Virginia Standards of Learning Algebra 2 - McDougal … Standards of Learning, Algebra 2 ... Lesson 4.5 320 320 PE/Lesson 6.2 420 427 ... exponential, logarithmic,

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VirginiaStandards of LearningAlgebra 2

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McDougal Littell Algebra 2 © 2007 correlated to theVirginia Standards of Learning, Algebra 2

Standards: Virginia Standards of Learning, Algebra 2

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AII.1 The student will identify field properties, axioms of equality and inequality, and properties of order that are valid for the set of real numbers and its subsets, complex numbers, and matrices.

PE/Lesson 1.1 3 4

PE/Lesson 1.1 6 9PE/Lesson 1.3 18 18PE/Lesson 1.6 42 42PE/Chapter 1 Summary 60 60PE/Chapter 1 Review, Lesson 1.1 61 61PE/Chapter 1 Test 65 65PE/Lesson 3.5 188 188PE/Lesson 3.6 197 197PE/Lesson 4.3 253 253PE/Lesson 4.5 266 266PE/Lesson 4.6 276 276PE/Lesson 4.6 278 280PE/Chapter 4 Summary 317 317PE/Chapter 4 Review 320 321PE/Lesson 5.1 330 334PE/Lesson 6.2 420 422PE/Chapter 6 Summary 465 465PE/Chapter 6 Review 466 467PE/Lesson 7.5 507 509PE/Lesson 7.5 511 511PE/Lesson 7.6 515 515

AII.2 The student will add, subtract, multiply, divide, and simplify rational expressions, including complex fractions.

PE/Lesson 8.4 573 580

PE/Lesson 8.4 Activity 581 581PE/Lesson 8.5 582 588PE/Mixed Review of Problem Solving, Lessons 8.4–8.6

601 601

PE/Chapter 8 Summary 602 602PE/Chapter 8 Review, Lessons 8.4-8.5 605 605PE/Chapter 8 Test 607 607PE/Extra Practice 1017 1017

Content: McDougal Littell Algebra 2 ©2007

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AII.3 The student willAII.3.a add, subtract, multiply, divide, and simplify radical expressions containing positive rational numbers and variables and expressions containing rational exponents;

PE/Lesson 4.5 266 271

PE/Chapter 4 Review, Lesson 4.5 320 320PE/Lesson 6.2 420 427PE/Mixed Review of Problem Solving, Lessons 6.1-6.3

436 436

PE/Chapter 6 Summary 465 465PE/Chapter 6 Review, Lesson 6.2 467 467PE/Chapter 6 Test 469 469PE/Chapter 6 Standardized Test Practice 472 473PE/Cumulative Review for Chapters 1–6 474 474PE/Lesson 7.4 505 505PE/Lesson 8.6 595 595PE/Lesson 13.2 865 865PE/Lesson 13.5 888 888PE/Extra Practice 1013 1013PE/Extra Practice 1015 1015

AII.3.b write radical expressions as expressions containing rational exponents and vice versa.

PE/Lesson 6.1 415 415

PE/Lesson 6.1 417 418AII.4 The student will solve absolute value equations and inequalities graphically and algebraically. Graphing calculators will be used as a primary method of solution and to verify algebraic solutions.

PE/Investigating Algebra Activity, Lesson 1.7 50 50

PE/Lesson 1.7 51 58PE/Mixed Review of Problem Solving, Lessons 1.5–1.7

59 59

PE/Chapter 1 Summary 60 60PE/Chapter 1 Review, Lesson 1.7 64 64PE/Chapter 1 Test 65 65PE/Chapter 1 Standardized Test Practice 68 69PE/Lesson 2.2 88 88PE/Lesson 2.5 111 111PE/Lesson 2.8 135 136PE/Lesson 3.3 169 169PE/Lesson 3.3 171 172PE/Chapter 3 Test 227 227PE/Extra Practice 1010 1010PE/Extra Practice 1020 1020

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AII.5 The student will identify and factor completely polynomials representing the difference of squares, perfect square trinomials, the sum and difference of cubes, and general trinomials.

