CME Project Common Core Algebra 1, Geometry, Algebra 2, Precalculus 2013

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1 A Correlation of CME Project Common Core,,, to the for Mathematics High School

2 ,,, Introduction This document demonstrates how CME Project Common Core,,,,, meets the standards of the for Mathematics. Correlation references are to the pages of the Student and Teacher s Editions. The CME Project offers a Common Core curriculum organized around the familiar structure of,,, and. The program meets the dual goals of mathematical rigor and accessibility for all students through innovative, researchbased instruction and a curriculum that is designed around problem-based, studentcentered tasks. 100% aligned to the Common Core Standards for Mathematical Content with Standards for Mathematical Practice embedded throughout the program Content ordered specifically for the Common Core Traditional Pathway course sequence Low Threshold/High Ceiling ensures success for all students Problem-based, student-centered curriculum Engaging lessons that focus on developing students' Habits of Mind Accessible approach to capture and engage students of all ability levels Copyright 2014 Pearson Education, Inc. or its affiliate(s). All rights reserved

3 ,,, Table of Contents CCSS Math Practices... 1 Number and Quantity... 9 Algebra Functions Statistics & Probability Copyright 2014 Pearson Education, Inc. or its affiliate(s). All rights reserved

4 ,,, CCSS Math Practices MP1 Make sense of problems and persevere in solving them Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, Does this make sense? They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. The goal of the CME project is for students to engage in different activities to develop a deep understanding of mathematics. In addition to providing extensive practice in critical thinking and problem-solving skills, the problems are geared to engage students in communicating and exploring mathematics with In-Class Experiments and Projects. Each investigation includes a Getting Started lesson that activates prior knowledge and explores new ideas. Mind in Action offers opportunities for communication and reflection through studentstudent and student-teacher dialogues. Checking Your Understanding: 124 (#6), 170 (#5), 276 (#5-6), 338 (#2-3), 344 (#3), 390 (#3), 485 (#7-9), 492 (#1-3), 494 (#11), 495 (#12) On Your Own: 147 (#11), 222 (#6-7), 235 (#11), 236 (#13), 243 (#10), 559 (#9), 596 (#11), 652 (#14) Maintain Your Skills: 27 (#16), 229 (#12), 266 (#10-12), 278 (#13-15) Checking Your Understanding: 149 (#2-8), 201 (#1), 244 (#1), 225 (#5) On Your Own: 110 (#9), 150 (#13-17), 154 (#9-14), 155 (#15-28), 156 (#32), 228 (#11), 311 (#6), 319 (#4), 329 (#8), 383 (#5), 413 (#14) Checking Your Understanding: 35 (#3-4), 106 (#2), 122 (#2), 289 (#4, 6), 481 (#8), 745 (#1) On Your Own: 27 (#17), 65 (#10), 133 (#10), 216 (#12), 253 (#14) Maintain Your Skills: 28 (#21), 52 (#15-18) Checking Your Understanding: 16 (#5), 53 (#5), 65 (#1-2), 141 (#2), 627 (#2) On Your Own: 27 (#8), 36 (#8), 37 (#10-12), 53 (#8), 66 (#8), 138 (#18), 207 (#10), 312 (#27), 395 (#9) 1

5 ,,, CCSS Math Practice MP2 Reason abstractly and quantitatively Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. The goal of the CME project is for students to engage in different activities to develop a deep understanding of mathematics. In addition to providing extensive practice in critical thinking and problem-solving skills, the problems are geared to engage students in communicating and exploring mathematics with In-Class Experiments and Projects. Each investigation includes a Getting Started lesson that activates prior knowledge and explores new ideas. Mind in Action offers opportunities for communication and reflection through studentstudent and student-teacher dialogues. Checking Your Understanding: 95 (#4-5), 150 (#7), 164 (#2), 174 (#3), 175 (#6), 176 (#9), 207 (#6), 295 (#1), 296 (#11), 390 (#40, 493 (#7) On Your Own: 32 (#8), 97 (#11), 107 (#5), 147 (#13), 208 (#10), 287 (#10), 628 (#8), 635 (#11-12), 715 (#10) Maintain Your Skills: 166 (#13) Checking Your Understanding: 271 (#7-8), 341 (#3), 643 (#3) On Your Own: 97 (#5), 102 (#7-8), 233 (#8), 239 (#6, 9), 336 (#10), 380 (#9), 412 (#9) Maintain Your Skills: 273 (#16), 406 (#12-14), 644 (#11-12) Checking Your Understanding: 13 (#8), 227 (#3), 313 (#8), 345 (#2), 381 (#4), 787 (#6, 8), 794 (#5) On Your Own: 43 (#10), 234 (#16), 263 (#15), 771 (#10) Maintain Your Skills: 323 (#12-13), 330 (#20-21) Checking Your Understanding: 35 (#6), 95 (#7), 114 (#1), 201 (#7), 424 (#2), 455 (#2) On Your Own: 26 (#7), 54 (#11), 91 (#7), 96 (#13), 114 (#8), 127 (#11), 153 (#21), 333 (#10-12), 425 (#9) 2

