correlated to the New York State Learning Standards for Mathematics Algebra 2 and Trigonometry

Transcription

1 correlated to the New York State Learning Standards for Mathematics Algebra 2 and Trigonometry

2 McDougal Littell Algebra correlated to the New York State Learning Standards for Mathematics Algebra 2 and Trigonometry Algebra 2 and Trigonometry Problem Solving Strand Students will build new mathematical knowledge through problem solving. A2.PS.1. Use a variety of problem solving strategies to understand new mathematical content A2.PS.2. Recognize and understand equivalent representations of a problem situation or a mathematical concept for example: 34-40, 48, 59, 60, 63, 66-68, 105, 218, 272, 360, 460, 523, 596, 640, 714, 781, 834, 895, 938 for example: 15 (#61), 24 (#74), 39 (#28), 57 (#78), 95 (#67), 104 (#57), 105, 119 (#27), 129 (#41), 157 (#38), 173 (#37), 216 (#45), 258 (#68), 290 (#66). 314 (#50), 343 (#56), 367 (#38), 392 (#42), 434 (#46) Students will solve problems that arise in mathematics and in other contexts. A2.PS.3. Observe and explain patterns to formulate generalizations and conjectures A2.PS.4. Use multiple representations to represent and explain problem situations (e.g., verbally, numerically, algebraically, graphically) PE/TE: 8 (#59), 283, 347, 350, 354, (#52-55, 57), 512 (#73), 695 (#37), , 692, 695, , , , 818, , , 839, , 843, , for example: 451 (#39), 485 (#42), 521 (#59), 562 (#39), 570 (#32), 631 (#68), 647 (#42), 703 (#40), 729 (#47), 754 (#21), 779 (#12), 808 (#66), 816 (#61), 857 (#34), 887 (#46), 914 (#32), 929 (#41), 937 (#43), 938 (#61) PE/TE = Pupil s Edition/Teacher s Edition 1

3 Students will apply and adapt a variety of appropriate strategies to solve problems. A2.PS.5. Choose an effective approach to solve a problem from a variety of strategies (numeric, graphic, algebraic) A2.PS.6. Use a variety of strategies to extend solution methods to other problems A2.PS.7. Work in collaboration with others to propose, critique, evaluate, and value alternative approaches to problem solving for example: 34-40, 46-47, 48, 57-58, 59, 68, 78-79, 105, 218, 272, 360, 460, 523, 596, 640, 714, 781, 834, 895, 938 for example: 8 (#60), 32 (#36), 47 (#59), 59 (#36), 69 (#20, 21), 79 (#49), 88 (#48), 95 (#68), 106 (#5), 111 (#44), 119 (#28), 129 (#40), 137 (#48), 139 (#6), 158 (#39), 166 (#60), 173 (#39), 185 (#47), 192 (#33), 202 (#44) pages: 34-40, 46-47, 48, 57-58, 59, 68, 78-79, 105, 218, 272, 360, 460, 523, 596, 640, 714, 781, 834, 895, 938 Students will monitor and reflect on the process of mathematical problem solving. A2.PS.8. Determine information required to solve the problem, choose methods for obtaining the information, and define parameters for acceptable solutions A2.PS.9. Interpret solutions within the given constraints of a problem A2.PS.10. Evaluate the relative efficiency of different representations and solution methods of a problem for example: 15 (#58), 91, 104 (#55), 108, 110 (#39, 40), , 146, , 335 (#53), 344 (#58), 383, 416, , 497 (#59), 535 (#34), 557 (#41), 640, , 904 (#1) for example: 7 (#49), 15 (#56, 59), 23 (#72), 31 (#24), 38 (#27), 38 (#27), 47 (#59), 59 (#3), 68, 69 (#20, 21), 78-79, 87 (#44), 88 (#47, 48), 95 (#63, 68), 103 (#53), 106 (#35), 111 (#44), 120 (#29), 128 (#38), 129 (#40), 137 (#46) pages: 48, 105, 218, 272, 360, 460, 523, 596, 640, 714, 781, 834, 895, 938 PE/TE = Pupil s Edition/Teacher s Edition 2

