4: The Sine Function: ; Graphing Trigonometric Functions: 742; 13-5: The Cosine Function: ; 13-6: The Tangent Function: ; 13-7: Translating Sine and Cosine Functions: ; 13-8: Reciprocal Trigonometric Functions: ; Application, Practice, and Review: 85, 106, , 112, 113, , 116, 124, 144, 151, 180, 191, 198, 219, 236, 244, 265, 277, 279, 280, 288, , 302, 304, 311, 319, 323, 326, 344, 357, 360, 362, 363, , 366, 405, 425, 426, 427, 428, 438, 460, 469, , , 482, 483, 486, 513, 527, , 542, 543, 544, , 553, 554, , 560, 565, 566, 567, , 582, 587, 595, 598, 605, 617, 755, , 774, 776, 813, , 830 6

7 Lessons 2-1, 2-2, 2-3, 2-4, 2-5, 2-6, 5-1, 5-2, 6-1, 7-6, 7-7, 7-8, 8-1, 8-2, 8-3, 9-1, 9-2, 9-3, 13-4, 13-5, 13-6, 13-7, 13-8 TECH: Technology Activities: Fitting Exponential Curves to Data: 438, Linear and Exponential Models: 469, Graphing Rational Functions: 494, Graphing Conic Sections: 554, Using Parametric Equations: 567; Examples and Exercises: 496, 505, 579, 587; Student/Teacher Express CD- ROMs, Presentation Express CD-ROM, Interactive 2. Identify the domain and range of the absolute value, quadratic, radical, sine, and cosine functions. SE/TE: 2-5: Absolute Value Functions and Graphs: 88-92; 2-6: Families of Functions: ; 5-1: Modeling Data with Quadratic Functions: ; 5-2: Properties of Parabolas: ; Graphing Square Root and Other Radical Functions: ; 13-4: The Sine Function: ; Graphing Trigonometric Functions: 742; 13-5: The Cosine Function: ; 13-6: The Tangent Function: ; 13-7: Translating Sine and Cosine Functions: ; 13-8: Reciprocal Trigonometric Functions: ; Application, Practice, and Review: 244, 265, 277, 279, 280, 287, , 302, 304, 344, 357, , 366, 425, 426, 428, 437, 460, 483, 495, 499, 544, , 560, , 595, 598, 755, , 773, 776, 813 Lessons 2-5, 2-6, 5-1, 5-2, 13-4, 13-5, 13-6, 13-7,

8 TECH: Activities: Modeling Using Residuals: 244, Graphing Trigonometric Functions: 742; Exercises and Examples: 89-91, , 247 (TE), , , , , 761, ; Graphing Calculator Hint: 89, 763; 3. Use function notation. SE/TE: 7-6: Function Operations: ; Application, Practice, and Review: 124, 219, 277, 279, 288, , 303, 307, 311, 312, 319, 323, 344, 357, 360, 363, 364, 366, 405, 406, , , 419, 425, 426, 427, 431, , 444, 452, 460, 468, 501, 520, 598 Lesson 7-6 TECH: Exercises and Examples: 402 (#70); 4. Find the compositions or combinations of two simple functions. SE/TE: 7-6: Function Operations: ; Application, Practice, and Review: 405, 412, 425, 426, 468, 501, 503, 520 Lesson 7-6 TECH: Exercises and Examples: 402 (#70); 8

9 5. Find the inverse of a function by interchanging the values of domain and range, reflecting across the line y = x, or by using algebra. SE/TE: 7-7: Inverse Relations and Functions: ; Graphing Inverses: 413; 8-3: Logarithmic Functions as Inverses: ; 14-2: Solving Trigonometric Equations Using Inverses: ; Application, Practice, and Review: 419, 425, 426, 428, 475, 527, 776, , 799, 806, 807, Lessons 7-7, 8-3, 14-2 TECH: Activity: Graphing Inverses: 413; Exercises and Examples: 785, 788; 6. Relate the sine, cosine, tangent, cosecant, secant, and cotangent to the unit circle. 7. Express angle measure in degrees or radians when given the trigonometric value. SE/TE: 13-2: Angles and the Unit Circle: ; Application, Practice, and Review: 733, , 743, 749, 770, , 774, 784, , 793, 827, 830 Lesson 13-2 TECH: Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive SE/TE: 14-2: Solving Trigonometric Equations Using Inverses: ; Application, Practice, and Review: , 725, 741, , 770, , 802, 804, 806, 807, , , 830 9