6 ,,, CCSS Math Practice MP3 Construct viable arguments and critique the reasoning of others Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and if there is a flaw in an argument explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. The goal of the CME project is for students to engage in different activities to develop a deep understanding of mathematics. In addition to providing extensive practice in critical thinking and problem-solving skills, the problems are geared to engage students in communicating and exploring mathematics with In-Class Experiments and Projects. Each investigation includes a Getting Started lesson that activates prior knowledge and explores new ideas. Mind in Action offers opportunities for communication and reflection through studentstudent and student-teacher dialogues. Checking Your Understanding: 112 (#2), 384 (#2), 391 (#6), 453 (#4), 454 (#7), 535 (#5), 652 (#9) On Your Own: 96 (#8), 108 (#11), 112 (#3-4), 156 (#24), 166 (#10), 171 (#12), 332 (#11), 351 (#9), 356 (#10), 385 (#10), 403 (#10-11), 404 (#13) Maintain Your Skills: 630 (#13) Checking Your Understanding: 102 (#4), 109 (#7), 154 (#1-5), 335 (#3-4), 678 (#1-2) On Your Own: 97 (#6), 110 (#10-11), 121 (#6, 8), 155 (#30), 159 (#18-23), 245 (#8), 286 (#10-11) Maintain Your Skills: 150 (#21-25), 156 (#33-37), 252 (#16) Checking Your Understanding: 35 (#6), 133 (#7), 227 (#4), 233 (#7), 313 (#8), 516 (#7), 727 (#4), 793 (#4) On Your Own: 124 (#18), 234 (#13), 713 (#14) Maintain Your Skills: 44 (#13) Checking Your Understanding: 120 (#1, 3), 176 (#7), 311 (#12), 455 (#5) On Your Own: 11 (#12), 130 (#9), 177 (#12), 178 (#15), 379 (#12), 448 (#10), 491 (#12), 595 (#13), 603 (#11) 3

7 ,,, CCSS Math Practice MP4 Model with mathematics Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. The goal of the CME project is for students to engage in different activities to develop a deep understanding of mathematics. In addition to providing extensive practice in critical thinking and problem-solving skills, the problems are geared to engage students in communicating and exploring mathematics with In-Class Experiments and Projects. Each investigation includes a Getting Started lesson that activates prior knowledge and explores new ideas. Mind in Action offers opportunities for communication and reflection through studentstudent and student-teacher dialogues. Checking Your Understanding: 39 (#7), 155 (#11-13), 199 (#4), 233 (#3), 249 (#5, 7), 269 (#2-3), 270 (#5), 379 (#5), 401 (#1), 431 (#4) On Your Own: 194 (#15), 215 (#6-7), 236 (#12), 251 (#8-9), 304 (#11), 312 (#9), 380 (#10), 381 (#12), 396 (#9), 438 (#6) Maintain Your Skills: 194 (#17-19), 216 (#10), 457 (#17-18), 577 (#12-13), 588 (#9-10), 726 (#13), 780 (#14-15) Checking Your Understanding: 20 (#1-4), 271 (#7), 299 (#7-8), 411 (#3), 418 (#5) On Your Own: 228 (#12), 300 (#9-11), 336 (#11), 419 (#11), 425 (#7, 9) Maintain Your Skills: 26 (#11-13), 239 (#11-13) Checking Your Understanding: 49 (#2-3), 243 (#4), 467 (#6) On Your Own: 51 (#12), 75 (#6), 461 (#18), 467 (#10), 517 (#9, 12), 746 (#11-12) Maintain Your Skills: 253 (#18), 518 (#15-16) Checking Your Understanding: 26 (#5), 27 (#9-10), 66 (#6), 95 (#3), 461 (#2), 581 (#5) On Your Own: 17 (#10-11), 103 (#11), 108 (#12), 187 (#12), 240 (#7), 466 (#7-8) Maintain Your Skills: 208 (#15-16) 4

8 ,,, CCSS Math Practice MP5 Use appropriate tools strategically Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. The goal of the CME project is for students to engage in different activities to develop a deep understanding of mathematics. In addition to providing extensive practice in critical thinking and problem-solving skills, the problems are geared to engage students in communicating and exploring mathematics with In-Class Experiments and Projects. Each investigation includes a Getting Started lesson that activates prior knowledge and explores new ideas. Mind in Action offers opportunities for communication and reflection through studentstudent and student-teacher dialogues. Checking Your Understanding: 310 (#2), 623 (#7), 733 (#3), 752 (#3) On Your Own: 266 (#9), 754 (#9) Chapter Projects: 315 (Chapter 3 Project), (Chapter 5 Project), (Chapter 6 Project) Checking Your Understanding: 40 (#1-2), 41 (#3), 43 (#1-4), 54 (#1-4), 62 (#5-6), 109 (#7), 417 (#3) On Your Own: 56 (#10), 63 (#9), 290 (#9), 492 (#110) Maintain Your Skills: 18 (#7-12), 38 (#8), 46 (#15-17), 63 (#11), 90 (#7-9) Checking Your Understanding: 262 (#6), 346 (#7), 506 (#2), 746 (#3, 5-6) On Your Own: 52 (#13), 59 (#13), 277 (#13), 508 (#10), 747 (#19), 752 (#13) Maintain Your Skills: 316 (#26), 713 (#16) Checking Your Understanding: 26 (#3), 41 (#3), 47 (#2-3), 215 (#8), 473 (#4), 481 (#2), 566 (#3), 568 (#8), 635 (#4) On Your Own: 16 (#7), 42 (#10), 187 (#13, 15), 216 (#16-17) 5