4 Reasoning and Proof Strand Students will recognize reasoning and proof as fundamental aspects of mathematics. A2.RP.1. Support mathematical ideas using a variety of strategies Students will make and investigate mathematical conjectures. A2.RP.2. Investigate and evaluate conjectures in mathematical terms, using mathematical strategies to reach a conclusion A2.RP.3. Evaluate conjectures and recognize when an estimate or approximation is more appropriate than an exact answer A2.RP.4. Recognize when an approximation is more appropriate than an exact answer PE/TE: 48, 105, 218, 272, 360, 460, 523, 596, 640, 714, 781, 834, 895, 938 PE/TE: 50, 112, , 152, 177, 283, 308, 336, 437, 528, 550, 649, 706, 747, 819, 826, 874, 881, 923, 948 pages: 50, 112, , 152, 177, 283, 308, 336, 437, 528, 550, 649, 706, 747, 819, 826, 874, 881, 923, 948 pages: 50, 112, , 152, 177, 283, 308, 336, 437, 528, 550, 649, 706, 747, 819, 826, 874, 881, 923, 948 Students will develop and evaluate mathematical arguments and proofs. A2.RP.5. Develop, verify, and explain an argument, using appropriate mathematical ideas and language A2.RP.6. Construct logical arguments that verify claims or counterexamples that refute claims for example: 7 (#49-54), 25 (#7), 49 (#1), 56 (#65), 87 (#28), 103 (#48), 118 (#22), 128 (#34), 183 (#37), 219 (#4), 256 (#57), 273 (#10), 289 (#10), 289 (#60), 297 (#66), 334 (#43-45), 345 (#9), 384 9#50), 391 (#31), 443 (#44), for example: 128 (#34), 183 (#37), 273 (#10), 384 (#50), 386 (#64), 443 (#44), 450 (#28-33), 485 (#43), 491 (#35), 505 (#62), 557 (#41), 639 (#52), 640 (#2), 647 (#42), 666 (#15), 714 (#4), 716 (#17), 722 (#35) PE/TE = Pupil s Edition/Teacher s Edition 3

5 A2.RP.7. Present correct mathematical arguments in a variety of forms A2.RP.8. Evaluate written arguments for validity PE/TE: 491 (#35), 497 (#60), 505 (#62), 522 (#60), 630 (#60), 639 (#52), 646 (#36), 656 (#46), 720 (#35), 723 (#41), 823 (#33), 835 (#6), 837 (#8), 945 (#21), 960 (#48) PE/TE: 21 (#2), 25 (#8), 55 (#2), 109 (#2), 190 (#2), 296 (#2), 374 (#2), 424 (#2), 432 (#2), 449 (#2), 456 (#2) Students will select and use various types of reasoning and methods of proof. A2.RP.9. Support an argument by using a systematic approach to test more than one case A2.RP.10. Devise ways to verify results, using counterexamples and informal indirect proof A2.RP.11. Extend specific results to more general cases A2.RP.12. Apply inductive reasoning in making and supporting mathematical conjectures Communication Strand pages: 128 (#34), 183 (#37), 273 (#10), 384 (#50), 386 (#64), 443 (#44), 450 (#28-33), 485 (#43), 491 (#35), 505 (#62), 557 (#41), 639 (#52), 640 (#2), 647 (#42), 666 (#15), 714 (#4), 716 (#17), 722 (#35) PE/TE: 799 (#59-62), PE/TE: 32 (#36), 47 (#59), 79 (#49), 80-81, 88 (#48), 95 (#68), , 137 (#48), , 202 (#44), , , , , , , , PE/TE: Students will organize and consolidate their mathematical thinking through communication. A2.CM.1. Communicate verbally and in writing a correct, complete, coherent, and clear design (outline) and explanation for the steps used in solving a problem for example: 13 (#2), 21(#2), 30 (#2), 37 (#2), 44 (#2), 55 (#2), 76 (#2), 86 (#2), 93 (#2), 101 9#2f), 109 (#2), 117 (#2), 127 (#2), 135 (#2), 156 (#2), 164 (#2), 171 (#2), 182 (#2), 190 (#2), 199 (#2) PE/TE = Pupil s Edition/Teacher s Edition 4

