The content is based on the National Council of Teachers of Mathematics (NCTM) standards and is aligned to state standards.

Transcription

1 Core Precalculus Precalculus is a course that combines reviews of algebra, geometry, and functions into a preparatory course for calculus. The course focuses on the mastery of critical skills and exposure to new skills necessary for success in subsequent math co urses. The first semester includes linear, quadratic, expo nential, lo garithmic, radical, po lyno mial, and ratio nal functio ns; systems of equations; and conic sections. The second semester covers trigonometric ratios and functions; inverse trigonometric functions; applications of trigonometry, including vectors and laws of cosine and sine; polar functions and no tatio n; and arithmetic o f co mplex numbers. Within each Precalculus lesso n, students are supplied with a po st-study "Checkup" activity, pro viding them the o ppo rtunity to hone their computational skills by working through a low-stakes problem set before moving on to a formal assessment. Unitlevel Precalculus assessments include a co mputer-sco red test and a scaffo lded, teacher-sco red test. The content is based on the National Council of Teachers of Mathematics (NCTM) standards and is aligned to state standards. Length: Two semesters UNIT 1: FUNCTIONS LESSON 1: WHAT IS A FUNCT ION? St udy: Relat ing t o Funct io ns Learn abo ut functio ns, their graphs, and so me special functio ns. Complete a set of practice problems on functions. Quiz: What Is a Funct io n? LESSON 2: GRAPHING FUNCT IONS St udy: Test ing and Special Funct io ns Learn the vertical line and horizontal line tests for evaluating a function. Evaluate a function for given values and explore special functio ns. Complete a set of practice problems on graphing functions. Quiz: Graphing Funct io ns LESSON 3: LINEAR FUNCT IONS 1 of 20

2 St udy: Walking t he Line Learn about slope and the three main forms of linear functions. Complete a set of practice problems on linear functions. Quiz: Linear Funct io ns LESSON 4: ARIT HMET IC SEQUENCES AND SERIES St udy: It All Adds Up Learn abo ut arithmetic sequences and series. Complete a set of practice problems on arithmetic sequences and series. Quiz: Arit hmet ic Sequences and Series LESSON 5: LINEAR EQUAT IONS AND INEQUALIT IES St udy: On Equal Fo o t ing Learn ho w to so lve linear equatio ns and inequalities. Complete a set of practice problems on linear equations and inequalities. Quiz: Linear Equat io ns and Inequalit ies LESSON 6: LINEAR SYST EMS St udy: Finding t he Po int o f Int ersect io n Find the point of intersection of linear systems using algebra, graphing, and matrices. Complete a set of practice problems on linear systems. Quiz: Linear Syst ems LESSON 7: ARIT HMET IC OF FUNCT IONS St udy: Mixing and Mat ching Learn how to add, subtract, multiply, divide, and compose functions. 2 of 20

3 Complete a set of practice problems on the arithmetic of functions. Quiz: Arit hmet ic o f Funct io ns LESSON 8: FUNCT IONS WRAP-UP Review: Funct io ns Review key calculator skills. Pract ice: Funct io ns Complete a set of practice problems. Scoring: 50 points Test (CS): Funct io ns Scoring: 60 points Test (T S): Funct io ns Scoring: 100 points LESSON 9: DIAGNOST IC Diagno st ic: Funct io ns UNIT 2: QUADRATIC FUNCTIONS LESSON 1: FORMS OF QUADRAT IC FUNCT IONS St udy: Express Yo urself Express quadratic functio ns in a variety o f fo rms. Complete a set of practice problems on forms of quadratic functions. Quiz: Fo rms o f Quadrat ic Funct io ns 3 of 20

4 LESSON 2: GRAPHING QUADRAT IC FUNCT IONS St udy: Put t ing t he Pieces To get her Use key components such as vertex, axis of symmetry, and x- and y-intercepts to sketch the graphs of quadratic functions and so lve quadratic inequalities. Complete a set of practice problems on graphing quadratic functions. Quiz: Graphing Quadrat ic Funct io ns LESSON 3: T RANSFORMAT IONS St udy: Get t ing a Mo ve On Learn how to reflect about the x- and y-axes. Learn about horizontal and vertical shifts and horizontal and vertical stretches. Complete a set of practice problems on transformations. Quiz: Transfo rmat io ns LESSON 4: SOLVING QUADRAT IC EQUAT IONS St udy: Answers t o Yo ur Quest io ns Use factoring and the quadratic formula to solve an equation. Also relate solutions to zeros and work with complex numbers. Complete a set of practice problems on solving quadratic equations. Quiz: So lving Quadrat ic Equat io ns LESSON 5: APPLICAT IONS OF QUADRAT IC FUNCT IONS St udy: So lving Pro blems Using Quadrat ic Funct io ns Set up and solve application problems involving quadratic functions. Complete a set of practice problems on applications of quadratic functions. Quiz: Applicat io ns o f Quadrat ic Funct io ns 4 of 20