9 ,,, CCSS Math Practice MP6 Attend to precision Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. The goal of the CME project is for students to engage in different activities to develop a deep understanding of mathematics. In addition to providing extensive practice in critical thinking and problem-solving skills, the problems are geared to engage students in communicating and exploring mathematics with In-Class Experiments and Projects. Each investigation includes a Getting Started lesson that activates prior knowledge and explores new ideas. Mind in Action offers opportunities for communication and reflection through studentstudent and student-teacher dialogues. Checking Your Understanding: 227 (#4), 538 (#1), 581 (#1), 582 (#3-4), 697 (#2-11) On Your Own: 229 (#8), 539 (#6-9), 540 (#14), 551 (#9), 697 (#12), 727 (#10) Maintain Your Skills: 541 (#15), 583 (#11-12) Checking Your Understanding: 101 (#1), 108 (#1), 222 (#3), 251 (#1), 390 (#4) On Your Own: 222 (#5-6), 227 (#6-9), 245 (#4-7) Maintain Your Skills: 104 (#11), 111 (#15), 265 (#10), 337 (#15-18), 342 (#9-12), 381 (#10) Checking Your Understanding: 49 (#2-3) On Your Own: 20 (#11-12), 51 (#12), 52 (#13), 70 (#9-12), 349 (#19-20), 732 (#8), 779 (#14-16) Maintain Your Skills: 99 (#11-12), 229 (#17-19), 789 (#20) Checking Your Understanding: 10 (#2), 12 (#13), 48 (#5), 90 (#4), 214 (#1-2), 429 (#2) On Your Own: 430 (#7), 431 (#9-10) Maintain Your Skills: 17 (#15-16), 121 (#13), 127 (#17), 138 (#20), 426 (#17), 583 (#11) 6

10 ,,, CCSS Math Practice MP7 Look for and make use of structure Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 8 equals the well remembered , in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 7 and the 9 as They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 3(x y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. The goal of the CME project is for students to engage in different activities to develop a deep understanding of mathematics. In addition to providing extensive practice in critical thinking and problem-solving skills, the problems are geared to engage students in communicating and exploring mathematics with In-Class Experiments and Projects. Each investigation includes a Getting Started lesson that activates prior knowledge and explores new ideas. Mind in Action offers opportunities for communication and reflection through studentstudent and student-teacher dialogues. Checking Your Understanding: 27 (#15), 150 (#8), 379 (#4), 454 (#6), 546 (#7), 592 (#1-2), 627 (#2), 665 (#5) On Your Own: 32 (#8), 155 (#22), 229 (#9), 463 (#12), 647 (#6-10), 653 (#17), 744 (#15), 748 (#6-7), 779 (#9) Maintain Your Skills: 32 (#9), 156 (#25), 209 (#15), 271 (#17), 357 (#10-18), 397 (#13), 444 (#12), 448 (#12), 486 (#12), 525 (#17) Checking Your Understanding: 101 (#2-3), 238 (#3), 335 (#5) On Your Own: 227 (#5), 239 (#70, 329 (#7-8), 405 (#11), 679 (#8) Maintain Your Skills: 234 (#11-13) Checking Your Understanding: 25 (#7), 79 (#2), 289 (#9), 313 (#4), 335 (#7) On Your Own: 20 (#14), 21 (#18), 80 (#10-13), 253 (#16), 265 (#20) Maintain Your Skills: 38 (#21-22), 45 (#17), 76 (#10) Checking Your Understanding: 201 (#4), 223 (#4) On Your Own: 36 (#7), 75 (#12), 109 (#13), 196 (#13), 224 (#10), 235 (#13), 333 (#13), 355 (#4) Maintain Your Skills: 6 (#15), 373 (#11) 7