6 A2.CM.2. Use mathematical representations to communicate with functions, equations, charts, graphs, and diagrams PE/TE: 39 (#28), 139 (#6), 157 (#38), 186 (#7), 258 (#68), 265 (#67), 290 (#67), 299 (#73), 306 (#74), 316 (#3), 369 (#5), 434 (#46), 491 (#35), 535 (#35), 562 (#39), 570 (#35), 601 (#6), 631 (#68), 647 (#42), 914 (#32) Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others. A2.CM.3. Present organized mathematical ideas with the use of appropriate standard notations, including the use of symbols and other representations when sharing an idea in verbal and written form A2.CM.4. Explain relationships among different representations of a problem A2.CM.5. Communicate logical arguments clearly, showing why a result makes sense and why the reasoning is valid A2.CM.6. Support or reject arguments or questions raised by others about the correctness of mathematical work for example:6 (#2), 13 (#2), 21 (#2), 30 (#2), 56 (#2), 76 (#2), 86 (#2), 93 (#2), 101 (#2), 109 (#2), 117 (#2), 127 (#2), 156 (#2), 164 (#2), 171 9#2), 182 (#2), 190 (#2), 199 (#2), 207 (#2), 214 (#2) for example: 24 (#74), 39 (#28), 48, 105, 218, 292, 360, 460, 523, 596, 640, 714, 781, 834, 895, 938 PE/TE: 7 (#49-54), 25 (#7), 49 (#1), 56 (#65), 87 (#28), 103 (#48), 118 (#22), 128 (#34), 183 (#37), 219 (#4), 256 (#57), 273 (#10), 289 (#60), 297 (#66), 334 (43-45), 345 (#9), 384 (#50), 391 (#31), 443 (#44) pages: 7 (#49-54), 25 (#7), 49 (#1), 56 (#65), 87 (#28), 103 (#48), 118 (#22), 128 (#34), 183 (#37), 219 (#4), 256 (#57), 273 (#10), 289 (#60), 297 (#66), 334 (43-45), 345 (#9), 384 (#50), 391 (#31), 443 (#44) Students will analyze and evaluate the mathematical thinking and strategies of others. A2.CM.7. Read and listen for logical understanding of mathematical thinking shared by other students for example: 17 (#13), 30 (#16-17), 38 (#19-20), 45 (#34-35), 56 (#41-42), 77 (#14-15), 86 (#15-16), 93 (#21-22), 214 (#11), 102 (#18-19), 110 (#35), 118 (#17), 128 (#29-30), 136 (# 19-20), 156 (#16), 164 (#27), 171 (#16), 182 (#21-22), 190 (#3), 199 (#19-20) PE/TE = Pupil s Edition/Teacher s Edition 5

7 A2.CM.8. Reflect on strategies of others in relation to one s own strategy A2.CM.9. Formulate mathematical questions that elicit, extend, or challenge strategies, solutions, and/or conjectures of others for example: 17 (#13), 30 (#16-17), 38 (#19-20), 45 (#34-35), 56 (#41-42), 77 (#14-15), 86 (#15-16), 93 (#21-22), 214 (#11), 102 (#18-19), 110 (#35), 118 (#17), 128 (#29-30), 136 (# 19-20), 156 (#16), 164 (#27), 171 (#16), 182 (#21-22), 190 (#3), 199 (#19-20) pages: 8 (#60), 32 (#36), 47 (#59), 59 (#3, 6), 69 (#20, 21), 79 (#49), 88 (#48), 95 (#68), 106 (#6), 111 (#44), 119 (#28), 129 (#40), 137 (#48), 139 (#6), 158 (#39), 166 (#60), 173 (#39), 185 (#47), 192 (#33), 202 (#44) Students will use the language of mathematics to express mathematical ideas precisely. A2.CM.10. Use correct mathematical language in developing mathematical questions that elicit, extend, or challenge other students conjectures A2.CM.11. Represent word problems using standard mathematical notation A2.CM.12. Understand and use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and rationale pages: 8 (#60), 32 (#36), 47 (#59), 59 (#3, 6), 69 (#20, 21), 79 (#49), 88 (#48), 95 (#68), 106 (#6), 111 (#44), 119 (#28), 129 (#40), 137 (#48), 139 (#6), 158 (#39), 166 (#60), 173 (#39), 185 (#47), 192 (#33), 202 (#44) for example: 8, 15, 23, 31-32, 38-39, 46-47, 57, 78, 87, 88, 94-95, , , 119, , 137, , 184, 192, , for example: 15 (#61), 24 (#74), 39 (#28), 57 (#78), 95 (#67), 104 (#57), 105, 119 (#27), 129 (#41), 157 (#38), 173 (#37), 216 (#45), 242 (#59), 258 (#68), 290 (#66), 314 (#50), 343 (#56), 367 (#38), 392 (#42), 434 (#46) PE/TE = Pupil s Edition/Teacher s Edition 6