5 LESSON 6: QUADRAT IC FUNCT IONS WRAP-UP Review: Quadrat ic Funct io ns Review key calculator skills. Pract ice: Quadrat ic Funct io ns Complete a set of practice problems. Scoring: 50 points Test (CS): Quadrat ic Funct io ns Scoring: 60 points Test (T S): Quadrat ic Funct io ns Scoring: 100 points LESSON 7: DIAGNOST IC Diagno st ic: Quadrat ic Funct io ns UNIT 3: POLYNOMIAL AND RATIONAL FUNCTIONS LESSON 1: POLYNOMIAL EXPRESSIONS St udy: What Is a Po lyno mial? Learn what makes a polynomial and how to test for one. Complete a set of practice problems on polynomial expressions. Quiz: Po lyno mial Expressio ns LESSON 2: DIVIDING POLYNOMIALS St udy: Synt het ic Do esn't Mean Fake Learn the technique for dividing polynomials and testing for factors. Complete a set of practice problems on dividing polynomials. 5 of 20

6 Quiz: Dividing Po lyno m ials LESSON 3: SOLVING POLYNOMIAL EQUAT IONS St udy: T hese Ro o t s Gro w Deep Find all solutions to polynomial equations. Complete a set of practice problems on solving polynomial equations. Quiz: So lving Po lyno mial Equat io ns LESSON 4: GRAPHING POLYNOMIAL FUNCT IONS St udy: What Go es Up So met imes Co mes Do wn Explore the behavior of polynomial functions and find key points of the graph of the function. Complete a set of practice problems on graphing polynomial functions. Quiz: Graphing Po lyno mial Funct io ns LESSON 5: RAT IONAL FUNCT IONS St udy: To p and Bo t t o m Identify rational functions, find domain and range, look at asymptotes, and sketch complete graphs. Complete a set of practice problems on rational functions. Quiz: Rat io nal Funct io ns LESSON 6: POLYNOMIAL AND RAT IONAL FUNCT IONS WRAP-UP Review: Po lyno mial and Rat io nal Funct io ns Review key calculator skills. Pract ice: Po lyno mial and Rat io nal Funct io ns 6 of 20

7 Complete a set of practice problems. Scoring: 50 points Test (CS): Po lyno mial and Rat io nal Funct io ns Scoring: 60 points Test (T S): Po lyno mial and Rat io nal Funct io ns Scoring: 100 points LESSON 7: DIAGNOST IC Diagno st ic: Po lyno mial and Rat io nal Funct io ns UNIT 4: EXPONENTIAL AND LOGARITHMIC FUNCTIONS LESSON 1: EXPONENT S AND RADICALS St udy: Rat io nal Expo nent s and Radical Expressio ns Learn the rules of exponents and how to express radicals. Complete a set of practice problems on exponents and radicals. Quiz: Expo nent s and Radicals LESSON 2: EXPONENT IAL FUNCT IONS St udy: Expo nent ial Funct io ns and T heir Graphs Explo re the basic expo nential graphs. Complete a set of practice problems on exponential functions. Quiz: Expo nent ial Funct io ns LESSON 3: GEOMET RIC SEQUENCES St udy: Leaps and Bo unds Learn abo ut geo metric sequences and series. 7 of 20

8 Complete a set of practice problems on geometric sequences. Quiz: Geo met ric Sequences LESSON 4: INT RODUCT ION T O LOGARIT HMS St udy: Lo garit hms Learn how logarithms are used to express exponents. Complete a set of practice problems on logarithms. Quiz: Int ro duct io n t o Lo garit hms LESSON 5: GRAPHS OF LOGARIT HMIC FUNCT IONS St udy: Undo ing What Yo u Have Do ne Learn the graphs o f key lo garithmic functio ns. Complete a set of practice problems on graphs of logarithmic functions. Quiz: Graphs o f Lo garit hmic Funct io ns LESSON 6: APPLICAT IONS OF LOGARIT HMS St udy: Lo gs Are Nat ural So lve applicatio n pro blems invo lving expo nential and lo garithmic expressio ns. Complete a set of practice problems on applications of logarithms. Quiz: Applicat io ns o f Lo garit hms LESSON 7: EXPONENT IAL AND LOGARIT HMIC FUNCT IONS WRAP-UP Review: Expo nent ial and Lo garit hmic Funct io ns Review key calculator skills. 8 of 20