PE/Lesson 4.3 252 258

PE/Lesson 4.4 259 265PE/Lesson 4.6 282 282PE/Lesson 4.7 284 291PE/Lesson 4.9 303 303PE/Chapter 4 Summary 317 317PE/Chapter 4 Review, Lessons 4.3-4.4, 4.7 319 321PE/Chapter 4 Test 323 323PE/Chapter 4 Standardized Test Preparation 324 325PE/Chapter 4 Standardized Test Practice 326 327PE/Chapter 5 Opener 328 328PE/Lesson 5.2 344 344PE/Lesson 5.4 353 359PE/Lesson 5.5 368 368PE/Lesson 5.6 377 377PE/Lesson 5.9 399 399PE/Chapter 5 Summary 401 401PE/Chapter 5 Review, Lesson 5.4 404 404PE/Chapter 5 Test 407 407PE/Lesson 6.4 445 445PE/Cumulative Review for Chapters 1–6 474 475PE/Lesson 7.1 485 485PE/Chapter 8 Opener 548 548PE/Lesson 8.2 563 563PE/Lesson 8.3 571 571PE/Lesson 9.1 619 619PE/Cumulative Review for Chapters 1–9 678 679PE/Extra Practice 1013 1014

AII.6 The student will select, justify, and apply a technique to solve a quadratic equation over the set of complex numbers. Graphing calculators will be used for solving and for confirming the algebraic solutions.

PE/Lesson 4.6 275 275

PE/Lesson 4.6 279 279PE/Lesson 4.7 291 291PE/Lesson 4.8 293 293

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AII.7 The student will solve equations containing rational expressions and equations containing radical expressions algebraically and graphically. Graphing calculators will be used for solving and for confirming the algebraic solutions.

PE/Lesson 6.6 452 459

PE/Problem Solving Workshop: Using Alternative Methods, Lesson 6.6

460 461

PE/Mixed Review of Problem Solving, Lessons 6.4-6.6

464 464

PE/Chapter 6 Summary 465 465PE/Chapter 6 Review, Lesson 6.6 468 468PE/Chapter 6 Test 469 469PE/Chapter 6 Standardized Test Practice 472 473PE/Cumulative Review for Chapters 1–6 474 474PE/Lesson 8.6 589 595PE/Problem Solving Workshop: Using Alternative Methods, Lesson 8.6

596 597

PE/Chapter 8 Review, Lesson 8.6 606 606PE/Chapter 8 Standardized Test Practice 611 611PE/Extra Practice 1015 1015PE/Extra Practice 1017 1017

AII.8 The student will recognize multiple representations of functions (linear, quadratic, absolute value, step, and exponential functions) and convert between a graph, a table, and symbolic form. A transformational approach to graphing will be employed through the use of graphing calculators.

PE/Lesson 2.1 72 79

PE/Lesson 2.1 Extension 80 81PE/Lesson 2.7 Activity 121 122PE/Lesson 2.7 123 129PE/Lesson 2.7 Extension 131 131PE/Chapter 2 Summary 140 140PE/Chapter 2 Review, Lesson 2.1 141 141PE/Chapter 2 Review, Lesson 2.7 144 144PE/Chapter 2 Test 145 145PE/Chapter 2 Standardized Test Practice 148 149PE/Lesson 4.1 236 243PE/Lesson 4.1 Activity 244 244PE/Lesson 4.2 245 251PE/Lesson 4.4 265 265PE/Lesson 4.10 Activity 308 308PE/Lesson 4.10 309 315

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316 316

PE/Chapter 4 Review, Lessons 4.1-4.2 318 319PE/Chapter 4 Review, Lesson 4.10 322 322PE/Chapter 4 Test 323 323PE/Chapter 4 Standardized Test Practice 326 327PE/Lesson 7.1 478 485PE/Lesson 7.2 486 491PE/Lesson 7.3 492 498PE/Mixed Review of Problem Solving, Lessons 7.1-7.4

506 506

PE/Lesson 7.7 Activity 528 528PE/Lesson 7.7 529 536PE/Chapter 7 Review, Lessons 7.1-7.2 539 540PE/Chapter 7 Review, Lesson 7.7 542 542PE/Chapter 7 Standardized Test Practice 546 547PE/Extra Practice 1011 1011PE/Extra Practice 1013 1013PE/Extra Practice 1015 1015

AII.9 The student will find the domain, range, zeros, and inverse of a function; the value of a function for a given element in its domain; and the composition of multiple functions. Functions will include exponential, logarithmic, and those that have domains and ranges that are limited and/ or discontinuous. The graphing calculator will be used as a tool to assist in investigation of functions.