8 A2.CM.13. Draw conclusions about mathematical ideas through decoding, comprehension, and interpretation of mathematical visuals, symbols, and technical writing Connections Strand PE/TE: 25 (#7), 50, 112, , 152, 177, 283, 308, 336, 437, 514 (#13), 528, 550, 774, 826, 874, 881, 923, 948 Students will recognize and use connections among mathematical ideas. A2.CN.1. Understand and make connections among multiple representations of the same mathematical idea A2.CN.2. Understand the corresponding procedures for similar problems or mathematical concepts for example: 15 (#61), 24 (#74), 39 (#28), 57 (78), 95 (#67), 104 (#57) 105, 119 (#27), 129 (#41), 157 (#38), 173 (#37), 216 (#45), 242 (#59), 258 (#68), 290 (#60), 314 (#50), 343 (#56), 367 (#38), 392 (#42), 434 (#46) for example: 11 (#7), 21 (#11), 29 (#14-15), 36 (#3), 44 (#13), 74 (#3), 91 (#10), 101 (#10), 109 (#5), 126 (#4), 135 9#11), 239 (#8), 247 (#8), 254 (#9) Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole. A2.CN.3. Model situations mathematically, using representations to draw conclusions and formulate new situations A2.CN.4. Understand how concepts, procedures, and mathematical results in one area of mathematics can be used to solve problems in other areas of mathematics A2.CN.5. Understand how quantitative models connect to various physical models and representations PE/TE: 25 (#7), 50, 112, , 152, 177, 283, 308, 336, 437, 514 (#13), 528, 550, 774, 826, 874, 881, 923, 948 PE/TE: 22 (#51-54), 31 (#18-20), 78 (#44-46), 111 (#42), 165 (#41-43), 204, 216 (#49), 257 (#59-62), 291 (#68), 385 (#54), 350 (#48-51), 357 (#51-53), 367 (#36-37) 376 (#47-48), 392 (#44), 400 (#1), 399 (#29), 425 (#66-68), 451 (#40) PE/TE: 25 (#7), 50, , 152, 177, 283, 308, 336, 437, 514 (#13), 528, 550, 774, 826, 874, 881, 923, 948 PE/TE = Pupil s Edition/Teacher s Edition 7

9 Students will recognize and apply mathematics in contexts outside of mathematics. A2.CN.6. Recognize and apply mathematics to situations in the outside world A2.CN.7. Recognize and apply mathematical ideas to problem situations that develop outside of mathematics A2.CN.8. Develop an appreciation for the historical development of mathematics Representation Strand for example: 8, 15, 23, 31-32, 38-39, 46-47, 57, 78, 87-88, 94-95, , , 119, , 137, , 184, 192, , for example: 8, 15, 23, 31-32, 38-39, 46-47, 57, 78, 87-88, 94-95, , , 119, , 137, , 184, 192, , pages: Students will create and use representations to organize, record, and communicate mathematical ideas. A2.R.1. Use physical objects, diagrams, charts, tables, graphs, symbols, equations, or objects created using technology as representations of mathematical concepts A2.R.2. Recognize, compare, and use an array of representational forms A2.R.3. Use representation as a tool for exploring and understanding mathematical ideas for example: 15 (#61), 24 (#74), 39 (#28), 57 (#78), 95 (#67), 104 (#57), 105, 119 (#27), 129 (#41), 157 (#38), 173 (#37), 216 (#45), 242 (#59), 258 (#68), 290 (#66), 314 (#50), 343 (#56), 367 (#38), 392 (#42), 434 (#46) for example: 15 (#61), 24 (#74), 39 (#28), 57 (#78), 95 (#67), 104 (#57), 105, 119 (#27), 129 (#41), 157 (#38), 173 (#37), 216 (#45), 242 (#59), 258 (#68), 290 (#66), 314 (#50), 343 (#56), 367 (#38), 392 (#42), 434 (#46) PE/TE: 25 (#7), 50, 112, , 152, 177, 283, 308, 336, 437, 514 (#13), 528, 550, 774, 826, 874, 881, 923, 948 PE/TE = Pupil s Edition/Teacher s Edition 8

