Prentice Hall Algebra 2 and Trigonometry, New York - Pearson
Transcript of Prentice Hall Algebra 2 and Trigonometry, New York - Pearson
Prentice Ha l lAlgebra 2 and Trigonometry,New York Edition © 2011
C O R R E L A T E D T O
New York Learning Standards for Mathematics
A l g e b ra 2 and Tr i g o n o m e t r y
Prentice Hall Algebra 2 and Trigonometry, New York Edition © 2011 Correlated to:
New York Learning Standards for Mathematics (Algebra 2 and Trigonometry)
NEW YORK LEARNING STANDARDS
FOR MATHEMATICS (ALGEBRA 2 AND TRIGONOMETRY)
Prentice Hall Algebra 2 and Trigonometry,
New York Edition © 2011 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
SE/TE: 90-91, 163, 164-165, 215, 232, 265, 295, 317, 420, 522, 578, 594, 619, 651, 882
A2.PS.2 Recognize and understand equivalent representations of a problem situation or a mathematical concept
SE/TE: 134-137, 138-141, 142-145, 146-148, 174-178, 179-181, 784-788, 789-792
Students will solve problems that arise in mathematics and in other contexts.
A2.PS.3 Observe and explain patterns to formulate generalizations and conjectures
SE/TE: 4-6, 7-10, 17, 25, 48, 51, 53, 295, 317, 420, 522, 578, 594, 619, 651, 882
A2.PS.4 Use multiple representations to represent and explain problem situations (e.g., verbally, numerically, algebraically, graphically)
SE/TE: 134-137, 138-141, 142-145, 146-148, 174-178, 179-181, 784-788, 789-792
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)
SE/TE: 134-137, 138-141, 142-145, 146-148, 174-178, 179-181, 784-788, 789-792
A2.PS.6 Use a variety of strategies to extend solution methods to other problems
SE/TE: 134-137, 138-141, 142-145, 146-148, 149-152, 152-155, 166-170, 171-173, 621-626, 627-629, 630-633, 634-636, 638-641, 642-644, 645-649, 650-652
A2.PS.7 Work in collaboration with others to propose, critique, evaluate, and value alternative approaches to problem solving
SE/TE: 49, 121, 182, 266, 346, 421, 486, 552, 602, 662, 742, 808, 883, 950
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
SE/TE: 9, 16, 31, 39, 119, 139, 207, 213, 286, 294, 343, 365, 419, 440, 512, 522, 592, 599, 679, 686, 738, 761, 841, 849, 917, 925
A2.PS.9 Interpret solutions within the given constraints of a problem
SE/TE: 159, 160-161, 172, 180, 184-185, 187, 228, 229-231, 234, 237-238, 242-244, 244-246
A2.PS.10 Evaluate the relative efficiency of different representations and solution methods of a problem
SE/TE: 134-137, 138-141, 142-145, 145-148, 155, 173, 174-178, 179-181, 183, 184, 186, 187, 191, 201, 381-385, 385-388, 389
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
SE/TE: 9-10, 17, 24, 49, 66-67, 71, 73, 121, 140, 148, 154, 182, 266, 346, 421, 440, 449, 458, 486, 552, 602, 662, 742, 808, 883, 950
1 SE = Student Edition TE = Teacher Edition
Prentice Hall Algebra 2 and Trigonometry, New York Edition © 2011 Correlated to:
New York Learning Standards for Mathematics (Algebra 2 and Trigonometry)
NEW YORK LEARNING STANDARDS
FOR MATHEMATICS (ALGEBRA 2 AND TRIGONOMETRY)
Prentice Hall Algebra 2 and Trigonometry,
New York Edition © 2011 Students will make and investigate mathematical conjectures.
A2.RP.2 Investigate and evaluate conjectures in mathematical terms, using mathematical strategies to reach a conclusion
SE/TE: 7, 9-10, 16, 17, 22, 24, 30, 31, 37, 39, 49, 66-67, 71, 72, 73, 78, 121, 140, 148, 154, 182, 266, 346, 421, 440, 449, 458, 486, 552, 602, 662, 742, 808, 883, 950
A2.RP.3 Evaluate conjectures and recognize when an estimate or approximation is more appropriate than an exact answer
SE/TE: 733-736, 737-739, 740-741, 748, 749, 762, 771
A2.RP.4 Recognize when an approximation is more appropriate than an exact answer
SE/TE: 733-736, 737-739, 740-741
Students will develop and evaluate mathematical arguments and proofs.