10 Lesson 14-2 TECH: Exercises and Examples: 785, 788; Objective 2.2 Evaluate, solve, and analyze mathematical situations using algebraic properties and symbols. 1. Solve quadratic equations. SE/TE: 5-5: Quadratic Equations: ; 5-7: Completing the Square: ; 5-8: The Quadratic Formula: ; Application, Practice, and Review: , 280, 281, 288, 298, , 302, 304, 332, 340, 341, 344, 366, 391, 419, 452, 486, 568 Lessons 5-5, 5-7, 5-8 TECH: Exercises and Examples: , 295; 2. Solve first-degree absolute value equations. SE/TE: 1-5: Absolute Value Equations and Inequalities: 33-38; Application, Practice, and Review: 45, 49, 50, 138 Lesson

11 3. Solve radical equations including those with extraneous roots. TECH: Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive SE/TE: 7-5: Solving Square Root and Other Radical Equations: ; Application, Practice, and Review: 404, 425, 426, 459, 513 Lesson 7-5 TECH: Technology Tip: 392 (TE); 4. Solve single-variable quadratic and absolute value inequalities. SE/TE: 1-5: Absolute Value Equations and Inequalities: 33-38; Activity: Quadratic Inequalities: ; Application, Practice, and Review: 45, 49, 50, 52, 133, 878 Lesson TECH: Activities: Quadratic Inequalities: ; Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive 5. Write a quadratic equation when given the rational roots or zeroes of the function. SE/TE: Activity: Writing Equations from Roots: 273; Application, Practice, and Review: 272,

12 Reteaching, and Enrichment Worksheets available for all lessons TECH: Using graphs from graphing calculator: 273; Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive 6. Solve systems of equations with no more than three variables using technology. SE/TE: 3-1: Graphing Systems of Equations: ; 3-2: Solving Systems Algebraically: ; Activity: Solving Systems Using Tables: 132; 3-6: Systems with Three Variables: ; 4-7: Inverse Matrices and Systems: ; 4-8: Augmented Matrices and Systems: ; Application, Practice, and Review: 131, 138, , 164, 165, 166, 173, 205, 211, 220, 231, 232, 243, 287, 327, 333, 340 Lessons 3-1, 3-2, 3-6, 4-7, 4-8 TECH: Activity: Analyzing Graphs: 118; Exercises and Examples: 119, , 132, 154 (TE), , , 333; Student/Teacher Express CD- ROMs, Presentation Express CD-ROM, Interactive 7. Solve and graph systems of linear inequalities. SE/TE: 3-3: Systems of Inequalities: ; 3-4: Linear Programming: ; Activity: Linear Programming: 145; Application, Practice, and Review: 151, 160, , 164, 189, 227, , 258, 363,

13 Lesson 3-3 TECH: Technology Activities: Linear Programming: 145; Technology Tip: 145; Exercises and Examples: 135; Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive Textbook Online; for Homework Help, Lesson and Vocabulary Quizzes, 8. Add, subtract, multiply, and divide simple rational expressions and solve simple rational equations. SE/TE: 9-4: Rational Expressions: ; 9-5: Adding and Subtracting Rational Expressions: ; 9-6: Solving Rational Equations: ; Application, Practice, and Review: 521, 530, 537, 538, , 542, 580, 631, 852 Lessons 9-4, 9-5, Recognize that a -n is defined as the reciprocal of a n, i.e., TECH: Activities: Exercises and Examples: Technology Tip: 523 (TE); Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive Textbook Online; for Homework Help, Lesson and Vocabulary Quizzes, SE/TE: 7-4: Rational Exponents: ; Application, Practice, and Review: 368, 396, 422, 424, 426, 430, 433, 438, 439, , 461, 470, 478, 480, 848 Lesson

14 10. Recognize that rational exponents are used to represent radicals, i.e., TECH: Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive SE/TE: 7-4: Rational Exponents: ; Application, Practice, and Review: , 404, 424, 426, 439, 446, 452, 461, 478, 480, 848 Lesson 7-4 TECH: Graphing Calculator Hint: 386; 11. Represent intervals with correct symbolic notation; e.g., a < x < b, (a, b), [a, b]. SE/TE: Application, Practice, and Review: 233, 427, 460, , Reteaching, and Enrichment Worksheets available for all lessons TECH: Students set the intervals for the horizontal and vertical components of the windows on their graphing calculator, e. g.: ; 14