11 ,,, CCSS Math Practice MP8 Look for and express regularity in repeated reasoning Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y 2)/(x 1) = 3. Noticing the regularity in the way terms cancel when expanding (x 1)(x + 1), (x 1)(x2 + x+ 1), and (x 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. The goal of the CME project is for students to engage in different activities to develop a deep understanding of mathematics. In addition to providing extensive practice in critical thinking and problem-solving skills, the problems are geared to engage students in communicating and exploring mathematics with In-Class Experiments and Projects. Each investigation includes a Getting Started lesson that activates prior knowledge and explores new ideas. Mind in Action offers opportunities for communication and reflection through studentstudent and student-teacher dialogues. Checking Your Understanding: 124 (#6), 503 (#2), 504 (#3), 523 (#6-8), 534 (#1-2), 535 (#6), 554 (#4), 778 (#4) On Your Own: 312 (#7), 505 (#9), 595 (#9), 596 (#10) Maintain Your Skills: 524 (#15-16), 530 (#16), 536 (#12-13), 541 (#17), 546 (#11), 618 (#16), 630 (#12-13) Checking Your Understanding: 318 (#1-3) Maintain Your Skills: 290 (#11), 329 (#10), 337 (#16-18), 384 (#10), 432 (#11-14), 476 (#9-10) Checking Your Understanding: 13 (#7), 392 (#4), 621 (#6), 626 (#5), 629 (#3), 661 (#4-7), 670 (#3), 678 (#1) On Your Own: 622 (#12-13), 662 (#9), 663 (#14-15), 684 (#4) Maintain Your Skills: 59 (#16), 375 (#14, 16), 627 (#11), 684 (#6) Checking Your Understanding: 10 (#3), 53 (#7), 311 (#15) On Your Own: 86 (#11), 315 (#36), 330 (#7), 417 (#11-12) Maintain Your Skills: 104 (#15-16), 109 (#22-23), 225 (#17), 241 (#11-12), 296 (#4) 8

12 ,,, Number and Quantity The Real Number System Extend the properties of exponents to rational exponents. HSN-RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5 1/3 to be the cube root of 5 because we want (5 1/3 ) 3 = 5 (1/3)3 to hold, so (5 1/3 ) 3 must equal (#3) 440 (Example #2), 441 (#4), 442 (#8-11), 443 (#9), , 447, 448 (#15-16), 449 (#5) HSN-RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents , 441 (#4-5), 442 (#8-11), 443 (#19), , 447 (#9, 11, 13), 449 (#5, 8) Use properties of rational and irrational numbers. HSN-RN.B.3 Explain why the sum or product of two rational numbers is rational; that the For related content, please see: sum of a rational number and an irrational 213 number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Quantities* Reason quantitatively and use units to solve problems. HSN-Q.A.1 Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units (#12), , , , , ,174 (#2-4), , 177 consistently in formulas; choose and interpret 295 (#7), 296 (#11), , 338 (#4), 339 the scale and the origin in graphs and data (#8), 340 (#9-10), 341 (#14, 16), , displays. 366 (#1-3), 415 (Chapter 4 Project), 733 (#4), 735 (#5-7), , 760 (#1) 238 (#1, 3,5), 339 (#7-8), , 245 (#3-8), , , (Chapter 5 Project), , 265 9

13 ,,, (Continued) HSN-Q.A.1 Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays , 43 (#8), 44 (#11), 46-48, 49 (#2-4), 51 (#12), 52 (#15-18), 53-55, 58 (#6), 60-61, 63-64, 72-74, 75-76, (Chapter 1 Project), 106 (#1-2), 462, 467 (#7), 769 (#13-14), , 499 (#1), 500 (#4-5), , 506 (#3), , , 516, 517 (#9, 12-13), 518 (#15-16), , , , 751 (#1, 3), , 770, 771 (#10) 595 (#15), , 619 (#6), , 628 (#5), , 637 (#14) HSN-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling , 341 (#14-15) 46-48, 49-51, 52 (#13), 72-74, 75, 76 (#7-8) , 496 (#11), 497 (#15) HSN-Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities , , , 410 (#3), , 413 (#10) 46-48, 49-51, 52 (#13), 72-74, 75, 76 (#7-8) , The Complex Number System Perform arithmetic operations with complex numbers. HSN-CN.A.1 Know there is a complex number i such that i 2 = 1, and every complex number has the form a + bi with a and b real. 215 (#8),

14 ,,, HSN-CN.A.2 Use the relation i 2 = 1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. HSN-CN.A.3 (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers , , , , 235 (#4-5), 239 (#8), 240 (#15) 85-86, 87-89, 90-91, , , , , , 87-89, Represent complex numbers and their operations on the complex plane. HSN-CN.B.4 (+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number , 239, , , , 251 (#1-2), 252 (#6-7, 10), , 262 (#8), 263 (#17), 264 (#21), 266 (#1-2), 269 (#1-2), 270 (#9) 87-90, 91 (#8, 11, 17), 92-94, 95 (#3, 6), 125 (#2), 126 (#3), 127 (#15), , 135 (#3-4), 136 (#9), , 141 (#2) HSN-CN.B.5 (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, ( i) 3 = 8 because ( i) has modulus 2 and argument 120. HSN-CN.B.6 (+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints , , , , 278 (#16) 92-94, 95 (#8-11), 96 (#12, 15), , , 104 (#12), , , Use complex numbers in polynomial identities and equations. HSN-CN.C.7 Solve quadratic equations with real coefficients that have complex solutions. For related content, please see: 211 (#8), 218 For related content, please see: 125 (#2) 11

