A Correlation of. to the. South Carolina Academic Standards for Mathematics Precalculus

Transcription

1 A Crrelatin f Suth Carlina Academic Standards fr Mathematics Precalculus

2 INTRODUCTION This dcument demnstrates hw Precalculus (Blitzer), 4 th Editin 010, meets the indicatrs f the. Crrelatin page references are Student Editin and Instructr s Editin Manual and are cited at the page level. Blitzer creates intriguing applicatins that shw students the relevance f math. Appealing t a wide range f interests and majrs, the prgram s applicatins captivate students imaginatin with his passin fr integrating math in wrlds f cntemprary sciety, culture, art, and science. Features: Clear and accessible presentatin ensures that students can fllw the bk when they get hme frm class. Vice ballns ffer the supprt and guidance f a teacher s vice. These specific anntatins clarify prcedures and cncepts, mimicking what a teacher wuld say in class when translating the math int plain English. See it, Hear it, Try it is the cnsistent frmat f every textbk example. Extensive exercise sets at the end f each sectin are rganized int six categries: Practice Exercises, Applicatin Exercises, Writing in Mathematics, Technlgy Exercises, Critical Thinking Exercises, and Grup Exercises. This variety lets teachers create well-runded hmewrk assignments, while hlding students interest with an nging selectin f nvel applicatins. Practice Plus Prblems are mre challenging prblems that test cnceptual understanding by requiring students t cmbine skills and t revisit key cncepts in rder t slve. New t this editin are Make Sense? Classrm discussin exercises that cntain fur critical thinking prblems that test fr cnceptual understanding. This is an pprtunity fr students t express their pinins and fr teachers t prvide feedback n thse thughts. Assessment includes Mid-Chapter Checkpints, Cumulative Review Exercises at the end f each chapter, and End-f-chapter tests. These ensure that students remember previusly learned material, keeping the fundamental skills and cncepts fresh in their minds. Integrated study aids help students make the mst f their time utside f the classrm. Chapter Test Prep Vides (included with the Student Editin) cntain wrked-ut slutins t every exercise in every chapter test. A teacher walks students thrugh all examples step-by-step, allwing students t pause and watch again as needed. Study Tip bxes appear thrughut the bk. These ffer suggestins fr prblem slving, pint ut cmmn student errrs, and prvide infrmal tips and suggestins. Technlgy bxes illustrate the many capabilities f graphing utilities that g beynd just graphing. This dcument demnstrates the success students will achieve by using Precalculus by Blitzer.

3 Standard PC-1: The student will understand and utilize the mathematical prcesses f prblem slving, reasning and prf, cmmunicatin, cnnectins, and representatin. PC-1.1 Cmmunicate knwledge f algebraic and trignmetric relatinships by using mathematical terminlgy apprpriately. PC-1. Cnnect algebra and trignmetry with ther branches f mathematics. PC-1.3 Apply algebraic methds t slve prblems in real-wrld cntexts. PC-1.4 Judge the reasnableness f mathematical slutins. PC-1.5 Demnstrate an understanding f algebraic and trignmetric relatinships by using a variety f representatins (including verbal, graphic, numerical, and symblic). PC-1.6 Understand hw algebraic and trignmetric relatinships can be represented in cncrete mdels, pictrial mdels, and diagrams. PC-1.7 Understand hw t represent algebraic and trignmetric relatinships by using tls such as handheld cmputing devices, spreadsheets, and cmputer algebra systems (CASs). SE/TE: 18 (#14-#131), 0 (#33-#38), 51 (#75-#8), 300 (#77-#8), 35 (#57-#64), 337 (#65-#71), (#10-#110), 378 (#40-#47), 399 (#77-#80), 41 (#10-#17), 4 (#105-#11), 450 (#59-#67), 535 (#89- #97), 576 (#63-#69), 595 (#75-#78) SE/TE: 54, 55, 66, 68, 81, , , 46-49, 59-60, 97, 30, 409, , , SE/TE: , , 93-97, , , , , , , , , , , , SE/TE: 103, 105, 107, 108, 109, 110, 15, 47, 738, 739, 751, 75, 769, 770, 774 SE/TE: , , , 04-19, 5-66, , , , , , , , , , SE/TE: , 187, 57-59, 365, 373, , 53, 568, 570, 571, 651, 656, 659, 660, 783 SE/TE: , 15, 154, 47, 57, 307, 40, , 53, 558, 587, , 669, 731, 90 Standard PC-: The student will demnstrate thrugh the mathematical prcesses an understanding f the characteristics and behavirs f functins and the effect f peratins n functins. PC-.1 Carry ut a prcedure t graph parent functins (including y = x n, y = lg a x, y SE/TE: , , , , , , 545 = ln x, y = x 1, y = e x, y = a x, y = sin x, y = cs x, y = tan x, y = csc x, y = sec x, and y = ct x). 3

