correlated to the Washington D.C. Public Schools Learning Standards Algebra II

correlated to the Washington D.C. Public Schools Learning Standards Algebra II

McDougal Littell Algebra 2 2007 correlated to the Washington DC Public Schools Learning Standards Algebra II NUMBER SENSE AND OPERATIONS INDICATORS AII.N.1 Know and use the properties of operations on real numbers, including the existence of the identity and inverse elements for addition and multiplication and the existence of nth roots of positive real numbers for any positive integer n, and the nth power of positive real numbers. PE/TE: Lesson 1.1: Apply Properties of Real Numbers, 3-4, 6 (#11-22) Lesson 1.2: Evaluate and Simplify Algebraic Expressions, 11 (#1-7), 13 (#4-7) Activity 1.2: Evaluate Expressions, 17 (#1-12) Chapter Review, 61 (#7-9) Lesson 6.1: Evaluate nth Roots and Use Rational Exponents, 414-419 AII.N.2 Simplify numerical expressions with powers and roots, including fractional and negative exponents. PE/TE: Chapter 1 Opening: Equations and Inequalities, 1 (#1-3) Activity 1.2: Evaluate Expressions, 17 (#1-6) Lesson 6.1: Evaluate nth Roots and Use Rational Exponents, 415 (#5-12), 417 (#22-46) Lesson 6.2: Apply Properties of Rational Exponents, 421 (#1-4), 424, 427 (#9-10, 12) AII.N.3 Know the representation of complex numbers (e.g., a + bi where a and b are real numbers) and the procedures for adding, multiplying and inverting complex numbers. Understand the associative, commutative, and identity properties for complex arithmetic. PE/TE: Lesson 4.6: Perform Operations with Complex Numbers, 275-282 Chapter Review, 321 (#29-34) Chapter Test, 323 (#16-18) 1

PATTERNS, RELATIONS, AND ALGEBRA INDICATORS AII.P.1 Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative and recursive patterns such as Fibonacci Numbers and Pascal s Triangle. PE/TE: Lesson 1.1: Apply Properties of Real Numbers, 8 (#59) Lesson 5.3: Add, Subtract and Multiply Polynomials 350 (#57) Lesson 7.5: Apply Properties of Logarithms, 512 (#73) Lesson 10.2: Use Combinations and the Binomial Theorem, 692, 695 (#36-37) Activity 12.5: Exploring Recursive Rules, 826 Lesson 12.5: Use Recursive Rules with Sequences and Functions, 828, 830-831, 833 AII.P.2 Identify arithmetic and geometric sequences and finite arithmetic and geometric series. Use the properties of such sequences and series to solve problems, including finding the formula for the general term and the sum, recursively and explicitly. PE/TE: Lesson 12.1: Define and Use Sequences and Series, 794-800 Activity 12.1: Work with Sequences, 801 Lesson 12.2: Analyze Arithmetic Sequences and Series, 802-809 Lesson 12.3: Analyze Geometric Sequences and Series, 810-817 Activity 12.5: Exploring Recursive Rules, 826 Lesson 12.5: Use Recursive Rules with Sequences and Functions, 827-832 AII.P.3 Understand functional notation, evaluate a function at a specified point in its domain, and perform operations on functions with emphasis on the domain and range. PE/TE: Lesson 2.1: Represent Relations and Functions, 75, 78 (#34-39, 44-45) Lesson 2.6: Draw Scatter Plots and Best-Fitting Lines, 120 (#36-41) AII.P.4 Understand exponential and logarithmic functions and their basic arithmetic properties, including change of base and formulas for exponential of a sum and logarithm of a product. PE/TE: Lesson 7.1: Graph Exponential Growth Functions, 480-481, 483 (#31), 484, 485 (#41-44) Lesson 7.2: Graph Exponential Decay Functions, 488, 490-491 Lesson 7.4: Evaluate Logarithms and Graph Logarithmic Functions, 501-503, 504 (#37-53) Lesson 7.5: Apply Properties of Logarithms, 507-511, 513 (#16-19) AII.P.5 Given algebraic, numeric and/or graphical representations, recognize functions as polynomial, rational, logarithmic, or exponential, and describe their behavior. PE/TE: Activity 5.2: End Behavior of Polynomial Functions, 336 Lesson 5.2: Evaluate and Graph Polynomial Functions, 339-340, 342 (#24-27, 51) Lesson 7.1: Graph Exponential Growth Functions, 478-479 Lesson 7.2: Graph Exponential Decay Functions, 486-487, 489 (#3-6, 15) Lesson 7.4: Evaluate Logarithms and Graph Logarithmic Functions, 502-503 Lesson 8.2: Graph Simple Rational Functions, 558-559 Lesson 8.3: Graph General Rational Functions, 565-566 2