15 ,,, HSN-CN.C.8 (+) Extend polynomial identities to the complex numbers. For example, rewrite x as (x + 2i)(x 2i). HSN-CN.C.9 (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Vector & Matrix Quantities Represent and model with vector quantities. HSN-VM.A.1 (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, v, v, v). 229 (#14) 127 (#10, 12-15), , 130 (#6, 11), 131 (#16), , 135, 136 (#11) 226, 228 (#5), 229 (#19) , 634 (#7-11), 635 (#16, 18-19), , 251 (#1-3), , 261 (#1), 262 (#8), 263 (#17), 264 (#21), 269 (#2), 270 (#8), , 276 (#4), 277 (#13, 15) 501 (#1), , 507 (#5), , 514 (#8), 515 (#12), , 522 (#6) HSN-VM.A.2 (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point , , HSN-VM.A.3 (+) Solve problems involving velocity and other quantities that can be represented by vectors , 515 (#13, 15) Perform operations on vectors. HSN-VM.B.4 (+) Add and subtract vectors , 632 (#9-14), 633 (#3-5) (#1) 12

16 ,,, HSN-VM.B.4a Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. 632, 633 (#40, 634 (#7, 9-11), 635 (#17), 639 (#6) , 251 (#1-4) HSN-VM.B.4b Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. 633 (#4), 634 (#7, 9-11), 635 (#17), 639 (#6) HSN-VM.B.4c Understand vector subtraction v w as v + ( w), where w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise , 633 (#4), 634 (#7, 9-11), 635 (#17), 639 (#6) , 251 (#1-2), 252 (#9) 501 (#2), , 506 (#3), 507 (#4-5, 7), 508 (#10-11) HSN-VM.B.5 (+) Multiply a vector by a scalar. 633 (#6), 640 (#9, 15) , 251 (#5), 252 (#6-7, 11), 253 (#14-16), , , 278 (#16) 504 (#6), , 507 (#8-9) HSN-VM.B.5a Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(v x, v y ) = (cv x, cv y ). 253 (#14-16) , 507 (#8-9) HSN-VM.B.5b Compute the magnitude of a scalar multiple cv using cv = c v. Compute the direction of cv knowing that when c v 0, the direction of cv is either along v (for c > 0) or against v (for c < 0) , 276 (#3-7), 277 (#15), 278 (#16) , 507 (#8-9), ,

17 ,,, Perform operations on matrices and use matrices in applications. HSN-VM.C.6 (+) Use matrices to represent and manipulate data, e.g., to represent , 324, 328 (#5-6), 329 (#7, payoffs or incidence relationships in a 12-14), 330 (#15), , 347 (#12-13), network. 348 (#14), 349 (#23), 350 (#24-26) , HSN-VM.C.7 (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled , , 330 (#15) For related content, please see: 502 (#9) HSN-VM.C.8 (+) Add, subtract, and multiply matrices of appropriate dimensions , , 330 (#15), , HSN-VM.C.9 (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. HSN-VM.C.10 (+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. HSN-VM.C.11 (+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors , 343 (#5), , 365 (#2-3), 366 (#11-12) , 365 (#4), 366 (#9, 16) , , , HSN-VM.C.12 (+) Work with 2 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area ,

18 ,,, Algebra Seeing Structure in Expressions Interpret the structure of expressions. HSA-SSE.A.1 Interpret expressions that represent a quantity in terms of its context , 96 (#6, 9-10), 97 (#11-13), 98, 100 (#1, 3-5), 101 (#7), 102 (#11), 113 (#8), 609, 610 (#5), 611 (#8-11, 13-15), , 633, 634 (#8-9), 635 (#13-14), 642 (#11-13), 668 (#14, 24), , (#4-7), 80 (315-18), 91 (#4), 92 (#6), 94 (#4), 95 (#16-17), 160 (#9-10), 171 (#6-7), 175 (#1-2), 176, 177 (#1), 178 (#2), 179 (#1-3), 187 (#4-9), 188, 190 (#4), 191 (#6), 193 (#1, 5), 194 (#10) 85 (#1), 86 (#14), 107, 109 (#15, 17), 113, 114 (#4), 115 (#15), , 120 (#1, 3, 5, 7), 121 (#10-11) HSA-SSE.A.1a Interpret parts of an expression, such as terms, factors, and coefficients. 93, , 108 (#10), 109 (#15), , , 616 (#5), 633, 635 (#13-14), 643, 644 (#5-7), 645, 646 (#1, 4), 648 (#16-20), 650 (#1), 651 (#2), 652 (#11-14), 653 (#15-16, 18-21), , 668 (#20-21, 24-25) 90-91, 93 (#2), 94 (#10), , 65 (#1), 66 (#8), 92-94, 95 (#3-4) HSA-SSE.A.1b Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r) n as the product of P and a factor not depending on P. 113 (#5-7), , 356 (#5, 8-10), , 674 (#1-2), , , 148 (#1-5), 149 (#8), , 171 (#2, 9-10, 12), 175, 176 (#5, 7, 12), , , 86 (#2), 187 (#4-6), , 193 (#1-2, 5), , 638 (#1) 18-21, 22-23, , 120 (#1-7) 15