A2.RP.5 Develop, verify, and explain an argument, using appropriate mathematical ideas and language
SE/TE: 7, 15, 22, 37, 45, 96, 103, 111, 118, 145, 152, 160, 198, 206, 212, 221, 229, 261, 329, 342, 378, 394, 456, 461, 503, 557, 583, 598, 617, 650, 700, 715, 724, 737, 879, 881
A2.RP.6 Construct logical arguments that verify claims or counterexamples that refute claims
SE/TE: 16, 32, 37, 39, 505, 532, 623, 629, 634, 678
A2.RP.7 Present correct mathematical arguments in a variety of forms
SE/TE: 32, 39, 505, 532, 623, 629, 634, 660, 678-679
A2.RP.8 Evaluate written arguments for validity SE/TE: 7, 16, 22, 24, 30, 31, 37, 39, 97, 105, 112, 180, 200, 244, 253, 316, 323, 372, 379, 439, 448, 503, 522, 583, 591, 651, 658, 738, 760, 832, 841, 907, 915
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
SE/TE: 72
A2.RP.10 Devise ways to verify results, using counterexamples and informal indirect proof
SE/TE: 34, 72, 81, 203, 298, 307, 462, 464, 623, 837, 838, 920, 935, 936, 938, 943, 945
A2.RP.11 Extend specific results to more general cases
SE/TE: 41-45, 45-48, 149-152, 152-155, 166-170, 171-173, 240, 623, 630, 787-788
A2.RP.12 Apply inductive reasoning in making and supporting mathematical conjectures
SE/TE: 4-6, 7-10, 17, 25, 48, 51, 53, 295, 317, 420, 522, 578, 594, 619, 651, 882
Communication Strand
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
SE/TE: 26-29, 32, 34-37, 39, 53, 55, 79, 81, 203, 298, 307, 462, 464, 623, 837, 838, 920, 935, 936, 938, 943, 945
A2.CM.2 Use mathematical representations to communicate with appropriate accuracy, including numerical tables, formulas, functions, equations, charts, graphs, and diagrams
SE/TE:60-64, 64-66, 68-70, 71-73, 74-77, 78-80, 145, 152, 160, 198, 206, 212, 221, 229, 674-677, 678-680, 686, 688-689, 696-699, 700-701
2 SE = Student Edition TE = Teacher Edition
Prentice Hall Algebra 2 and Trigonometry, New York Edition © 2011 Correlated to:
New York Learning Standards for Mathematics (Algebra 2 and Trigonometry)
NEW YORK LEARNING STANDARDS
FOR MATHEMATICS (ALGEBRA 2 AND TRIGONOMETRY)
Prentice Hall Algebra 2 and Trigonometry,
New York Edition © 2011 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
SE/TE: 7, 15, 22, 37, 34, 96, 103, 111, 118, 145, 152, 160, 198, 206, 212, 221, 229, 261, 329, 342, 378, 394, 456, 461, 503, 557, 583, 598, 617, 650, 700, 715, 724, 737, 879, 881
A2.CM.4 Explain relationships among different representations of a problem
SE/TE: 4-6, 7-10, 60-63, 65-66, 70, 71-72, 134-136, 138-139, 196-198, 199-200, 202-205, 206-208
A2.CM.5 Communicate logical arguments clearly, showing why a result makes sense and why the reasoning is valid
SE/TE: 32, 34, 62, 81, 203, 298, 307, 464, 623, 629, 674, 837, 838, 920, 929, 935, 936, 938, 943, 945
A2.CM.6 Support or reject arguments or questions raised by others about the correctness of mathematical work
SE/TE: Students practice the skills required for this standard through Error Analysis exercises: 7, 16, 22, 24, 30, 31, 37, 39, o7, 105, 180, 200, 244, 253, 316, 323, 372, 379, 439, 448, 503, 522, 583, 591, 651, 658, 738, 760, 832, 841, 907, 915
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
SE/TE: 7, 16, 22, 24, 30, 31, 37, 39, o7, 105, 180, 200, 244, 253, 316, 323, 372, 379, 439, 448, 503, 522, 583, 591, 651, 658, 738, 760, 832, 841, 907, 915
A2.CM.8 Reflect on strategies of others in relation to one’s own strategy
SE/TE: 7, 16, 22, 24, 30, 31, 37, 39, o7, 105, 180, 200, 244, 253, 316, 323, 372, 379, 439, 448, 503, 522, 583, 591, 651, 658, 738, 760, 832, 841, 907, 915
A2.CM.9 Formulate mathematical questions that elicit, extend, or challenge strategies, solutions, and/or conjectures of others
SE/TE: 49, 121, 182, 266, 346, 421, 486, 552, 602, 662, 742, 808, 883, 950
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