15 1. Interpret rates of change by analyzing graphical and numerical data for quadratic and radical functions. Objective 2.3 Represent quantitative relationships using mathematical models and symbols. SE/TE: 5-1: Modeling Data with Quadratic Functions: ; Activity: Modeling Using Residuals: 244; 7-8: Graphing Square Root and Other Radical Functions: 416, 418; Application, Practice, and Review: 251, 257, 265, 286, 300, 426 Lessons 5-1, 7-8 TECH: Activity: Modeling Using Residuals: 244; Exercises and Examples: , 416; 2. Find the vertex, maximum or minimum values, intercepts, and axis of symmetry of a quadratic or absolute value function, algebraically, graphically, and numerically. SE/TE: 2-5: Absolute Value Functions and Graphs: 88-92; 2-6: Families of Functions: ; 5-1: Modeling Data with Quadratic Functions: ; 5-2: Properties of Parabolas: ; 5-3: Transforming Parabolas: ; 10-2: Parabolas: ; Application, Practice, and Review: , 111, 112, 219, 244, 265, , 273, 280, , 292, 294, , , 302, 303, 304, 566, , 594 Lessons 2-5, 2-6, 5-1, 5-2, 5-3,

16 TECH: Activities: Modeling Using Residuals: 244, Quadratic Inequalities: ; Examples and Exercises: 89-91, 98, , 247 (TE), 257 (#57), ; Technology Tip: 89 (TE); Graphing Calculator Hint: 89; Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive Textbook Online; for Homework Help, Lesson and Vocabulary Quizzes, 3. Write the equation of a parabola in the form y = a(x - h) 2 + k and a circle in the form y = a(x - h) 2 + (y - k) 2 = r 2 by completing the square. Standard 3 SE/TE: 5-3: Transforming Parabolas: ;10-3: Circles: ; Application, Review, and Practice: 265, , , 302, 592, 594 Lessons 5-3, 10-3 TECH: Activity: Using Parametric Equations: 567; Exercises and Examples: 257 (#57), 562; Graphing Calculator Hint: 562; Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive Textbook Online; for Homework Help, Lesson and Vocabulary Quizzes, Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling. Objective 3.2 Specify locations and describe spatial relationships using coordinate geometry. 1. Sketch the graph of a quadratic and absolute value function. SE/TE: 2-5: Absolute Value Functions and Graphs: 88-92; 2-6: Families of Functions: ; 5-1: Modeling Data with Quadratic Functions: ; 5-2: Properties of Parabolas: ; 5-3: Transforming Parabolas: ; 10-2: Parabolas: ; Application, Practice, and Review: , 111, 112, 219, 244, 265, , 273, 280, , 292, 294, , , 302, 303, 304, 566, ,

17 Lessons 2-5, 2-6, 5-1, 5-2, 5-3, 10-2 TECH: Activities: Modeling Using Residuals: 244, Quadratic Inequalities: ; Examples and Exercises: 89-91, 98, , 247 (TE), 257 (#57), ; Technology Tip: 89 (TE); Graphing Calculator Hint: 89; Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive Textbook Online; for Homework Help, Lesson and Vocabulary Quizzes, 2. Sketch the solutions of absolute value and quadratic inequalities of one variable on a number line. SE/TE: 1-5: Absolute Value Equations and Inequalities: 33-38; Activity: Quadratic Inequalities: 297; Application, Practice, and Review: 45, 49, 50, 52, 133, 878 Lesson 1-5 TECH: Activity: Quadratic Inequalities: ; 3. Sketch the solutions of absolute value and quadratic inequalities of two variables on a Cartesian coordinate system. SE/TE: 2-7: Two-Variable Inequalities: ; 3-3: Systems of Inequalities: ; Activity: Quadratic Inequalities: ; Application, Practice, and Review: 111,

18 Lessons 2-7, 3-3 TECH: Activity: Quadratic Inequalities: ; Exercises and Examples: 105; Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive Textbook Online; for Homework Help, Lesson and Vocabulary Quizzes, 4. Sketch the graph of a square root function. SE/TE: 7-8: Graphing Square Root and Other Radical Functions: ; Activity: Radical Inequalities: ; Application, Practice, and Review: 425, 426 Lesson 7-8 TECH: Activity: Radical Inequalities: ; Exercises and Examples: ; 5. Write an equation of a parabola in the form y = a(x - h) 2 + k when given a graph. SE/TE: 5-3: Transforming Parabolas: ; 10-2: Parabolas: 559; Application, Practice, and Review: 273, 300, 592, 594 Lessons 5-3,

19 TECH: Exercises and Examples: 257 (#57); 6. Graph sine and cosine functions. SE/TE: 13-4: The Sine Function: ; Activity: Graphing Trigonometric Functions: 742; 13-5: The Cosine Function: ; 13-7: Translating Sine and Cosine Functions: ; Application, Practice, and Review: 763, 765, 769, , 774, , , 791, 799, 806 Lessons 13-4, 13-5, 13-7 TECH: Activity: Graphing Trigonometric Functions: 742; Exercises and Examples: 735, 740, , 761; Graphing Calculator Hint: 745, 761; Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive 19