19 ,,, HSA-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. For example, see x 4 y 4 as (x 2 ) 2 (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 y 2 )(x 2 + y 2 ) , 109 (#15), 174 (#4), 176 (#6), 177 (#12-14), , 356 (#5, 8-10), , 616 (#5), 617 (#11), , 624 (#12), 660 (#11), 661, 668 (#20-21, 25), , 675 (#7) 175, 176 (#5, 7), , 179, , 186 (#2), 187 (#4-6), , 193 (#1-5), 218, 222 (#11), , 227 (#1), , 233 (#3-5, 10), 234 (#14, 19), 429 (#7), 430 (#18, 21-22), , 435 (#11), 436 (#15), , 448 (#16) Write expressions in equivalent forms to solve problems. HSA-SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain 581 (#1), 592 (#4), , 616, properties of the quantity represented by the 617 (#7), 618 (#15), , 624 (#11-12), expression. 626, 627 (#2, 4), 628 (#5), 661, 665 (#1), , 675 (#7), 677, 685 (#13, 20) 92, 94 (#4), 95 (#14), 167, 169 (#3), 172 (#13), , 179 (#1-3), , 186 (#2), 187 (#4-6, 9), , 193 (#1-2, 5), 221 (#1), 223 (#13), 227 (#1, 3), 233 (#5, 10) 107 (#2), 109 (#13, 16-17) HSA-SSE.B.3a Factor a quadratic expression to reveal the zeros of the function it defines , 674 (#4), 675 (#7), , 683 (#1, 5), 685 (#14, 19), 687 (#3-4) , 179 (#1, 3). HSA-SSE.B.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines , 683 (#1, 5), 685 (#14, 19), , 725 (#1-2), 726 (#6-12) 16

20 ,,, HSA-SSE.B.3c Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. HSA-SSE.B.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments , 581 (#1), 582 (#4), 583 (#11), , 592 (#1-2), 593 (#3), 594 (#8), 597 (#1-2) , 473 (#6), 475 (#11, 15), 476 (#17) , 670 (#4) Arithmetic with Polynomials & Rational Expressions Perform arithmetic operations on polynomials. HSA-APR.A.1 Understand that polynomials form a system analogous to the integers, namely, they , 640 (#10-11) are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Understand the relationship between zeros and factors of polynomials. HSA-APR.B.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x a is p(a), so p(a) = 0 if and only if (x a) is a factor of p(x) , 164 (#1-3), 165 (#7-9), 166 (#14-15) 183, 196 (#16-17) HSA-APR.B.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial , 623 (#2), 624 (#9), , 734 (#9), , 743 (#8, 10) For related content, please see: 179 (#1, 3), 187 (#4) 168 (#4), 169 (#8, 11, 13) Use polynomial identities to solve problems. HSA-APR.C.4 Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x 2 + y 2 ) 2 = (x 2 y 2 ) 2 + (2xy) 2 can be used to generate Pythagorean triples. 171 (#6-7), 211 (#4), 536 (#3) 85 (#7), 91 (#15) 17

21 ,,, HSA-APR.C.5 (+) Know and apply the Binomial Theorem for the expansion of (x + y) n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal s Triangle. Rewrite rational expressions. HSA-APR.D.6 Rewrite simple rational expressions in different forms; write a(x) / b(x) in the form q(x) + r(x) / b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree ofr(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. HSA-APR.D.7 (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions (#5-9), , , 199 (#5) For related content, please see: , , , 199 (#5) For related content, please see: , Creating Equations Create equations that describe numbers or relationships. HSA-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. 130 (#14), 136 (#9), 137 (#10, 12- Include equations arising from linear and 14, 17), , , , , quadratic functions, and simple rational and , , 154 (#1-10), 155 (#15-21), exponential functions. 156 (#25), 157 (#2-5, 8), 159 (#1), 161 (#9-10), , 164 (#2), , , , 171 (#10, 12), 395 (#1-2), 396 (#8), , 401 (#1), , 404 (#12-13), 405 (#15-17), 431 (#3-4), 432 (#5, 9-10), 433 (#11), 485 (#8-9), , , 495 (#12-13), 575, 577 (#13), 720 (#8), , 726 (#10), 733 (#4), 734 (#5-7) HSA-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. HSA-CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods , 344 (#6), 345 (#11), 704 (#10-11), 705 (#25) For related content, please see: 174 (#3), 175 (#5-6), 176 (#10-11), 177 (#12), 371, 372 (#2), 378 (#1, 3), 379 (#5), 380 (#9-10), 391 (#8-9), 413 (#2), 415 (Chapter 4 Project),