9 Pract ice: Expo nent ial and Lo garit hmic Funct io ns Complete a set of practice problems. Scoring: 50 points Test (CS): Expo nent ial and Lo garit hmic Funct io ns Scoring: 60 points Test (T S): Expo nent ial and Lo garit hmic Funct io ns Scoring: 100 points LESSON 8: DIAGNOST IC Diagno st ic: Expo nent ial and Lo garit hmic Funct io ns UNIT 5: CONIC SECTIONS LESSON 1: INT RODUCT ION T O CONIC SECT IONS St udy: Ho w Do Yo u Cut a Co ne? Explore the various ways a cone can be cut to produce conic sections such as a circle. Complete a set of practice problems on conic sections. Quiz: Int ro duct io n t o Co nic Sect io ns LESSON 2: ELLIPSES St udy: St ret ching Circles Learn how ellipses are defined and formed. Complete a set of practice problems on ellipses. Quiz: Ellipses LESSON 3: HYPERBOLAS St udy: Turning Inside Out Learn how hyperbolas are defined and formed. 9 of 20

10 Complete a set of practice problems on hyperbolas. Quiz: Hype rbo las LESSON 4: PARABOLAS St udy: A Familiar Friend Learn how parabolas are defined and formed. Complete a set of practice problems on parabolas. Quiz: Parabo las LESSON 5: SYST EMS OF CONIC SECT IONS St udy: Finding t he Int ersect io ns Find the solutions to systems of conic sections. Complete a set of practice problems on systems of conic sections. Quiz: Syst ems o f Co nic Sect io ns LESSON 6: CONIC SECT IONS WRAP-UP Review: Co nic Sect io ns Review key calculator skills. Pract ice: Co nic Sect io ns Complete a set of practice problems. Scoring: 50 points Test (CS): Co nic Sect io ns 10 of 20

11 Scoring: 60 points Test (T S): Co nic Sect io ns Scoring: 100 points LESSON 7: DIAGNOST IC Diagno st ic: Co nic Sect io ns UNIT 6: PRECALCULUS SEMESTER 1 REVIEW AND EXAM LESSON 1: PREPARING FOR T HE SEMEST ER EXAM Review: Precalculus Semest er 1 Prepare fo r the semester exam by reviewing key co ncepts co vered in Precalculus Semester min Exam: Semest er Exam (Co mput er-sco red) Take a computer-scored exam to demonstrate your mastery of concepts and skills covered in Precalculus Semester 1. Scoring: 150 points Final Exam: Semest er Exam (Teacher-Sco red) Take a teacher-sco red exam to demo nstrate yo ur mastery o f co ncepts and skills co vered in Precalculus Semester 1. Scoring: 100 points UNIT 7: INTRODUCTION TO TRIGONOMETRY LESSON 1: RIGHT T RIANGLES St udy: All t he Right Mo ves Review right triangles and get an introduction to trigonometric ratios. Complete a set of practice problems on trigonometry. Quiz: Int ro duct io n t o Trigo no met ry LESSON 2: ANGLES AND RADIANS St udy: A Slice o f Pi Learn abo ut angles expressed in degrees and radians. Complete a set of practice problems on angles and radians. Quiz: Angle s and Radians 11 of 20

12 LESSON 3: T RIGONOMET RIC RAT IOS AND T HE UNIT CIRCLE St udy: Terminal Co ndit io ns Learn the six trigonometric ratios and how the unit circle defines them. St udy: Pyt hago rean T heo rem Review the Pythago rean theo rem. Duration: 0 hr 30 min Complete a set of practice problems on trigonometric functions and the unit circle. Quiz: Trigo no met ric Funct io ns and t he Unit Circle LESSON 4: INT RODUCT ION T O T RIGONOMET RY WRAP-UP Review: Int ro duct io n t o Trigo no met ry Review key calculator skills. Pract ice: Int ro duct io n t o Trigo no met ry Complete a set of practice problems. Scoring: 50 points Test (CS): Int ro duct io n t o Trigo no met ry Scoring: 60 points Test (T S): Int ro duct io n t o Trigo no met ry Scoring: 100 points LESSON 5: DIAGNOST IC Diagno st ic: Int ro duct io n t o Trigo no met ry UNIT 8: TRIGONOMETRIC FUNCTIONS LESSON 1: GRAPHS OF SINE AND COSINE St udy: What Is a Sinuso id Anyway? Learn to build the graphs of sine and cosine. 12 of 20