4 PC-. Carry ut a prcedure t graph transfrmatins (including f(x), a f(x), f(x) + d, f(x - c), f(-x), f(b x), f(x), and f( x )) f parent functins and cmbinatins f transfrmatins. PC-.3 Analyze a graph t describe the transfrmatin (including f(x), a f(x), f(x) + d, f(x - c), f(-x), f(b x), f(x), and f( x )) f parent functins. PC-.4 Carry ut prcedures t algebraically slve equatins invlving parent functins r transfrmatins f parent functins (including y SE/TE: 04-19, , , , , , , , SE/TE: 04-19, , , , , , , , SE/TE: 86-87, 98, , 43, 433, , 641 = x n, y = lg a x, y = ln x, y = x 1, y = e x, y = a x, y = sin x, y = cs x, y = tan x, y = csc x, y = sec x, and y = ct x). PC-.5 Analyze graphs, tables, and equatins t determine the dmain and range f parent functins r transfrmatins f parent functins (including y = x n, y = lg a x, y = ln x, SE/TE: , , 411, 478, 479, 517, 56, 538, 541, 54, 543, 545 y = x 1, y = e x, y = a x, y = sin x, y = cs x, y = tan x, y = csc x, y = sec x, and y = ct x). PC-.6 Analyze a functin r the symmetry f its graph t determine whether the functin is even, dd, r neither. PC-.7 Recgnize and use cnnectins amng significant pints f a functin (including rts, maximum pints, and minimum pints), the graph f a functin, and the algebraic representatin f a functin. PC-.8 Carry ut a prcedure t determine whether the inverse f a functin exists. PC-.9 Carry ut a prcedure t write a rule fr the inverse f a functin, if it exists. SE/TE: , 05, , 517, 56, 537, 538, 541, 54, 543 SE/TE: 159, , 57, 58, 59, 71, 86-95, 98, 99, , , , , , SE/TE: 35-39, 40-43, 73-74, , SE/TE: 35-39, 40-43, 73-74, , Standard PC-3: The student will demnstrate thrugh the mathematical prcesses an understanding f the behavirs f plynmial and ratinal functins. PC-3.1 Carry ut a prcedure t graph quadratic and higher-rder plynmial functins by analyzing intercepts and end behavir. SE/TE: 86-9, 98, , 307, 308, 309, , 31, 313, 315, 380, 38 4

5 PC-3. Apply the ratinal rt therem t determine a set f pssible ratinal rts f a plynmial equatin. PC-3.3 Carry ut a prcedure t calculate the zers f plynmial functins when given a set f pssible zers. PC-3.4 Carry ut prcedures t determine characteristics f ratinal functins (including dmain, range, intercepts, asympttes, and discntinuities). PC-3.5 Analyze given infrmatin t write a plynmial functin that mdels a given prblem situatin. PC-3.6 Carry ut a prcedure t slve plynmial equatins algebraically. PC-3.7 Carry ut a prcedure t slve plynmial equatins graphically. PC-3.8 Carry ut a prcedure t slve ratinal equatins algebraically. PC-3.9 Carry ut a prcedure t slve ratinal equatins graphically. PC-3.10 Carry ut a prcedure t slve plynmial inequalities algebraically. PC-3.11 Carry ut a prcedure t slve plynmial inequalities graphically. SE/TE: 37-33, 335, 336, 380, 383, 386 SE/TE: 37-33, 335, 336, 386 SE/TE: , 381, 383 SE/TE: 93, 95, 96, 97, 99, 316, 35,337, 339 SE/TE: 33, 34, 35, 36, , 336, 339, 383, 386 SE/TE: , , 33, 34, 35, 38, 330, 333, 385, 386 SE/TE: 86-87, 98, 131 SE/TE: , 355, 386 SE/TE: , 366, 384, 386 SE/TE: 359, 361, 36, 366, 384, 386 Standard PC-4: The student will demnstrate thrugh the mathematical prcesses an understanding f the behavirs f expnential and lgarithmic functins. PC-4.1 Carry ut a prcedure t graph expnential functins by analyzing intercepts and end behavir. PC-4. Carry ut a prcedure t graph lgarithmic functins by analyzing intercepts and end behavir. PC-4.3 Carry ut prcedures t determine characteristics f expnential functins (including dmain, range, intercepts, and asympttes). PC-4.4 Carry ut prcedures t determine characteristics f lgarithmic functins (including dmain, range, intercepts, and asympttes). SE/TE: , 43, 453, 454 SE/TE: , 43, 454 SE/TE: , 43, 453, 454 SE/TE: , 43, 454 5