SE/TE: 4, 11, 18, 26, 33, 41, 90-91, 92, 99, 107, 114, 163, 164-165, 215, 232, 265, 295, 317, 420, 434, 442, 451, 462, 522, 578, 594, 619, 651, 882
A2.CM.11 Represent word problems using standard mathematical notation
SE/TE: 19-20, 22-23, 25, 28, 30-31, 35, 37-39, 45, 46-48, 51-52, 53, 436-438, 439-440, 445, 447, 448-449
A2.CM.12 Understand and use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and rationale
SE/TE: 7, 15, 22, 37, 45, 96, 103, 111, 118, 145, 152, 160, 198, 206, 212, 221, 229, 261, 329, 342, 378, 394, 456, 461, 503, 557, 583, 598, 617, 650, 700, 715, 724, 737, 879, 881
3 SE = Student Edition TE = Teacher Edition
Prentice Hall Algebra 2 and Trigonometry, New York Edition © 2011 Correlated to:
New York Learning Standards for Mathematics (Algebra 2 and Trigonometry)
NEW YORK LEARNING STANDARDS
FOR MATHEMATICS (ALGEBRA 2 AND TRIGONOMETRY)
Prentice Hall Algebra 2 and Trigonometry,
New York Edition © 2011 A2.CM.13 Draw conclusions about mathematical ideas through decoding, comprehension, and interpretation of mathematical visuals, symbols, and technical writing
SE/TE: 90-91, 163, 164-165, 215, 232, 256-257, 265, 318, 325, 413, 459-460, 477, 484-485, 506, 524-525, 549, 550-551, 578, 594, 621, 661, 694-695, 724, 740-741, 763, 772-773, 835, 852, 927
Connections Strand
Students will recognize and use connections among mathematical ideas.
A2.CN.1 Understand and make connections among multiple representations of the same mathematical idea
SE/TE: 134-137, 138-141, 142-145, 146-148, 174-178, 179-181, 784-788, 789-792
A2.CN.2 Understand the corresponding procedures for similar problems or mathematical concepts
SE/TE: 134-137, 138-141, 142-145, 146-148, 149-152, 152-155, 166-170, 171-173, 621-626, 627-629, 630-633, 634-636, 638-641, 642-644, 645-649, 650-652
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
SE/TE: 93-95, 96-98, 159, 160-161, 210-211, 212-214, 228, 229-231, 234, 238, 242, 244, 436-438, 439-440, 445, 447, 448-449, 477
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
SE/TE: 828-831, 832-834, 836-839, 840-842, 898, 920-921, 924-925, 950, 951, 953, 955
A2.CN.5 Understand how quantitative models connect to various physical models and representations
SE/TE: 198, 199-201, 205, 207, 210-211, 212-214, 228, 229-231, 233, 235, 238-239, 244, 245-246, 269, 273
Students will recognize and apply mathematics in contexts outside of mathematics.
A2.CN.6 Recognize and apply mathematics to situations in the outside world
SE/TE: 159, 160-161, 705, 708, 710-711, 715-717, 719-720, 721-723, 725-726, 728, 730-731, 736, 737-738
A2.CN.7 Recognize and apply mathematical ideas to problem situations that develop outside of mathematics
SE/TE: 383, 453, 456-457, 461, 465, 466-467, 475-476, 482-483, 485, 806-807, 907, 909-910, 923, 932, 941
A2.CN.8 Develop an appreciation for the historical development of mathematics
SE/TE: 315
Representation Strand
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
SE/TE: 674-677, 678-680, 683, 685-686, 690, 692, 694-695, 696-699, 700-702, 705, 707, 709-711, 725-726, 733-736, 740-741
A2.R.2 Recognize, compare, and use an array of representational forms
SE/TE: 134-137, 142-145, 155, 173, 174-178, 179-181, 183, 184, 186, 187, 191, 201, 381-385, 385-388, 389, 459-460, 477, 674-677, 678-680
4 SE = Student Edition TE = Teacher Edition
Prentice Hall Algebra 2 and Trigonometry, New York Edition © 2011 Correlated to:
New York Learning Standards for Mathematics (Algebra 2 and Trigonometry)
NEW YORK LEARNING STANDARDS
FOR MATHEMATICS (ALGEBRA 2 AND TRIGONOMETRY)
Prentice Hall Algebra 2 and Trigonometry,
New York Edition © 2011 A2.R.3 Use representation as a tool for exploring and understanding mathematical ideas
SE/TE: 90-91, 163, 164-165, 215, 232, 256, 265, 318, 325, 331-334, 335-337, 352, 353, 413
Students will select, apply, and translate among mathematical representations to solve problems.