10 Students will select, apply, and translate among mathematical representations to solve problems. A2.R.4. Select appropriate representations to solve problem situations A2.R.5. Investigate relationships among different representations and their impact on a given problem PE/TE: 48, 105, 218, 272, 360, 460, 523, 596, 640, 714, 781, 834, 895, 938 pages: 15 (#61), 24 (#74), 39 (#28), 57 (#78), 95 (#67), 104 (#54), 105, 119 (#27), 129 (#41), 157 (#88), 173 (#34), 216 (#45), 242 (#59), 258 (#68), 290 (#66) Students will use representations to model and interpret physical, social, and mathematical phenomena. A2.R.6. Use mathematics to show and understand physical phenomena (e.g., investigate sound waves using the sine and cosine functions) A2.R.7. Use mathematics to show and understand social phenomena (e.g., interpret the results of an opinion poll) A2.R.8. Use mathematics to show and understand mathematical phenomena (e.g., use random number generator to simulate a coin toss) Number Sense and Operations Strand PE/TE: 439, 447, 453, 457 (#56), 464 (#8), 475 (#56), 480, 488, 504 (#58), 910, 913, 916, 921, 927, 929, 942 PE/TE: 95 (#65), 100, 103 (#50), 106 (#3), 119 (#25), 128 (#37), 137 (#44), 166 (#61), 172 (#34), 438 (#45), 475 (#55), 481, 484 (#38), 497 (#57) PE/TE: 189, 193 (#35), 201 (#42), 208 (#40), 215 (#43), 216 (#49), 247, 250 (#52), 271 (#42), 287, 290 (#63), 298 (#68) Students will understand meanings of operations and procedures, and how they relate to one another. Operations A2.N.1. Evaluate numerical expressions with negative and/or fractional exponents, without the aid of a calculator (when the answers are rational numbers) A2.N.2. Perform arithmetic operations (addition, subtraction, multiplication, division) with expressions containing irrational numbers in radical form PE/TE: , 352 (#1-4), 402 (#5, 6, 9), , , 436 (#6), 459 (#63-68, 75-80), 465, 466, 467, 469 (#1-16), 473 (#8-13), 474 (#31-34), 1034 PE/TE: , 317, , , 1034 PE/TE = Pupil s Edition/Teacher s Edition 9

11 A2.N.3. Perform arithmetic operations with polynomial expressions containing rational coefficients A2.N.4. Perform arithmetic operations on irrational expressions A2.N.5. Rationalize a denominator containing a radical expression A2.N.6. Write square roots of negative numbers in terms of i PE/TE: , , , 377 (#7-8), 392 (#55-62), , 407 (#1-4, 8-13), 411 (#11), 412 (#4-6), 419 (#75-82), 427 (# ), 445 (#1-4), 451 (#51-54), 467, 469 (#17-20), 474 (#31-38, 42-43) PE/TE: , 317, , , 595 (#45-52), 1034 PE/TE: PE/TE: 275 A2.N.7. Simplify powers of i PE/TE: , 293, , 323 (#17), 335 (#66, 68, 69) A2.N.8. Determine the conjugate of a complex number A2.N.9. Perform arithmetic operations on complex numbers and write the answer in the form a + bi. Note: This includes simplifying expressions with complex denominators. PE/TE: 278, 280, 291 (#11, 12), 321 (#34), 323 (#18) PE/TE: , 291 (#7-12), 293, , 323 (#16-18), 335 (#64-69) A2.N.10. Know and apply sigma notation PE/TE: 796, 799, 805, 807, 815, 817, 821 (#33), 823, 837, 839, , 843, 848 (#37-40), 872 (#51-56), 979 Algebra Strand Students will represent and analyze algebraically a wide variety of problem solving situations. Equations and Inequalities A2.A.1. Solve absolute value equations and inequalities involving linear expressions in one variable A2.A.2. Use the discriminant to determine the nature of the roots of a quadratic equation PE/TE: 41-47, 50, 51-58, 60, 64, 65 (#19-27), 88 (#62-67), 111 (#46-51), 129 (#43-48), 158 (#44-46), 167 (#67-69), 173 (#45-47) PE/TE: 294, 296, 291 (#69-74), 321, 377 (#62-69) PE/TE = Pupil s Edition/Teacher s Edition 10

12 A2.A.3. Solve systems of equations involving one linear equation and one quadratic equation algebraically Note: This includes rational equations that result in linear equations with extraneous roots. A2.A.4. Solve quadratic inequalities in one and two variables, algebraically and graphically A2.A.5. Use direct and inverse variation to solve for unknown values A2.A.6. Solve an application which results in an exponential function Students will perform algebraic procedures accurately. Variables and Expressions A2.A.7. Factor polynomial expressions completely, using any combination of the following techniques: common factor extraction, difference of two perfect squares, quadratic trinomials A2.A.8. Apply the rules of exponents to simplify expressions involving negative and/or fractional exponents A2.A.9. Rewrite algebraic expressions that contain negative exponents using only positive exponents A2.A.10. Rewrite algebraic expressions with fractional exponents as radical expressions A2.A.11. Rewrite algebraic expressions in radical form as expressions with fractional exponents A2.A.12. Evaluate exponential expressions, including those with base e PE/TE: , 668, 672, 678 (#30-32) PE/TE: , 315 (#4-9), 322, 323 (#25-27), 326 (#5), 359 (#70-75) PE/TE: , 120 (#11-14), 143, 145 (#14-17), 392 (#45-50), 550, , 571 (#14), 603, 607 (#1-6), 611 (#10-11), 639 (#58-63), 678 (#28-30) PE/TE: , , , , , PE/TE: , , , 317, 319, 320, 323 (#4-9), 324, 328 (#7-9), , , 377 (#1-6), 399 (#33-38), 404, 407 (#14-16), 619 (#64-69), 985 PE/TE: , 352 (#1-4), 402 (#5, 6, 9), , , 436 (#6), 459 (#63-68, 75-80), 465, 466, 467, 469 (1-16), 473 (#8-13), 474 (#31-34), 1034 PE/TE: , 352, 402, 419 (#75-82), , 459, 465, 466, 469 (#1-8), 473 (#12, 13) PE/TE: , , 451 (#51-58), 459 (#75-80), 465, , 469 PE/TE: , , 451 (#51-58), 459 (#75-80), 465, , 469 PE/TE: , 338, 341, 352 (#1-4), 392 (#55-62), 402, 415, 417, 419, , 459, , 469 (#1-6), A2.A.13. Simplify radical expressions PE/TE: , , , 595 (#45-52), 1034 PE/TE = Pupil s Edition/Teacher s Edition 11