13 Complete a set of practice problems on graphs of sine and cosine. Quiz: Graphs o f Sine and Co sine LESSON 2: GRAPHS OF OT HER FUNCT IONS St udy: Graphing Mo re Trigo no met ric Funct io ns Learn the graphs of the other four trigonometric functions. Complete a set of practice problems on graphs of other functions. Quiz: Graphs o f Ot her Funct io ns LESSON 3: SIMPLE T RANSFORMAT IONS OF SINUSOIDS St udy: St ret ches, Shift s, and Flips, Oh My! Learn ho w to transfo rm trigo no metric graphs with reflectio ns, shifts, and stretches. Complete a set of practice problems on transformations of periodic graphs. Quiz: Simple Transfo rmat io ns o f Sinuso ids LESSON 4: GENERAL T RANSFORMAT IONS OF PERIODIC GRAPHS St udy: Put t ing It All To get her Learn ho w to transfo rm trigo no metric graphs with reflectio ns, shifts, and stretches. Complete a set of practice problems on transformations of trigonometric functions. Quiz: General Transfo rmat io ns o f Perio dic Graphs LESSON 5: T RIGONOMET RIC FUNCT IONS WRAP-UP Review: Trigo no met ric Funct io ns 13 of 20

14 Review key calculator skills. Pract ice: Trigo no met ric Funct io ns Complete a set of practice problems. Scoring: 50 points Test (CS): Trigo no met ric Funct io ns Scoring: 60 points Test (T S): Trigo no met ric Funct io ns Scoring: 100 points LESSON 6: DIAGNOST IC Diagno st ic: Trigo no met ric Funct io ns UNIT 9: WORKING WITH TRIGONOMETRIC FUNCTIONS LESSON 1: INVERSE T RIGONOMET RIC FUNCT IONS St udy: Arc! Who Go es T here? Learn how to solve for angles using the inverse trigonometric ratios. Complete a set of practice problems on inverse trigonometric functions. Quiz: Inverse Trigo no met ric Funct io ns LESSON 2: SOLVING T RIGONOMET RIC EQUAT IONS St udy: 2 Pi o r No t 2 Pi? Learn to find all solutions to a trigonometric equation. Complete a set of practice problems on solving trigonometric equations. Quiz: So lving Trigo no met ric Equat io ns LESSON 3: MODELING SIMPLE HARMONIC MOT ION St udy: Yo u Are Get t ing Sleepy 14 of 20

15 Explo re simple harmo nic mo tio n settings. Complete a set of practice problems on simple harmonic motion. Quiz: Mo deling Simple Harmo nic Mo t io n LESSON 4: WORKING WIT H T RIGONOMET RIC FUNCT IONS WRAP-UP Review: Wo rking wit h Trigo no met ric Funct io ns Review key calculator skills. Pract ice: Wo rking wit h Trigo no met ric Funct io ns Complete a set of practice problems. Scoring: 50 points Test (CS): Wo rking wit h Trigo no met ric Funct io ns Scoring: 60 points Test (T S): Wo rking wit h Trigo no met ric Funct io ns Scoring: 100 points LESSON 5: DIAGNOST IC Diagno st ic: Wo rking wit h Trigo no met ric Funct io ns UNIT 10: TRIGONOMETRIC IDENTITIES LESSON 1: IDENT IT IES AND PROOF St udy: Overco ming an Ident it y Crisis Learn how to prove identities. Complete a set of practice problems on identities and proof. Quiz: Ident it ies and Pro o f 15 of 20