A2.R.4 Select appropriate representations to solve problem situations
SE/TE: 134-137, 138-141, 142-145, 145-148, 155, 173, 174-178, 179-181, 183, 184, 186, 187, 191, 201, 381-385, 385-388, 389, 459-460, 477
A2.R.5 Investigate relationships among different representations and their impact on a given problem
SE/TE: 134-137, 138-141, 142-145, 145-148, 155, 173, 174-178, 179-181, 183, 184, 186, 187, 191, 201, 381-385, 385-388, 389
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)
SE/TE: 453, 456-457, 461, 465, 466-467, 475-476, 482-483, 485, 806-807, 907, 909-910, 923, 932, 941
A2.R.7 Use mathematics to show and understand social phenomena (e.g., interpret the results of an opinion poll)
SE/TE: 159, 160-161, 705, 708, 710-711, 715-717, 719-720, 721-723, 725-726, 728, 730-731, 736, 737-738
A2.R.8 Use mathematics to show and understand mathematical phenomena (e.g., use random number generator to simulate a coin toss)
SE/TE: 630-633, 634-636, 638-641, 642-644, 645-649, 650-652, 724, 756-759, 760-762, 764-768, 769-771, 772-773
Number Sense and Operations Strand
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)
SE/TE: 381-382, 384-385, 385-388, 389, 397, 424, 427
A2.N.2 Perform arithmetic operations (addition, subtraction, multiplication, division) with expressions containing irrational numbers in radical form
SE/TE: 367-370, 370-373, 374-377, 378-380, 381-382, 385-386, 388, 389, 420, 423-424, 427
A2.N.3 Perform arithmetic operations with polynomial expressions containing rational coefficients
SE/TE: 21, 24, 216, 303-307, 308-310, 311, 313, 317, 320-321, 349, 353, 357
A2.N.4 Perform arithmetic operations on irrational expressions
SE/TE: 367-370, 370-373, 374-377, 378-380, 381-382, 385-386, 388, 389, 420, 423-424, 427
A2.N.5 Rationalize a denominator containing a radical expression
SE/TE: 377, 378-380, 382, 385, 387, 389, 397, 420, 423-424, 427, 430
A2.N.6 Write square roots of negative numbers in terms of i
SE/TE: 248-249, 252, 253, 255, 264, 272, 273, 275, 317, 324
5 SE = Student Edition TE = Teacher Edition
Prentice Hall Algebra 2 and Trigonometry, New York Edition © 2011 Correlated to:
New York Learning Standards for Mathematics (Algebra 2 and Trigonometry)
NEW YORK LEARNING STANDARDS
FOR MATHEMATICS (ALGEBRA 2 AND TRIGONOMETRY)
Prentice Hall Algebra 2 and Trigonometry,
New York Edition © 2011 A2.N.7 Simplify powers of i SE/TE: 251, 255, 265, 272, 273, 310, 330
A2.N.8 Determine the conjugate of a complex number
SE/TE: 251, 253, 255, 272, 273, 276, 330, 356
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.
SE/TE: 250-251, 253-255, 264, 265, 272, 273, 275-276, 302, 314, 315-316, 330, 350, 353, 356
A2.N.10 Know and apply sigma notation SE/TE: 589-590, 591-593, 596, 598, 599-601, 605, 607, 636
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
SE/TE: 41-45, 45-48, 52, 53, 55-56, 57, 67, 73, 106, 128-129
A2.A.2 Use the discriminant to determine the nature of the roots of a quadratic equation
SE/TE: 242-244, 244-246, 255, 271, 273, 275, 277, 356
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.