20 7. Perform the transformations of stretching, shifting, and reflecting the graphs of linear, absolute value, quadratic, and radical functions. SE/TE: 2-2: Linear Equations: 62-70; 2-3: Direct Variation: 71, 77; 2-4: Using Linear Models: 78, 80-81; Activity: Finding a Line of Best Fit: 86-87; 2-5: Absolute Value Functions and Graphs: 88-92; 2-6: Families of Functions: ; 5-1: Modeling Data with Quadratic Functions: ; Activity: Modeling Using Residuals: 244; 5-2: Properties of Parabolas: ; 5-3: Transforming Parabolas: ; 7-8: Graphing Square Root and Other Radical Functions: ; Activity: Radical Inequalities: ; 10-2: Parabolas: ; 10-6: Translating Conic Sections: ; Application, Practice, and Review: 100, , , 112, 219, 265, , 273, 280, , 292, 294, , , 302, 303, 304, 425, 426, 566, , 594 Lessons 2-2, 2-3, 2-4, 2-5, 2-6, 5-1, 5-2, 5-3, 7-8, 10-2, 10-6 TECH: Activities: Finding a Line of Best Fit: 86-87, A Family of Functions: 93, Modeling Using Residuals: 244, Quadratic Inequalities: ; Exercises and Examples: 89-91, 98, , 247 (TE), 257 (#57), , , 587; Technology Tip: 89 (TE); Graphing Calculator Hint: 89; Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive 8. Perform transformation on the sine and cosine functions involving amplitude, period, phase shift, vertical shift, and reflections. SE/TE: 13-4: The Sine Function: ; Activity: Graphing Trigonometric Functions: 742; 13-5: The Cosine Function: ; 13-7: Translating Sine and Cosine Functions: ; Application, Practice, and Review: 763, 765, 769, , 774, , , 791, 799,

21 Lessons 13-4, 13-5, 13-7 TECH: Activity: Graphing Trigonometric Functions: 742; Exercises and Examples: 735, 740, , 761; Graphing Calculator Hint: 745, 761; Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive Objective 3.3 Solve problems using visualization, spatial reasoning, and geometric modeling. 1. Solve problems involving absolute value and quadratic functions algebraically and graphically. SE/TE: 2-5: Absolute Value Functions and Graphs: 88-92; 2-6: Families of Functions: ; 5-1: Modeling Data with Quadratic Functions: ; Activity: Modeling Using Residuals: 244; 5-2: Properties of Parabolas: ; 5-3: Transforming Parabolas: ; 10-2: Parabolas: ; Application, Practice, and Review: , 111, 112, 219, 265, , 273, 280, , 292, 294, , , 302, 303, 304, 566, , 594 Lessons 2-5, 2-6, 5-1, 5-2, 5-3, 10-2 TECH: Activities: Modeling Using Residuals: 244, Quadratic Inequalities: ; Examples and Exercises: 89-91, 98, , 247 (TE), 257 (#57), ; Technology Tip: 89 (TE); Graphing Calculator Hint: 89; Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive Textbook Online; for Homework Help, Lesson and Vocabulary Quizzes, 21

22 2. Solve problems using graphs of sine and cosine functions. SE/TE: 13-4: The Sine Function: ; Activity: Graphing Trigonometric Functions: 742; 13-5: The Cosine Function: ; 13-7: Translating Sine and Cosine Functions: ; Application, Practice, and Review: 763, 765, 769, , 774, , , 791, 799, 806 Lessons 13-4, 13-5, 13-7 TECH: Activity: Graphing Trigonometric Functions: 742; Exercises and Examples: 735, 740, , 761; Graphing Calculator Hint: 745, 761; Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive Standard 4 Students will understand and apply measurement tools, formulas, and techniques. Objective 4.1 Understand measurable attributes of objects and the units, systems, and processes of measurement. 1. Convert angle measurements between radians and degrees. SE/TE: Activity: Measuring Radians: 725; 13-3: Radian Measure: ; Application, Practice, and Review: 741, 772, 774 Lesson 13-3 TECH: Exercises and Examples:731; 22