PE/Lesson 7.1 478 479

PE/Lesson 7.1 482 485PE/Lesson 7.2 486 491PE/Lesson 7.3 493 494PE/Lesson 7.3 496 496PE/Lesson 7.3 498 498PE/Lesson 7.4 501 505PE/Mixed Review of Problem Solving, Lessons 7.1-7.4

506 506

PE/Lesson 7.5 (mixed review) 513 513PE/Lesson 7.7 (mixed review) 536 536PE/Chapter 7 Review, Lessons 7.1-7.4 539 541PE/Chapter 7 Test 543 543PE/Chapter 7 Standardized Test Preparation 545 545PE/Chapter 7 Standardized Test Practice 546 547PE/Extra Practice 1016 1016

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AII.10 The student will investigate and describe through the use of graphs the relationships between the solution of an equation, zero of a function, x-intercept of a graph, and factors of a polynomial expression.

PE/Lesson 5.6 372 372

PE/Lesson 5.6 374 376PE/Lesson 5.7 380 380PE/Lesson 5.7 382 385PE/Lesson 5.8 387 392PE/Mixed Review of Problem Solving, Lessons 5.6–5.9

400 400

PE/Chapter 5 Summary 401 401PE/Chapter 5 Review, Lesson 5.8 406 406PE/Chapter 5 Test 407 407PE/Chapter 5 Standardized Test Practice 410 411PE/Extra Practice 1014 1014

AII.11 The student will use matrix multiplication to solve practical problems. Graphing calculators or computer programs with matrix capabilities will be used to find the product.

PE/Lesson 3.6 198 198

PE/Lesson 3.6 200 202PE/Chapter 3 Review 225 225PE/Chapter 3 Test 227 227PE/Chapter 3 Standardized Test Practice 231 231

AII.12 The student will represent problem situations with a system of linear equations and solve the system, using the inverse matrix method. Graphing calculators or computer programs with matrix capability will be used to perform computations.

PE/Lesson 3.8 213 213

PE/Lesson 3.8 215 216PE/Lesson 3.8 218 219PE/Mixed Review of Problem Solving, Lessons 3.5-3.8

220 220

PE/Chapter 3 Standardized Test Practice 231 231AII.13 The student will solve practical problems, using systems of linear inequalities and linear programming, and describe the results both orally and in writing. A graphing calculator will be used to facilitate solutions to linear programming problems.

PE/Lesson 3.3 170 170

PE/Lesson 3.3 172 173PE/Lesson 3.3 Extension 174 176PE/Mixed Review of Problem Solving, Lessons 3.1-3.4

186 186

PE/Cumulative Review for Chapters 1–3 233 233

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AII.14 The student will solve nonlinear systems of equations, including linear-quadratic and quadratic- quadratic, algebraically and graphically. The graphing calculator will be used as a tool to visualize graphs and predict the number of solutions.

PE/Lesson 9.7 658 664


667 667

PE/Chapter 9 Review, Lesson 9.7 672 672PE/Chapter 9 Test 673 673PE/Chapter 9 Standardized Test Practice 677 677PE/Extra Practice 1018 1018

AII.15 The student will recognize the general shape of polynomial, exponential, and logarithmic functions. The graphing calculator will be used as a tool to investigate the shape and behavior of these functions.

PE/Lesson 5.2 Activity 336 336

PE/Lesson 5.2 339 344PE/Lesson 5.2 Activity 345 345PE/Lesson 5.8 387 392PE/Mixed Review of Problem Solving, Lessons 5.6–5.9

400 400

PE/Chapter 5 Summary 401 401PE/Chapter 5 Review, Lesson 5.2 403 403PE/Chapter 5 Review, Lesson 5.8 406 406PE/Chatper 5 Test 407 407PE/Lesson 7.1 478 485PE/Lesson 7.2 486 491PE/Lesson 7.3 493 494PE/Lesson 7.3 496 498PE/Lesson 7.4 502 505PE/Mixed Review of Problem Solving, Lessons 7.1-7.4

506 506

PE/Chapter 7 Summary 538 538PE/Chapter 7 Review, Lessons 7.1-7.2, 7.4 539 541PE/Chapter 7 Test 543 543PE/Chapter 7 Standardized Test Practice 546 547PE/Extra Practice 1014 1014PE/Extra Practice 1016 1016

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AII.16 The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve practical problems, including writing the first n terms, finding the nth term, and evaluating summation formulas. Notation will include Sigma and a(sub n).