SE/TE: 259, 261-263, 272, 273, 276, 287
A2.A.4 Solve quadratic inequalities in one and two variables, algebraically and graphically
SE/TE: 256-257, 261, 263-264, 272, 273, 275-276, 310, NY10-NY11
A2.A.5 Use direct and inverse variation to solve for unknown values
SE/TE: 69-70, 71-73, 123, 127, 129, 483, 494, 498-502, 503-505, 514, 523, 554
A2.A.6 Solve an application which results in an exponential function
SE/TE: 435-438, 439-441, 445, 447, 448-449, 471, 473-474, 483, 484, 488, 491, 492, 494
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
SE/TE: 216-220, 221-223, 224, 226, 229-231, 235-236, 237-239, 247, 270-271, 273, 274-275, 287, 288, 291, 293-295, 296-298, 300-302, 310, 311, 348-349, 353
A2.A.8 Apply the rules of exponents to simplify expressions involving negative and/or fractional exponents
SE/TE: 360, 380, 381-385, 385-388, 389, 397, 412, 424, 427, 429
A2.A.9 Rewrite algebraic expressions that contain negative exponents using only positive exponents
SE/TE: 360, 384-385, 385-388, 389, 424, 427
A2.A.10 Rewrite algebraic expressions with fractional exponents as radical expressions
SE/TE: 381-382, 384-385, 385-387, 389, 424, 427, 429
6 SE = Student Edition TE = Teacher Edition
Prentice Hall Algebra 2 and Trigonometry, New York Edition © 2011 Correlated to:
New York Learning Standards for Mathematics (Algebra 2 and Trigonometry)
NEW YORK LEARNING STANDARDS
FOR MATHEMATICS (ALGEBRA 2 AND TRIGONOMETRY)
Prentice Hall Algebra 2 and Trigonometry,
New York Edition © 2011 A2.A.11 Rewrite algebraic expressions in radical form as expressions with fractional exponents
SE/TE: 382, 385, 386, 389, 424
A2.A.12 Evaluate exponential expressions, including those with base e
SE/TE: 431, 434-436, 438, 439-441, 442-444, 448, 461, 488
A2.A.13 Simplify radical expressions SE/TE: 362-364, 364-366, 368, 370-373, 376, 378-379, 385, 388, 389, 412, 423, 427
A2.A.14 Perform addition, subtraction, multiplication, and division of radical expressions
SE/TE: 367-370, 371-373, 375-377, 378-380, 385-386, 388, 389, 420, 423-424, 427
A2.A.15 Rationalize denominators involving algebraic radical expressions
SE/TE: 369-370, 371-373, 377, 378-380, 382, 389, 420, 424, 427
A2.A.16 Perform arithmetic operations with rational expressions and rename to lowest terms
SE/TE: 528-529, 530-533, 535-537, 539-541, 548, 556, 557, 558-559, 601, 609
A2.A.17 Simplify complex fractional expressions SE/TE: 535-538, 539-541, 548, 556, 557, 559-560, 561, 577
A2.A.18 Evaluate logarithmic expressions in any base
SE/TE: 452-453, 456, 461, 464-465, 466, 468, 483, 489, 491, 493, 533, 601
A2.A.19 Apply the properties of logarithms to rewrite logarithmic expressions in equivalent forms
SE/TE: 462-465, 465-468, 470-472, 473-476, 478-479, 480-483, 487, 489-490, 491, 492-494, 505, 541
Equations and Inequalities
A2.A.20 Determine the sum and product of the roots of a quadratic equation by examining its coefficients
SE/TE: NY6-NY7
A2.A.21 Determine the quadratic equation, given the sum and product of its roots
SE/TE: NY6-NY7
A2.A.22 Solve radical equations SE/TE: 390-394, 394-397, 404, 425, 427, 468, 494, 559
A2.A.23 Solve rational equations and inequalities SE/TE: 542-545, 545-548, 549, 550-551, 556, 557, 571
A2.A.24 Know and apply the technique of completing the square
SE/TE: 235-236, 237-239, 240, 247, 271, 274, 611, 626, 628-629, 635
A2.A.25 Solve quadratic equations, using the quadratic formula
SE/TE: 240-242, 244-247, 252, 253, 255, 264, 271-272, 273, 295, 310, 324
A2.A.26 Find the solution to polynomial equations of higher degree that can be solved using factoring and/or the quadratic formula
SE/TE: 296-298, 300-301, 310, 311, 320, 322-323, 330, 349-351, 353
A2.A.27 Solve exponential equations with and without common bases
SE/TE: 469-471, 473-475, 479, 481-483, 490, 491, 494
A2.A.28 Solve a logarithmic equation by rewriting as an exponential equation
SE/TE: 472, 473-476, 479, 480-483, 490, 491, 505