22 ,,, HSA-CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm s law V = IR to highlight resistance R. 174 (#3), 175 (#6-7), 176 (#9), 177 (#13-14), 628 (#7-8) Reasoning with Equations & Inequalities Understand solving equations as a process of reasoning and explain the reasoning. HSA-REI.A.1 Explain each step in solving a simple equation as following from the equality of , , 150 (#8), 153 numbers asserted at the previous step, starting (#1), 156 (#24) from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. HSA-REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. 533 (#4), 569 (#6), 572 (#7, 10) For related content, please see: 193 (#6), 197 (#5), 198 (#7) 207 (#9), 215 (#6), 216 (#17), 217 (#20), 466 (#6), 467 (#10) Solve equations and inequalities in one variable. HSA-REI.B.3 Solve linear equations and inequalities in one variable, including equations , 132 (#3), , 143- with coefficients represented by letters. 147, , 153, 154 (#1-10), 156 (#25), 157 (#3-5, 8), 166 (#13), , , 623 (#1) HSA-REI.B.4 Solve quadratic equations in one variable. 623 (#2), 624 (#9), 667 (#13), 674 (#2-3), 676 (#10, 13), , 682 (#1), 683 (#5), 684 (#12), 685 (#14, 19), 687 (#5), 697, , 704 (#1-8, 12-16), 705 (#27), 707, 710 (#5), 715 (#11) 94 (#5), 179 (#4-5), 180 (#8), 215 (#1), 216 (#130 HSA-REI.B.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p) 2 = q that has the same solutions. Derive the quadratic formula from this form , 682 (#1), 683 (#3, 5), 684 (#12), 685 (#14, 19-20), 687 (#5), 697, , 704 (#1-8, 12-16), 705 (#27) 19

23 ,,, HSA-REI.B.4b Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b , 667 (#13, 17), 668 (#18, 20-21, 23), , 674 (#2-4), 676 (#10, 13), , 682 (#1), 683 (#5), 684 (#12), 685 (#14, 19), 687 (#5), , 704 (#1-8, 12-16), 705 (#27), 707, 710 (#5), 715 (#11) 94 (#5), , 179, 180 (#8-9), 215 (#1, 5-6), 222 (#12), 229 (#1-2), 300 (#7-11), 301, , 305 (#1-2, 7), 306 (#9, 12-13), 317 (#1) Solve systems of equations. HSA-REI.C.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions , 390, 391 (#5, 8-9), 392 (#11-12), 393 (#5) HSA-REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 373 (#11), , , 381 (#11-13), 390 (#4), 392 (#10) 299 (#1-3), , , , 317 (#1-2) HSA-REI.C.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = 3x and the circle x 2 + y 2 = , 281 (#6), , 754 (#9) HSA-REI.C.8 (+) Represent a system of linear equations as a single matrix equation in a vector variable , , 316, 317 (#3-5), , 356 (#1-3), 358 HSA-REI.C.9 (+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 3 or greater) , 356 (#1-3),

24 ,,, Represent and solve equations and inequalities graphically. HSA-REI.D.10 Understand that the graph of an equation in two variables is the set of all its , , , , solutions plotted in the coordinate plane, often , 283, 286, 287 (#8), , 295 forming a curve (which could be a line). (#3-7), 296 (#11, 13), 297 (#15, 17-18), , 303 (#1-5, 7), 304 (#16) 106 (#1-2, 6), 107 (#9), , 132 (#3-5), 133 (#9-10), 134 (#11), 141 (#12), 142 (#14-18), , 458 (#1), 459 (#8), 461 (#22), , 506 (#3), 507 (#5), 508 (#11), 509 (#16), , 537 (#8, 12), 538 (#16), , 746 (#3, 5-6, 8-9), 747 (#17, 19), , 751 (#1, 3-4), 752 (#11-13) 443 (#11-12), , 447 (#3), 448 (#6), 461 (#2), 465 (#4), 466 (#7-8), 474 (#11, 13), 481 (#1-2), 482 (#5-6), 483 (#11), 489 (#2), 490 (#3) HSA-REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. 279, 281 (#5-6), 282 (#9), 395 (#3), 397 (#10), , , 752 (#3), 753 (#6) , 505, 506 (#3), 507 (#5) , 185 (#2-4), 186 (#10), 198, 201 (#1, 6), 443 (#11-12) HSA-REI.D.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes , 760 (#1-3), , ,

25 ,,, Functions Interpreting Functions Understand the concept of a function and use function notation. HSF-IF.A.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). HSF-IF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context , , 442 (#1), , 447, 448 (#7-8, 10-11), , 452 (#1), 453 (#4), 454 (#6, 8), 455 (#12), 456 (#14-15), 458 (#4) 5-7, 8-15, , 106, 107 (#9-12, 14), 108 (#19, 23) This standard is addressed throughout the text. See, for example, pages: , , 469 (#2-3), 470 (#4), 472 (#8-9, 11), 473 (#12-13), , 587 (#1), 592 (#1-2), 593 (#3-4), 594 (#5-6, 8), 595, 596 (#11), 597 (#10) This standard is addressed throughout the text. See, for example, pages: 18, 31-34, 36 (#10), 37 (#12, 14-15), 38 (#21-22), 451, 452 (#15), 453 (#16-17), 466 (#1), 467 (#6, 10), 469 (#13-15), 475 (#12, 16), 482 (#15), 483 (#16-17), 489, 492 (#1), 494 (#15), 520 (Chapter 5 Project), 655 (#1), 657 (#5, 7), , 661 (#4, 6-7), 662 (#8-9), This standard is addressed throughout the text. See, for example, pages: 13-15, 16 (#14), 31, 32, 33-34, 36 (#7), 37 (#15), 41 (#1-5), 43-46, 49 (#12), 52 (#2), 57, 60-64, 65 (#2), 66 (#8), 73-75, , 175 (#3), , 208 (#13), , 257 (#5), 258 (#9), 259 (#10-12), , HSF-IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n , 392,