6 PC-4.5 Apply the laws f expnents t slve prblems invlving ratinal expnents. PC-4.6 Analyze given infrmatin t write an expnential functin that mdels a given prblem situatin. SE/TE: 19-, 39-4, 43, 44, 45, 19, 131, 133 SE/TE: , 397, 398, 399, , 456 PC-4.7 prblems. Apply the laws f lgarithms t slve SE/TE: , 41, 43, 454, 457 PC-4.8 Carry ut a prcedure t slve expnential equatins algebraically. PC-4.9 Carry ut a prcedure t slve expnential equatins graphically. PC-4.10 Carry ut a prcedure t slve lgarithmic equatins algebraically. PC-4.11 Carry ut a prcedure t slve lgarithmic equatins graphically. SE/TE: 43-47, 431, 43, 433, 455 SE/TE: 44, 47, 430, 435, 443 SE/TE: , 43, 433, 455, 457, 458 SE/TE: 48, 433, 435, 455, 457, 458 Standard PC-5: The student will demnstrate thrugh the mathematical prcesses an understanding f the behavirs f trignmetric functins. PC-5.1 Understand hw angles are measured in either degrees r radians. PC-5. Carry ut a prcedure t cnvert between degree and radian measures. PC-5.3 Carry ut a prcedure t plt pints in the plar crdinate system. PC-5.4 Carry ut a prcedure t graph trignmetric functins by analyzing intercepts, peridic behavir, and graphs f reciprcal functins. PC-5.5 Carry ut prcedures t determine the characteristics f trignmetric functins (including dmain, range, intercepts, and asympttes). PC-5.6 Apply a prcedure t evaluate trignmetric expressins. PC-5.7 Analyze given infrmatin t write a trignmetric functin that mdels a given prblem situatin invlving peridic phenmena. SE/TE: , 473, 580, 583 SE/TE: , 514, 580, 583 SE/TE: , 67, 673, 685, 74 SE/TE: , , 581, 58 SE/TE: , , 581, 58 SE/TE: 487, 513, 515, , 563, 581, , 598, 603, 604, 609, 615, 63 SE/TE: 483, 488, 531, 53, 534, 535, 536, 547, 548, 549 6

7 PC-5.8 Analyze given infrmatin t write a trignmetric equatin that mdels a given prblem situatin invlving right triangles. PC-5.9 Carry ut a prcedure t calculate the area f a triangle when given the lengths f tw sides and the measure f the included angle. PC-5.10 Carry ut a prcedure t slve trignmetric equatins algebraically. PC-5.11 Carry ut a prcedure t slve trignmetric equatins graphically. PC-5.1 Apply the laws f sines and csines t slve prblems. PC-5.13 Apply a prcedure t graph the inverse functins f sine, csine, and tangent. PC-5.14 Apply trignmetric relatinships (including reciprcal identities; Pythagrean identities; even and dd identities; additin and subtractin frmulas f sine, csine, and tangent; and duble angle frmulas) t verify ther trignmetric identities. PC-5.15 Carry ut a prcedure t cmpute the slpe f a line when given the angle f inclinatin f the line. SE/TE: , 499, 500, 501, 581 SE/TE: 650, 653, 71, 73 SE/TE: , 636, 637 SE/TE: 66, 68, 69, 633, 637 SE/TE: , , 71, 73, A-A3 SE/TE: , , , 563 SE/TE: , 487, 586, , , 633, 639, 640, 641, 64 See prerequisite cncepts and skills. SE/TE: , 188, 71, , 500 (#66) Standard PC-6: The student will demnstrate thrugh the mathematical prcesses an understanding f the behavir f cnic sectins bth gemetrically and algebraically. PC-6.1 Carry ut a prcedure t graph the circle whse equatin is the frm (x h) + (y k) = r. PC-6. Analyze given infrmatin abut the center and the radius r the center and the diameter t write an equatin f a circle. PC-6.3 Apply a prcedure t calculate the crdinates f pints where a line intersects a circle. PC-6.4 Carry ut a prcedure t graph the ellipse whse equatin is the frm ( x h) + y k a ( ) b =1. SE/TE: 46-49, 50, 51, 5, 74 SE/TE: 46, 47, 50, 74 SE/TE: , 774, 775, 777, 801, 80 SE/TE: , 91, 946 7

8 PC-6.5 Carry ut a prcedure t graph the hyperbla whse equatin is the frm ( x h) ( y k) a PC-6.6 b = 1. Carry ut a prcedure t graph the parabla whse equatin is the frm y k = a(x h). SE/TE: , 91, 946 SE/TE: , 91, 947 8