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
SE/TE: 572-573, 575-576, 579, 580-582, 583-586, 593, 604-605, 607, 610
7 SE = Student Edition TE = Teacher Edition
Prentice Hall Algebra 2 and Trigonometry, New York Edition © 2011 Correlated to:
New York Learning Standards for Mathematics (Algebra 2 and Trigonometry)
NEW YORK LEARNING STANDARDS
FOR MATHEMATICS (ALGEBRA 2 AND TRIGONOMETRY)
Prentice Hall Algebra 2 and Trigonometry,
New York Edition © 2011 A2.A.30 Determine the common difference in an arithmetic sequence
SE/TE: 573-574, 575, 577, 579, 604, 607
A2.A.31 Determine the common ratio in a geometric sequence
SE/TE: 580-582, 583-584, 586, 593, 596, 598, 605, 607, 609
A2.A.32 Determine a specified term of an arithmetic or geometric sequence
SE/TE: 573-574, 575-577, 579, 580-582, 583-586, 593, 604-605, 607, 608
A2.A.33 Specify terms of a sequence, given its recursive definition
SE/TE: 569, 577, 578, 579, 604, 607, NY12-NY13
A2.A.34 Represent the sum of a series, using sigma notation
SE/TE: 589-590, 591-593, 596, 598, 599-601, 605, 607, 636
A2.A.35 Determine the sum of the first n terms of an arithmetic or geometric series
SE/TE: 587-588, 590, 591-593, 595-597, 598-599, 601, 605-606, 607, 610
A2.A.36 Apply the binomial theorem to expand a binomial and determine a specific term of a binomial expansion
SE/TE: 326-328, 328-330, 338, 346, 351, 353, 404, 727-728, 729
A2.A.37 Define a relation and function SE/TE: 60, 62, 64, 123
A2.A.38 Determine when a relation is a function SE/TE: 62-63, 64-67, 80, 88, 89, 123, 127, 129, 148, 190, 201
A2.A.39 Determine the domain and range of a function from its equation
SE/TE: 399, 401-402, 407-408, 410-411, 415, 419, 425-426, 427, 457, 515-518, 521, 523
A2.A.40 Write functions in functional notation SE/TE: 63-64, 65, 67, 73, 123, 127, 130, 190, 398-401, 401-404, 407-409, 409-412, 420, 421, 425-426, 427
A2.A.41 Use functional notation to evaluate functions for given values in the domain
SE/TE: 63-64, 65, 67, 73, 123, 127, 130, 190, 400, 403, 404, 409-410
A2.A.42 Find the composition of functions SE/TE: 399-401, 401-403, 409, 410-412, 421, 425, 427, 476, 541
A2.A.43 Determine if a function is one-to-one, onto, or both
SE/TE: 408, 409-412, 420, 426, 427, 431, 450, 483
A2.A.44 Define the inverse of a function SE/TE: 405-406, 409, 411, 413, 426
A2.A.45 Determine the inverse of a function and use composition to justify the result
SE/TE: 406-409, 409-412, 420, 421, 426, 427, 431, 450, 483
A2.A.46 Perform transformations with functions and relations: f(x+a), f(x)+a, f(-x), - f(x), a f(x)
SE/TE: 99-103, 103-106, 108-110, 111-113, 120, 125-126, 127, 128-129, 194-197, 198-201, 339-341, 343-345, 415-417, 418-420
Coordinate Geometry
A2.A.47 Determine the center-radius form for the equation of a circle in standard form
SE/TE: 635, NY19
A2.A.48 Write the equation of a circle, given its center and a point on the circle
SE/TE: 634-635, 637, 644, NY19
A2.A.49 Write the equation of a circle from its graph
SE/TE: 634, 637, 644, 670, NY18-NY19
8 SE = Student Edition TE = Teacher Edition
Prentice Hall Algebra 2 and Trigonometry, New York Edition © 2011 Correlated to:
New York Learning Standards for Mathematics (Algebra 2 and Trigonometry)
NEW YORK LEARNING STANDARDS
FOR MATHEMATICS (ALGEBRA 2 AND TRIGONOMETRY)
Prentice Hall Algebra 2 and Trigonometry,
New York Edition © 2011 A2.A.50 Approximate the solution to polynomial equations of higher degree by inspecting the graph
SE/TE: 298-300, 301, 349, 353
A2.A.51 Determine the domain and range of a function from its graph
SE/TE: 65-66, 80, 88, 123, 415-416, 419, 454-455, 508, 510, 512
A2.A.52 Identify relations and functions, using graphs
SE/TE: 62-63, 65-66, 80, 88, 123, 129, 148
A2.A.53 Graph exponential functions of the form x b y = for positive values of b, including e b =
SE/TE: 434-435, 437, 439-440, 442-446, 447-449, 454, 457-458, 461, 487, 489, 491
A2.A.54 Graph logarithmic functions, using the inverse of the related exponential function