AII.P.6 Find solutions to radical equations; find solutions to quadratic equations (with real coefficients and real or complex roots) graphically, by factoring, by completing the square, or by using the quadratic formula. PE/TE: Lesson 4.1: Graph Quadratic Functions in Standard Form, 242 (#59), 243 (#60) Lesson 4.3: Solve x 2 + bx + c = 0 by Factoring, 252-258 Lesson 4.4: Solve ax 2 + bx + c = 0 by Factoring, 259-265 Lesson 4.5: Solve Quadratic Equations by Finding Square Roots, 266-271 Lesson 4.6: Perform Operations with Complex Numbers, 275-282 Activity 4.7: Using Algebra Tiles to Complete the Square, 283 Lesson 4.7: Complete the Square, 284-291 Lesson 4.8: Use the Quadratic Formula and the Discriminant, 292-299 Lesson 6.6: Solve Radical Equations, 452-458 AII.P.7 Solve a variety of equations and inequalities using algebraic, graphical, and numerical methods, including the quadratic formula. Include polynomial, exponential, and logarithmic functions, expressions involving the absolute values, and simple rational expressions. PE/TE: Activity 1.7: Absolute Value Equations and Inequalities, 50 Lesson 1.7: Solve Absolute Value Equations and Inequalities, 51-57 Lesson 4.9: Graph and Solve Quadratic Inequalities, 300-307 Lesson 5.2: Evaluate and Graph Polynomial Functions, 338-344 Lesson 5.4: Factor and Solve Polynomial Equations, 355, 357 (#32-40), 359 (#76-79) Lesson 7.6: Solve Exponential and Logarithmic Equations, 515-522 Problem Solving Workshop: 523-525 Extension 7.6: Solve Exponential and Logarithmic Inequalities, 526-527 AI.P.8 Explore matrices and their operations, including using them to solve systems of linear equations. Apply to solutions of everyday problems. PE/TE: Lesson 3.5: Perform Basic Matrix Operations, 187-192 Activity 3.5: Use Matrix Operations, 194 Lesson 3.6: Multiply Matrices, 195-201, 202 (#44-45) Lesson 3.7: Evaluate Determinants and Apply Cramer s Rule, 205-206, 208 (#29-37) Lesson 3.8: Use Inverse Matrices to Solve Linear Systems, 212-213, 216 (#45-48), 217 (#8-13) Chapter Test: 227 (#27-30) Lesson 4.6: Perform Operations with Complex Numbers, 282 (#81-84) 3