13 A2.A.14. Perform addition, subtraction, multiplication, and division of radical expressions A2.A.15. Rationalize denominators involving algebraic radical expressions A2.A.16. Perform arithmetic operations with rational expressions and rename to lowest terms A2.A.17. Simplify complex fractional expressions A2.A.18. Evaluate logarithmic expressions in any base A2.A.19. Apply the properties of logarithms to rewrite logarithmic expressions in equivalent forms Equations and Inequalities A2.A.20. Determine the sum and product of the roots of a quadratic equation by examining its coefficients PE/TE: , 317, , , 1034 PE/TE: PE/TE: 479, , , 581, , 595 (#1-7), 602, 605, 607 (#17-24), 625 (#61-68) PE/TE: PE/TE: , 513 (#1-4), 541 (#17-20), 543 (#10-12) PE/TE: , 536 (#49-54), 541 (#25-31), 543 (#16-21), 657 (#64-66) pages: , , A2.A.21. Determine the quadratic equation, given the sum and product of its roots pages: , , A2.A.22. Solve radical equations PE/TE: , , 465, 468, 469 (#34-36), 474 (#12, 21), 498 (#67, 68), 513 (#78-83), 557 (#52-57)) A2.A.23. Solve rational equations and inequalities A2.A.24. Know and apply the technique of completing the square A2.A.25. Solve quadratic equations, using the quadratic formula A2.A.26. Find the solution to polynomial equations of higher degree that can be solved using factoring and/or the quadratic formula PE/TE: , , , 602, 606, 607 (#25-27), 619 (#73-75) PE/TE: 283, , 317, 321, , 664 (#4-7), 672, 673 (#24-39), 678 (#37-40) PE/TE: , 317, 321, 316 (#1-3), 323 (#22-24), 933 PE/TE: , , 378, 399 (#1-2), 401, 404, 405, 407 (#17-18), 411 (#12, 13), 419 (#69-74), 427 (#5-8), 445 (#61-66), 451 (#47-60) PE/TE = Pupil s Edition/Teacher s Edition 12

14 A2.A.27. Solve exponential equations with and without common bases A2.A.28. Solve a logarithmic equation by rewriting as an exponential equation PE/TE: , , , 536 (#1-4), 538, 542, 543 (#22) PE/TE: , , , 536 (#5-9), 538, 542, 543 (#23, 24) Students will recognize, use, and represent algebraically patterns, relations, and functions. Patterns, Relations, and Functions A2.A.29. Identify an arithmetic or geometric sequence and find the formula for its nth term A2.A.30. Determine the common difference in an arithmetic sequence A2.A.31. Determine the common ratio in a geometric sequence A2.A.32. Determine a specified term of an arithmetic or geometric sequence A2.A.33. Specify terms of a sequence, given its recursive definition A2.A.34. Represent the sum of a series, using sigma notation A2.A.35. Determine the sum of the first n terms of an arithmetic or geometric series A2.A.36. Apply the binomial theorem to expand a binomial and determine a specific term of a binomial expansion PE/TE: , 801, , , 818, 825 (#46-57), 833 (#7-9), , 843 (#1-12), PE/TE: 802, , , PE/TE: , , PE/TE: 802, , , , PE/TE: 826, , , 839, 842, 843 (#25-28), 848 (#41-43) PE/TE: , 799, 805, 807, 815, 817, 821 (#2-3), 823, 837, 839, , 843, 848 (#37-40), 872 (#51-56) PE/TE: 805, 807 (#40-48), , 815 (#48-53), 817 (#72-77), 817 (#7-15), 821, 823, 833 (#1-3), , 843 (#13-20), 847 (#10), 848 (#37-40), 872 (#51-56) PE/TE: A2.A.37. Define a relation and function PE/TE: 72-79, A2.A.38. Determine when a relation is a function A2.A.39. Determine the domain and range of a function from its equation A2.A.40. Write functions in functional notation PE/TE: 72-79, 96 (#1-3, 76,77), , 145 (#1-3) PE/TE: 73, 76, 391, , , 463, 479, 482, 485, 487, 489, 491 PE/TE: 75, 78, 93 (#15-20), 127 (#12-14) PE/TE = Pupil s Edition/Teacher s Edition 13