SE/TE: 454, 456-457, 458, 487
Trigonometric Functions
A2.A.55 Express and apply the six trigonometric functions as ratios of the sides of a right triangle
SE/TE: 912-915, 915-918, 919, 926, 951, 953, 955
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
SE/TE: 830-832, 833-834, 842, 844, 848, 851, 859, 861, 863-864, 866, 885, 887, 889, 904-905, 907-908
A2.A.57 Sketch and use the reference angle for angles in standard position
SE/TE: Angles in standard position and coterminal angles can be found on the following pages: 828-831, 832-834.
A2.A.58 Know and apply the co-function and reciprocal relationships between trigonometric ratios
SE/TE: 875-879, 879-882, 884, 888, 889, 891, 896-897, 899, 900-902, 910, 912, 934, 936-937, 940-941
A2.A.59 Use the reciprocal and co-function relationships to find the value of the secant, cosecant, and cotangent of 0º, 30º, 45º, 60º, 90º, 180º, and 270º angles
SE/TE: 876-878, 879-882, 888, 889, 891
A2.A.60 Sketch the unit circle and represent angles in standard position
SE/TE: 830-831, 833-834, 843, 853, 875-876, 883, 884, 885
A2.A.61 Determine the length of an arc of a circle, given its radius and the measure of its central angle
SE/TE: 838, 839-840, 842, 886
A2.A.62 Find the value of trigonometric functions, if given a point on the terminal side of angle θ
SE/TE: 911-912, 916, 953
A2.A.63 Restrict the domain of the sine, cosine, and tangent functions to ensure the existence of an inverse function
SE/TE: 903-904, 952
A2.A.64 Use inverse functions to find the measure of an angle, given its sine, cosine, or tangent
SE/TE: 903-907, 907-910, 914-915, 915-917, 922, 924, 926, 927, 930, 931-932, 934, 952-953, 955
A2.A.65 Sketch the graph of the inverses of the sine, cosine, and tangent functions
SE/TE: 904
A2.A.66 Determine the trigonometric functions of any angle, using technology
SE/TE: 863, 877, 879-880, 893, 914, 915-917, 919, 921-923, 924-925, 929-931, 931-933
9 SE = Student Edition TE = Teacher Edition
Prentice Hall Algebra 2 and Trigonometry, New York Edition © 2011 Correlated to:
New York Learning Standards for Mathematics (Algebra 2 and Trigonometry)
NEW YORK LEARNING STANDARDS
FOR MATHEMATICS (ALGEBRA 2 AND TRIGONOMETRY)
Prentice Hall Algebra 2 and Trigonometry,
New York Edition © 2011 A2.A.67 Justify the Pythagorean identities SE/TE: 898, 900
A2.A.68 Solve trigonometric equations for all values of the variable from 0º to 360º
SE/TE: 856, 906-907, 907-909, 918, 919, 937, 941, 952, 955
A2.A.69 Determine amplitude, period, frequency, and phase shift, given the graph or equation of a periodic function
SE/TE: 820-823, 823-826, 834, 842, 844-847, 847-850, 851, 854, 856-857, 859, 862, 863-864, 867-870, 872-874, 882, 883, 885, 889
A2.A.70 Sketch and recognize one cycle of a function of the form y=A sin Bx or y=A cos Bx
SE/TE: 843-847, 847-850, 851, 852, 853-856, 856-859, 886-887, 889
A2.A.71 Sketch and recognize the graphs of the functions y=sec(x), y=csc(x), y=tan(x), and y=cot(x)
SE/TE: 861-863, 863-865, 878, 879-882, 887-888, 889, 892, 902
A2.A.72 Write the trigonometric function that is represented by a given periodic graph
SE/TE: 847, 848, 857-859, 865, 871, 873, 880, 892
A2.A.73 Solve for an unknown side or angle, using the Law of Sines or the Law of Cosines
SE/TE: 921-923, 924-926, 927, 928-931, 931-934, 942, 953, 955
A2.A.74 Determine the area of a triangle or a parallelogram, given the measure of two sides and the included angle
SE/TE: 920-921, 924-926, 953, 955
A2.A.75 Determine the solution(s) from the SSA situation (ambiguous case)
SE/TE: 927
A2.A.76 Apply the angle sum and difference formulas for trigonometric functions
SE/TE: 938-940, 940-942, 943, 949, 954, 955
A2.A.77 Apply the double-angle and half-angle formulas for trigonometric functions
SE/TE: 943-946, 947-949, 954, 955
Measurement Strand
Students will determine what can be measured and how, using appropriate methods and formulas.