AII.P.9 Use symbolic, numeric, and graphical methods to solve systems of equations and/or inequalities involving algebraic, exponential, and logarithmic expressions. Describe the relationships among the methods. PE/TE: Activity 3.1: Solving Linear Systems Using Tables, 152 Lesson 3.1: Solve Linear Systems by Graphing, 153-158 Activity 3.1: Graph Systems of Equations, 159 Lesson 3.2: Solve Linear Systems Algebraically, 160-167 Lesson 3.3: Graph Systems of Linear Inequalities, 168-173 Lesson 3.4: Solve Systems of Linear Equations in Three Variables, 178-185 Lesson 3.6: Multiply Matrices, 202 (#58-63) Lesson 3.7: Evaluate Determinants and Apply Cramer s Rule, 209 (#53-56) Chapter Test: 227 (#1-14), Lesson 4.9: Graph and Solve Quadratic Inequalities, 301 (#4), 304 (#20-25), 307 (#87-92) Lesson 4.10: Write Quadratic Functions and Models, 315 (#59-64) AII.P.10 Solve everyday problems that can be modeled using polynomial, rational, exponential, logarithmic, and step functions; absolute values; and square roots. Apply appropriate graphical, tabular, or symbolic methods to the solution. Include compound interest, exponential growth and decay, and direct and inverse variation problems. PE/TE: Lesson 1.7: Solve Absolute Value Equations and Inequalities, 54, 57 Extension 2.7: Use Piecewise Functions, 130-131 Lesson 5.2: Evaluate and Graph Polynomial Functions, 343-344 Lesson 6.5: Graph Square Root and Cube Root Functions, 450-451 Lesson 7.1: Graph Exponential Growth Functions, 480-481, 484-485 Lesson 7.2: Graph Exponential Decay Functions, 488, 490-491 Lesson 7.4: Evaluate Logarithms and Graph Logarithmic Functions, 504-505 Lesson 8.1: Model Inverse and Joint Variation, 553-554, 556-557 Lesson 8.3: Graph General Rational Functions, 567, 569 (#31), 570, 571 (#36) AII.P.11 Recognize translations and scale changes of a given function f(x) resulting from substitutions for the various parameters a, b, c, and d in y = af(b(x+ c/b)) + d. In particular, describe qualitatively the effect of such changes on polynomial, rational, exponential, and logarithmic functions. PE/TE: Activity 2.7: Exploring Transformations, 121-122 Lesson 2.7: Use Absolute Value Functions and Transformations, 123, 126-127 Lesson 7.1: Graph Exponential Growth Functions, 479 (#3), 482 (#15-23) Lesson 7.2: Graph Exponential Decay Functions, 488 (#4-6), 489 (#16-24) Lesson 7.3: Use Functions Involving e, 493 Lesson 7.4: Evaluate Logarithms and Graph Logarithmic Functions, 503 (#18) Lesson 8.2: Graph Simple Rational Functions, 559, 561 (#3-22) AII.P.12 Simplify rational expressions. Solve rational equations and inequalities. PE/TE: Lesson 8.4: Multiply and Divide Rational Expressions, 573, 574 (#1-6), 577 (#3-17) Activity 8.4: Verify Operations with Rational Expressions, 581 Lesson 8.6: Solve Rational Equations, 589-594, 595 (#8-13) Extension 8.6: Solve Rational Inequalities, 598-600 Chapter Review: 606 (#26-36) Chapter Test: 607 (#25-27) 4

GEOMETRY INDICATORS AII.G.1 Define the sine, cosine, and tangent of an acute angle. Apply to the solution of problems. PE/TE: Lesson 13.1: Use Trigonometry with Right Angles, 852-853, 856 (#3-15) AII.G.2 Explain the identity sin 2 0 + cos 2 0 = 1. Relate the identity to the Pythagorean theorem. PE/TE: Lesson 14.3: Verify Trigonometric Identities, 924-925, 927 (#3, 6) AII.G.3 Relate geometric and algebraic representations of lines and simple curves. PE/TE: Lesson 2.3: Graph Equations of Lines, 94-95 Lesson 4.1: Graph Quadratic Functions in Standard Form, 241 (#41-42, 44-52), 242 (#57, 59), 243 (#60) Lesson 4.2: Graph Quadratic Functions in Vertex or Intercept Form, 249 (#3-11, 13-21), 250, 251 (#54-55) DATA ANALYSIS, STATISTICS AND PROBABILITY INDICATORS AII.D.1 Select an appropriate graphical representation for a set of data and use appropriate statistics (e.g., quartile or percentile distribution) to communicate information about the data, including box plots. PE/TE: Activity 11.5: Fitting a Model to Data, 774 Lesson 11.5: Choose the Best Model for Two-Variable Data, 775-779, 780 (#14-15) AII.D.2 Use combinatorics (e.g., fundamental counting principle, permutations, and combinations) to solve problems, including computing geometric probabilities and probabilities of compound events. PE/TE: Lesson 10.1: Apply the Counting Principle and Permutations, 682-689 Lesson 10.2: Use Combinations and the Binomial Theorem, 690-696, 697 (#53) Lesson 10.3: Define and Use Probability, 701, 703 (#35-37), 704 (#41, 58-61) Lesson 10.4: Find Probabilities of Disjoint and Overlapping Events, 707-712, 713 (#49-50) Standardized Test Preparation: 738-739 5

DC 32 6/2007 2007 CC2