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






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







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







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







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







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







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







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







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







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







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


prentice hall algebra 2 and trigonometry, new york - pearson

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