Units of Measurement
A2.M.1 Define radian measure SE/TE: 835, 836, 839, 841, 884, 886
A2.M.2 Convert between radian and degree measures
SE/TE: 835, 836-838, 839-842, 850, 851, 886, 889, 892, 942
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)
SE/TE: 718-720, 721-723, 747, 751
A2.S.2 Determine factors which may affect the outcome of a survey
SE/TE: 720, 721-723, 732, 747, 749
Organization and Display of Data
A2.S.3 Calculate measures of central tendency with group frequency distributions
SE/TE: 704-705, 708-709
10 SE = Student Edition TE = Teacher Edition
Prentice Hall Algebra 2 and Trigonometry, New York Edition © 2011 Correlated to:
New York Learning Standards for Mathematics (Algebra 2 and Trigonometry)
NEW YORK LEARNING STANDARDS
FOR MATHEMATICS (ALGEBRA 2 AND TRIGONOMETRY)
Prentice Hall Algebra 2 and Trigonometry,
New York Edition © 2011 A2.S.4 Calculate measures of dispersion (range, quartiles, interquartile range, standard deviation, variance) for both samples and populations
SE/TE: 706, 712-714, 715-717, 723, 724, 732, 742, 746
A2.S.5 Know and apply the characteristics of the normal distribution
SE/TE: 733-736, 737-739, 740-741, 748, 749, 762, 826, 882
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
SE/TE: 459-460, NY16-NY17
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
SE/TE: 94-95, 96-98, 106, 113, 125, 127, 211, 212-213, 223, 269, 331-334, 335-338, 445, 450, 459-460, 461, NY16-NY17
A2.S.8 Interpret within the linear regression model the value of the correlation coefficient as a measure of the strength of the relationship
SE/TE: 94-95, 97, 125
Students will understand and apply concepts of probability.
Probability
A2.S.9 Differentiate between situations requiring permutations and those requiring combinations
SE/TE: 677, 678-679, 703
A2.S.10 Calculate the number of possible permutations (nPr) of n items taken r at a time
SE/TE: 676-677, 678-680, 687, 703, 744, 749
A2.S.11 Calculate the number of possible combinations (nCr) of n items taken r at a time
SE/TE: 676-677, 678-680, 683, 686-687, 703, 723, 726-728, 729-731, 744, 747, 749, 752
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)
SE/TE: 674-677, 678-680, 683, 686, 699, 703, 726, 744, 747, 749
A2.S.13 Calculate theoretical probabilities, including geometric applications
SE/TE: 683-684, 685-687, 688-690, 691-693, 694-695, 696-699, 700-702, 703, 711, 717, 726-728, 729-732, 739, 744-745, 747, 749
A2.S.14 Calculate empirical probabilities SE/TE: 681-682, 685, 694-695, 696-697, 700, 702, 749
A2.S.15 Know and apply the binomial probability formula to events involving the terms exactly, at least, and at most
SE/TE: 726-728, 729-732, 739, 747, 749
A2.S.16 Use the normal distribution as an approximation for binomial probabilities
SE/TE: 740-741
11 SE = Student Edition TE = Teacher Edition