PE/Lesson 12.2 805 805

PE/Lesson 12.2 808 809PE/Lesson 12.3 813 813PE/Lesson 12.3 815 817PE/Mixed Review of Problem Solving, Lessons 12.1-12.3

818 818

PE/Lesson 12.4 Activity 819 819PE/Lesson 12.4 822 822PE/Lesson 12.4 824 825PE/Lesson 12.5 829 829PE/Lesson 12.5 832 833PE/Problem Solving Workshop: Using Alternative Methods, Lesson 12.5

834 835


838 838

PE/Chapter 12 Review, Lesson 12.2 841 841PE/Chapter 12 Review, Lesson 12.5 842 842PE/Chapter 12 Test 843 843PE/Chapter 12 Standardized Test Preparation 844 844PE/Chapter 12 Standardized Test Practice 846 847PE/Cumulative Review for Chapters 1–12 849 849

AII.17 The student will perform operations on complex numbers and express the results in simplest form. Simplifying results will involve using patterns of the powers of i.

PE/Lesson 4.6 276 282

PE/Lesson 4.7 291 291PE/Mixed Review of Problem Solving, Lessons 4.6-4.10

316 316

PE/Chapter 4 Summary 317 317PE/Chapter 4 Review, Lesson 4.6 320 321PE/Chapter 4 Test 323 323PE/Extra Practice 1013 1013

AII.18 The student will identify conic sections (circle, ellipse, parabola, and hyperbola) from his/her equations. Given the equations in (h, k) form, the student will sketch graphs of conic sections, using transformations.

PE/Lesson 9.2 620 625

PE/Lesson 9.3 626 632PE/Lesson 9.3 Activity 633 633PE/Lesson 9.4 634 639PE/Problem Solving Workshop: Using Alternative Methods, Lesson 9.4

640 641

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PE/Lesson 9.5 642 648PE/Investigating Algebra Activity, Lesson 9.6 649 649PE/Lesson 9.6 650 657PE/Mixed Review of Problem Solving, Lessons 9.5-9.7

667 667

PE/Chapter 9 Summary 668 668PE/Chapter 9 Review, Lessons 9.2-9.6 670 672PE/Chapter 9 Test 673 673PE/Chapter 9 Standardized Test Practice 676 677PE/Extra Practice 1018 1018

AII.19 The student will collect and analyze data to make predictions and solve practical problems. Graphing calculators will be used to investigate scatterplots and to determine the equation for a curve of best fit. Models will include linear, quadratic, exponential, and logarithmic functions.

PE/Lesson 2.6 116 120


139 139

PE/Chapter 2 Review, Lesson 2.6 143 143PE/Chapter 2 Test 145 145PE/Chapter 2 Standardized Test Preparation 146 147PE/Chapter 2 Standardized Test Practice 148 149PE/Lesson 4.10 Activity 308 308PE/Lesson 4.10 311 315PE/Mixed Review of Problem Solving, Lessons 4.6-4.10

316 316

PE/Chapter 4 Test 323 323PE/Chapter 4 Standardized Test Practice 327 327PE/Lesson 7.7 Activity 528 528PE/Lesson 7.7 530 536PE/Mixed Review of Problem Solving, Lessons 7.5-7.7

537 537

PE/Chapter 7 Test 543 543PE/Chapter 7 Standardized Test Practice 547 547

AII.20 The student will identify, create, and solve practical problems involving inverse variation and a combination of direct and inverse variations.

PE/Lesson 8.1 Activity 550 550

PE/Lesson 8.1 552 553PE/Lesson 8.1 556 557PE/Mixed Review of Problem Solving, Lessons 8.1-8.3

572 572

PE/Chapter 8 Test 607 607

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VA 3003/2006

2007CC2

Documents

Virginia Standards of Learning Algebra 2 - McDougal … Standards of Learning, Algebra 2 ... Lesson 4.5 320 320 PE/Lesson 6.2 420 427 ... exponential, logarithmic,