26 ,,, Interpret functions that arise in applications in terms of the context. HSF-IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity , 447, 448 (#7, 11), , , 454 (#8), 455, 457 (#17-18), , , 570 (#1), , 587 (#5-6), 588 (#7, 9-10), 722, , 726 (#13), , , 733 (#1, 3), 734 (#9), 735 (#12), 737 (#1-3), 743 (#8, 10), 744 (#17) , 459 (#8), 461 (#22), , 506 (#3), 508 (#10-11, 13), 509 (#16), 527, 528 (#16), 529 (#18, 21), 537 (#8-10, 12), 741 (#6, 8), , 745 (#1), 746 (#3, 5-6, 8-9), 747 (#17, 19) 13-15, 16 (#7), 17 (#11), 26 (#5), 27 (#8, 10, 12, 14), 38-39, 41 (#3), 42 (#8), 58 (#9, 11), 60-64, 65 (#1), 66 (#4-6, 8), 68-69, 71-72, 73 (#2-4), 74 (#6, 9), 75 (#12), 76 (#18), 169 (#11, 13), 176 (#6), , 215 (#6, 8), 217 (#22) HSF-IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function , 726 (#10, 13) 104, 106 (#1-2, 6), HSF-IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph ,

27 ,,, Analyze functions using different representations. HSF-IF.C.7 Graph functions expressed symbolically and show key features of the graph, 296 (#11, 13), 297 (#15, 17-18), by hand in simple cases and using technology for , 303 (#1-6), 304 (#12, 14, 16), 305- more complicated cases. 309, 310 (#1-2), , 315 (Chapter 3 Project), , 360 (#2-3), 362 (#28-39), , 447, 448 (#7, 11), , , 454 (#8), 455, 457 (#17-18), , , 570 (#1), , 587 (#5-6), 588 (#7, 9-10), 722, , 726 (#13), , , 733 (#1, 3), 734 (#9), 735 (#12), 737 (#1-3), 743 (#8, 10), 744 (#17) , 132 (#4), 134 (#11), , 459 (#8), 461 (#22), , 506 (#3), 508 (#10-11, 13), 509 (#16), 527, 528 (#16), 529 (#18, 21), 537 (#8-10, 12), 741 (#6, 8), , 745 (#1), 746 (#3, 5-6, 8-9), 747 (#17, 19) 13-15, 16 (#7), 17 (#11), 26 (#5), 27 (#8, 10, 12, 14), 38-39, 41 (#3), 42 (#8), 58 (#9, 11), 60-64, 65 (#1), 66 (#4-6, 8), 68-69, 71-72, 73 (#2-4), 74 (#6, 9), 75 (#12), 76 (#18), 169 (#11, 13), 176 (#6), , 215 (#6, 8), 217 (#22) HSF-IF.C.7a Graph linear and quadratic functions and show intercepts, maxima, and minima. 290, 295 (#2), 296 (#11), 298, 308, 312 (#9), 313 (#16), 722, 725, , , 733 (#1, 3), 734 (#9), 743 (#8, 10), 744 (#17) 142 (#14-15), 528 (#16), 537 (#8) HSF-IF.C.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions , 303 (#7), 304 (#16), 455 (#11) , 132 (#3-4), 133 (#9-10), 134 (#11) 24

28 ,,, HSF-IF.C.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showin139, 537 (#11)g end behavior. For related content, please see: 732, 733 (#1-2) For related content, please see: , 169 (#11, 13), 187 (#11-12) HSF-IF.C.7d (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. HSF-IF.C.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude , , , 217 (#19, 22) , 587 (#5), 588 (#9-10) , 458 (#1), 459 (#8), 461 (#22), , 506 (#3), 507 (#5), 508 (#10-11), 509 (#16), , 745 (#1-2), , , 752 (#11-12) 60-64, 65 (#1-2), 66 (#4-6, 8), 67 (#9-10), 68-72, 73 (#2-4), 74 (#6, 9), 75 (#12), 76 (#18), 77 (#1, 3), , 258 (#7) HSF-IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 453 (#4), (#4), , 349 (#1-7), 350 (#10-15), 351 (#16) HSF-IF.C.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context , 682 (#1), 683 (#5), 685 (#14, 19-20), , 725 (#1-2), 726 (#6-8, 10-13), , 733 (#1-2, 4), 734 (#5-6, 9), 737 (#1-3), 743 (#8-10), 744 (#17) , 578 (#4) 25