15 A2.A.41. Use functional notation to evaluate functions for given values in the domain A2.A.42. Find the composition of functions A2.A.43. Determine if a function is one-toone, onto, or both PE/TE: 75, 78, 120 (#36-41) PE/TE: , 435, 445 (#5-8), 451 (#55-58), 465, 467, 469 (#21-24), , 474 (#44-45) pages: 72-79, 80-81, 89-96, 97 A2.A.44. Define the inverse of a function PE/TE: 437, , 465, 467, 469 (#25-30), 473 (#7), 474 (#46-51), 491 (#46-49) A2.A.45. Determine the inverse of a function and use composition to justify the result A2.A.46. Perform transformations with functions and relations: f(x+a), f(x) + a, f(-x), -f(x), af(x) Coordinate Geometry A2.A.47. Determine the center-radius form for the equation of a circle in standard form A2.A.48. Write the equation of a circle, given its center and a point on the circle A2.A.49. Write the equation of a circle from its graph A2.A.50. Approximate the solution to polynomial equations of higher degree by inspecting the graph A2.A.51. Determine the domain and range of a function from its graph A2.A.52. Identify relations and functions, using graphs A2.A.53. Graph exponential functions of the form y = b x for positive values of b, including b = e PE/TE: 437, , 465, 467, 491 (#46-49) PE/TE: , , 138 (#1-3), 144, 145 (#20), , 468, 479, 487, PE/TE: , 633, , 668, 670, 672, 673, 678 (#37-40) PE/TE: PE/TE: PE/TE: 336, 339, 342 (#25-27), 390 (#15-20), , 406 PE/TE: 391 (#34-37), , 463, 479, 482, 487, 489, 491 PE/TE: 73-74, 77 PE/TE: , , , 523, 536 (#43-48), 538, 539, 543 (#1-9), 546 (#3), 557 (#49-51), 588 (#55-60), 776 PE/TE = Pupil s Edition/Teacher s Edition 14

16 A2.A.54. Graph logarithmic functions, using the inverse of the related exponential function Trigonometric Functions A2.A.55. Express and apply the six trigonometric functions as ratios of the sides of a right triangle A2.A.56. Know the exact and approximate values of the sine, cosine, and tangent of 0º, 30º, 45º, 60º, 90º, 180º, and 270º angles A2.A.57. Sketch and use the reference angle for angles in standard position A2.A.58. Know and apply the co-function and reciprocal relationships between trigonometric ratios A2.A.59. Use the reciprocal and cofunction relationships to find the value of the secant, cosecant, and cotangent of 0º, 30º, 45º, 60º, 90º, 180º, and 270º angles A2.A.60. Sketch the unit circle and represent angles in standard position A2.A.61. Determine the length of an arc of a circle, given its radius and the measure of its central angle A2.A.62. Find the value of trigonometric functions, if given a point on the terminal side of angle A2.A.63. Restrict the domain of the sine, cosine, and tangent functions to ensure the existence of an inverse function A2.A.64. Use inverse functions to find the measure of an angle, given its sine, cosine, or tangent A2.A.65. Sketch the graph of the inverses of the sine, cosine, and tangent functions A2.A.66. Determine the trigonometric functions of any angle, using technology PE/TE: , 514, 513 (#5-7), 538, 541, 543 (#13-15), 595 (#43) PE/TE: , 865 (#1-6), 897, 898, 901 (#1-8) PE/TE: , , 871 (#24-31), 880 (#5-8), 897, 901 (#8-11), 906 (#4-6), 930 (#55-60), 947 (#36-41), 962 (#1-4) PE/TE: , 899, 905 (#11), 906 (#7-9), 914 (#44-51), 954 (#46-51) PE/TE: PE/TE: , , 871 (#24-31), 880 (#5-8), 897, 901 (#8-11), 906 (#4-6), 930 (#55-60), 947 (#36-41), 962 (#1-4) PE/TE: , 880 (#1-4) PE/TE: , 922 (#64-69) PE/TE: , 880 (#1-4), 899 PE/TE: , 880 (#1-4), 899 PE/TE: , 880 (#1-4), 899 PE/TE: 874 PE/TE: , , 897, , 901 (#1-15) PE/TE = Pupil s Edition/Teacher s Edition 15