23 2. Calculate the exact values of the sine, cosine, and tangent functions for the special angles of the unit circle. SE/TE: 13-2: Angles and the Unit Circle: ; Application, Practice, and Review: 733, , 743, 749, 770, , 774, 784, , 793, 827, 830 Lesson 13-2 TECH: Exercises and Examples: 720, 722; Objective 4.2 Determine measurements using appropriate techniques, tools, and formulas. 1. Find the length of an arc using radian measure. SE/TE: 13-3: Radian Measure: ; Application, Practice, and Review: 645, 772 Lesson 13-3 TECH: Exercises and Examples: 728; 2. Find the area of a sector in a circle using radian measure. Students calculate the area under a curve and the area of a triangle using the Law of Sines. SE/TE: 11-6: Area Under a Curve: ; 12-7: Normal Distributions: 693; Activity: Area Under a Curve: 699; 14-4: Area and the Law of Sines: ; Application, Practice, and Review: 643, 644, 653, 698, 828,

24 Lesson 11-6, 12-7, 14-4 TECH: Activity: Area Under a Curve: 699; Exercises and Examples: ; Standard 5 Students will draw conclusions using concepts of probability after collecting, organizing, and analyzing a data set. Objective 5.1 Formulate and answer questions by collecting, organizing, and analyzing data. 1. Determine the quadratic regression equation for a given set of bivariate data using technology. SE/TE: 5-1: Modeling Data with Quadratic Functions: ; Activity: Modeling Using Residuals: 244; Application, Practice, and Review: 251, 265, 287, 288, 300, 308 Lesson 5-1 TECH: Activity: Modeling Using Residuals: 244; Exercises and Examples: ; Technology Tip: 240 (TE); Student/Teacher Express CD- ROMs, Presentation Express CD-ROM, Interactive 2. Analyze the meaning of the maximum or SE/TE: 5-1: Modeling Data with Quadratic minimum and intercepts of the regression equation Functions: ; Activity: Modeling Using as they relate to a given set of bivariate data. Residuals: 244; Application, Practice, and Review: 251, 265, 287, 288, 300,

25 3. Make predictions and estimations and determine their reasonableness using a regression equation. Lesson 5-1 TECH: Activity: Modeling Using Residuals: 244; Exercises and Examples: ; Technology Tip: 240 (TE); Student/Teacher Express CD- ROMs, Presentation Express CD-ROM, Interactive SE/TE: 2-4: Using Linear Models: 78-84;Activity: Finding a Line of Best Fit: 86-87; 5-1: Modeling Data with Quadratic Functions: ; Activity: Modeling Using Residuals: 244; 6-1: Section 2: Modeling Data with a Polynomial Function: ; 8-1: Exploring Exponential Models: ; Activity: Fitting Exponential Curves to Data: 438; Activity: Linear and Exponential Models: 469; Activity: ; Application, Practice, and Review: 85, 92, 100, , 112, 119, 121, 251, 265, 287, 288, 300, 428, 475, 493 Lessons 2-4, 5-1, 6-1, 8-1 TECH: Activities: Finding a Line of Best Fit: 86-87, Modeling Using Residuals: 244, Fitting Exponential Curves to Data: 438, Linear and Exponential Models: 469; Exercises and Examples: , , ; 25

26 Objective 5.2 Apply basic concepts of probability. 1. Identify the difference between a permutation and a combination. SE/TE: 6-7: Permutations and Combinations: ; Application, Practice, and Review: Activity: Pascal s Triangle: 352; 6-8: The Binomial Theorem: ; 358, 361, 362, 685, 687 Lesson 6-7 TECH: Exercises and Examples: 347, , 687; Technology Tip: 347 (TE); Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive Textbook Online; for Homework Help, Lesson and Vocabulary Quizzes, 2. Calculate a probability using the Fundamental Counting Principle. SE/TE: 1-6: Probability: 39-45; 9-7: Probability of Multiple Events: ; 12-1: Probability Distributions: ; 12-2: Conditional Probability: ; Extension: Comparing Conditional Probabilities: 659; Activity: Continuous Probability: 676; Binomial Distributions: ; Application, Practice, and Review: 49, 50, 151, , 361, 362, 541, 542, 667, , 704 Lessons 1-6, 9-7, 12-1, 12-2 TECH: Activities: Exercises and Examples: 40, 42, 652, 687, 690; Technology Tip: 42 (TE); Graphing Calculator Hint: 42; Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive Textbook Online; for Homework Help, Lesson and Vocabulary Quizzes, 26

27 3. Calculate simple combinations and permutations of n objects taken r at a time. SE/TE: 6-7: Permutations and Combinations: ; Application, Practice, and Review: 357, 358, 361, 362 Lesson 6-7 TECH: Exercises and Examples: 347, ; Technology Tip: 347 (TE); Student/Teacher Express CD-ROMs, Presentation Express CD-ROM, Interactive Textbook Online; for Homework Help, Lesson and Vocabulary Quizzes, 27

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