16 LESSON 2: T RIGONOMET RIC IDENT IT IES St udy: Just t he Fact s, Ma'am Learn the key trigo no metric identities. Complete a set of practice problems on trigonometric identities. Quiz: Trigo no met ric Ident it ies LESSON 3: APPLICAT IONS OF IDENT IT IES St udy: Use 'Em o r Lo se 'Em Use the key trigo no metric identities to so lve trigo no metric equatio ns. Complete a set of practice problems on identities. Quiz: Applicat io ns o f Ident it ies LESSON 4: T RIGONOMET RIC IDENT IT IES WRAP-UP Review: Trigo no met ric Ident it ies Review key calculator skills. Pract ice: Trigo no met ric Ident it ies Complete a set of practice problems. Scoring: 50 points Test (CS): Trigo no met ric Ident it ies Scoring: 60 points Test (T S): Trigo no met ric Ident it ies Scoring: 100 points LESSON 5: DIAGNOST IC 16 of 20

17 Diagno st ic: Trigo no met ric Ident it ies UNIT 11: APPLICATIONS OF TRIGONOMETRY LESSON 1: LAW OF COSINES St udy: It 's t he Law Use the law of cosines to solve triangles. Complete a set of practice problems using the law of cosines. Quiz: Law o f Co sines LESSON 2: LAW OF SINES St udy: T he Lo ng Arm o f t he Law Use the law of sines to solve triangles and to explore the ambiguous case. Complete a set of practice problems using the law of sines. Quiz: Law o f Sines LESSON 3: VECT ORS St udy: Get t ing Aro und Use vectors to describe motion. Complete a set of practice problems on vectors. Quiz: Vect o rs LESSON 4: APPLICAT IONS OF T RIGONOMET RY WRAP-UP Review: Applicat io ns o f Trigo no met ry Review key calculator skills. 17 of 20

18 Pract ice: Applicat io ns o f Trigo no met ry Complete a set of practice problems. Scoring: 50 points Test (CS): Applicat io ns o f Trigo no met ry Scoring: 60 points Test (T S): Applicat io ns o f Trigo no met ry Scoring: 100 points LESSON 5: DIAGNOST IC Diagno st ic: Applicat io ns o f Trigo no met ry UNIT 12: COMPLEX NUMBERS LESSON 1: POLAR COORDINAT ES St udy: T he Po lar Express Learn to use polar coordinates to express locations of points. Complete a set of practice problems on polar coordinates. Quiz: Po lar Co o rdinat es LESSON 2: GRAPHS OF POLAR FUNCT IONS St udy: Fro m Lemniscat es t o Limaço ns Produce a variety of new graphs using polar functions. Complete a set of practice problems on graphs of polar functions. Quiz: Graphs o f Po lar Funct io ns LESSON 3: POLAR FORM OF COMPLEX NUMBERS St udy: A Go o d Co mplex t o Have Express co mplex numbers in po lar fo rm. 18 of 20

19 Complete a set of practice problems on the polar form of complex numbers. Quiz: Po lar Fo rm o f Co mplex Numbers LESSON 4: ARIT HMET IC OF COMPLEX NUMBERS St udy: T his Mat h Isn't Co mplex Add, subtract, multiply, and divide co mplex numbers. Complete a set of practice problems on the arithmetic of complex numbers. Quiz: Arit hmet ic o f Co mplex Numbers LESSON 5: POWERS AND ROOT S OF COMPLEX NUMBERS St udy: Feel t he Po wer Express powers and roots of complex numbers. Complete a set of practice problems on powers and roots of complex numbers. Quiz: Po wers and Ro o t s o f Co mplex Numbers LESSON 6: COMPLEX NUMBERS WRAP-UP Review: Co mplex Numbers Review key calculator skills. Pract ice: Co mplex Numbers Complete a set of practice problems. Scoring: 50 points Test (CS): Co mplex Numbers Scoring: 60 points 19 of 20

20 Test (T S): Co mplex Numbers Scoring: 100 points LESSON 7: DIAGNOST IC Diagno st ic: Co mplex Numbers UNIT 13: PRECALCULUS SEMESTER 2 REVIEW AND EXAM LESSON 1: PREPARING FOR T HE SEMEST ER EXAM Review: Semest er Review Prepare fo r the semester exam by reviewing key co ncepts co vered in Precalculus Semester 2. Duration: 2 hr Exam: Semest er Exam (Co mput er-sco red) Take a computer-scored exam to demonstrate your mastery of concepts and skills covered in Precalculus Semester 2. Scoring: 150 points Final Exam: Semest er Exam (Teacher-Sco red) Take a teacher-sco red exam to demo nstrate yo ur mastery o f co ncepts and skills co vered in Precalculus Semester 2. Scoring: 100 points 20 of 20