17 A2.A.67. Justify the Pythagorean identities PE/TE: , 966 A2.A.68. Solve trigonometric equations for all values of the variable from 0º to 360º A2.A.69. Determine amplitude, period, frequency, and phase shift, given the graph or equation of a periodic function A2.A.70. Sketch and recognize one cycle of a function of the form y = AsinBx or y = AcosBx A2.A.71. Sketch and recognize the graphs of the functions y = csc(x), y = tan(x), and y = cot(x) A2.A.72. Write the trigonometric function that is represented by a given periodic graph A2.A.73. Solve for an unknown side or angle, using the Law of Sines or the Law of Cosines A2.A.74. Determine the area of a triangle or a parallelogram, given the measure of two sides and the included angle A2.A.75. Determine the solution(s) from the SSA situation (ambiguous case) A2.A.76. Apply the angle sum and difference formulas for trigonometric functions A2.A.77. Apply the double-angle and halfangle formulas for trigonometric functions Measurement Strand PE/TE: , , 947 (#7-9), 954 (#56-61), 962 (#5-6, 68), 964, 967, 969 (#13-18), 973 (#6) PE/TE: , PE/TE: , , 937 (#50-58), , 964, PE/TE: , , 937 (#50-58), , 964, PE/TE: PE/TE: 881, , , 897, 900, 901 (#16-24) PE/TE: 885, 887, 888, 891, 894 (#9-14), 901 (#22-27), 991 PE/TE: PE/TE: , 964, 968 PE/TE: , 964, 968 Students will determine what can be measured and how, using appropriate methods and formulas. Units of Measurement A2.M.1. Define radian measure PE/TE: , 899, 901 (#4-7) A2.M.2. Convert between radian and degree measures PE/TE: , 899, 901 (#4-7) PE/TE = Pupil s Edition/Teacher s Edition 16

18 Statistics and Probability Strand Students will collect, organize, display, and analyze data. Collection of Data A2.S.1. Understand the differences among various kinds of studies (e.g., survey, observation, controlled experiment) A2.S.2. Determine factors which may affect the outcome of a survey Organization and Display of Data A2.S.3. Calculate measures of central tendency with group frequency distributions A2.S.4. Calculate measures of dispersion (range, quartiles, interquartile range, standard deviation, variance) for both samples and populations A2.S.5. Know and apply the characteristics of the normal distribution PE/TE: , , 783, 786, 787 PE/TE: , , 783, 786, 787 PE/TE: , 750, , 783, 784, 787, 1005 PE/TE: , 750, , 783, 784, 787, 1005 PE/TE: , 780 (#1-3), 783, 785 Students will make predictions that are based upon data analysis. Predictions from Data A2.S.6. Determine from a scatter plot whether a linear, logarithmic, exponential, or power regression model is most appropriate A2.S.7. Determine the function for the regression model, using appropriate technology, and use the regression function to interpolate and extrapolate from the data A2.S.8. Interpret within the linear regression model the value of the correlation coefficient as a measure of the strength of the relationship PE/TE: , 143 PE/TE: 116, 308, 311, 396, 528, 530, 533, 535 PE/TE: 116 PE/TE = Pupil s Edition/Teacher s Edition 17

19 Students will understand and apply concepts of probability. Probability A2.S.9. Differentiate between situations requiring permutations and those requiring combinations A2.S.10. Calculate the number of possible permutations of n items taken r at a time A2.S.11. Calculate the number of possible combinations of n items taken r at a time A2.S.12. Use permutations, combinations, and the Fundamental Principle of Counting to determine the number of elements in a sample space and a specific subset (event) A2.S.13. Calculate theoretical probabilities, including geometric applications PE/TE: , , 699, 702, 704 (#58-61), , 737(#1-8), 741 (#10) PE/TE: , 699, , 737 (#1-4) PE/TE: , 704 (#58-61), 737 (#5-8), 741 (#10) PE/TE: , 720, PE/TE: 698 A2.S.14. Calculate empirical probabilities PE/TE: 700, 702 A2.S.15. Know and apply the binomial probability formula to events involving the terms exactly, at least, and at most A2.S.16. Use the normal distribution as an approximation for binomial probabilities PE/TE: pages: , , 783, 785 PE/TE = Pupil s Edition/Teacher s Edition 18

20 NY 117 4/ CC2