Honors Precalculus Period E (R,B,Y,P,W) Year Course: 2007-2008
Mrs. Murphy smurphy@academyoftheholycross.org; voice mail x546
Office hours: Math Lab one day a week after school; by appointment
Read and write and study the introductory material and examples before attempting the assignments. Get help with your questions BEFORE coming to class. If you still have questions, ask. Dates for lessons may change; test, quiz, group assignment dates will not change. Note: Lessons and Section # may not be the same. A lesson may take one class, less than one class, or more than one class.
NOTE: syllabus is available on schoolnotes.com
CHAPTER 4: TRIGONOMETRIC FUNCTIONS pp. 445-567 Assignment Guide (4 weeks)
“Do not worry about your difficulties in mathematics. I assure you mine are still greater.” Albert Einstein
NOTE: CHAPTER PROJECT DUE:
Summer Reading Assign. & Summer Review Packet Due
Introductory Lesson: 1.1 Graphs and Graphing Utilities pp. 128-137
Obj: To give a brief overview of course & expectations; to interpret graphs; to sketch solutions in the coordinate plane.
Asgn: pp.135-137(Use graph paper for points, equations) 1-12, 13-27 odd,29-32,42,44,46,55-60,67,69,72-78
Lesson 1: 4.1: Angles & Radian Measures: pp. 446-460.
Obj: To recognize & use the vocabulary of angles, use degree & radian measure, convert between degrees & radians, draw angles in standard position, find coterminal angles, find length of arc, linear & angular speed.
Assign: pp. 458-460: 7-39 odd, 41-55 (use circle graph), 57-75 odd, 87,92,93,97,98,110,111.
Lesson 2: 4.2: Trig Functions: The Unit Circle: pp. 461-472
Obj: To use the unit circle to define trig functions, use properties of trig functions, use fundamental identities, to evaluate trig functions.
Assign: pp. 472-474: 5-24,25-47 odd,53-60, 61-69 odd,82,85,88,90,94
Lesson 3:4.3: Right Triangle Trigonometry: pp. 475-487
Obj: To use right triangle to evaluate trig functions, use special angles, use cofunctions and complements, solve applications.
Assign: pp. 484-487: 2-8 even, 9-35 odd, 45,54,56,57,58,62,65,68-73
Lesson 4: 4.4: Trig Functions of Any Angle: pp. 487-501
Obj: To use the definitions of the trig functions of any angle, to find and use reference angles.
Assign: pp. 499-501: 2-16 even, 17-22,24,26,28,31,35-45 odd, 54,56,62-76 even, 99,100,103,105-109
Mid Chapter Check Point: pp. 500-501: 1-4, 6,7,9,10,11,12,14,15,16-24 even, 27-30
Quiz: 4.1-4.4; Study 4.5. Pair Project assigned, DUE 9-15. p.557: 2,4,6,8; p.558: 30-36 even,42,44,46; p.565: 44; p.566: 114,118,120
Lesson 5: 4.5: Graphs of Sin x and Cos x: pp. 501-521. Trig Applications
Obj: To graph sin x, cos x; to use transformations.
In class: complete pair project. pp. 518-521: 61,63,65,85,87,93,101,102 111,112
Assign: Complete problems; study section 4.6
Lesson 6: 4.6: Graphs of Other Trig Functions: pp. 521-534.
Obj: To graph tan x, cot x, sec x, csc x; to use transformations
Assign: pp. 531-534: 1-4,13-16,25-28, (use graph paper) 6-12 even, 18-24 even, 30-44 even, 59,65,68,71,77,79,87,89-91
Project: Modeling Real World Functions (hand in)
In class/ complete at home: SAT trig questions; trig graph worksheet
Lesson 7: 4.7: Inverses: pp. 534-549
Obj: To evaluate inverse trig functions.
Assign: pp. 547-549: 2-18 even, 34-46 even, 47-53 odd, 63,93,100-106
Lesson 8: 4.8: Applications pp. 549-560
Assign: pp. 557-560: 13-16,18,21, 38,42-62 even
For review: pp. 560-568: Summary, Ch.Rev.Ch. Test: 14-18,23-25; CHAPTER PROJECT DUE
Test; Study 5.1
CHAPTER 5: ANALYTIC TRIGONOMETRY pp.569-625 Assignment guide (3 weeks)
“Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty.” Archimedes
NOTE: CHAPTER PROJECT DUE: PORTFOLIO DUE .
Lesson 1: 5.1: Verifying Trig Identities : pp.570-580
. Obj. To use fundamental identities to verify identities
Assign: pp. 578-580: 1-17 odd,23,33,39,47,51.
Hand in (by 10-5): p. 578: 14,16,18,24,26,30,32,52
Lesson 2: 5.2: Sum, Difference Identity: pp.580-589.
Obj.. To use these formulas to solve problems.
Assign: pp. 587-589: 1,3,14,15,18,21,33,36,38,51,52,53,58,62,63,81-86
Hand in (by 10-11): Identity Worksheet
Lesson 3: 5.3: Double Angle, Power Reducing, Half Angle Formulas: pp. 590-600
Obj. To use double & half-angle identities, use power reducing formulas.
Assign: pp. 597-600: 4-6,8,12,23,26,35,40,42,43,47-49,55,79,85,86
Mid Chapter Check Point: p. 600: 1-7,12,16,19-23 26; Identity Worksheet DUE
QUIZ: 5.1-5.3 study 5.4 Chapter Project assigned DUE 10-23
Lesson 4: 5.4: Product-Sum, Sum to Product Formulas: pp. 601-608.
Obj. To use these identities to simplify expressions, to solve equations.
Assign: pp. 605-606: 1-4,5-11 odd, 13-16,17-33 odd
Lesson 5: 5.5: Solving Trig Equations :pp.608-621.
Obj. To solve trig equations
Assign: pp. 619-621: 11-31 odd, 39-61 odd, 85,87,97-113 odd, 135,136,137,138,152
Hand in (by 10-20): p. 621: 40, 63-73 odd, 139,142,143
For Review: p.622-625: Ch. Summary, Ch. Review, Ch.Test: 1-18
CHAPTER PROJECT DUE; PORTFOLIO DUE
TEST; study 6.1
CHAPTER 6: ADDITIONAL TOPICS IN TRIGONOMETRY pp627-707 Assignment guide (4 weeks)
Mathematics is a science, an art, a way of thinking. Appearing in nature, art, music, architecture, history, science, literature – its influence is present in every facet of the universe.
NOTE: CHAPTER PROJECT DUE:
Lesson 1: 6.1: Law of Sines: pp.628-638.
Obj. To use the identity to solve problems including the ambiguous case; to find area.
Assign: pp.635-638: 2,4,10-26 even, 34,36, 48-60 even, 72
Hand in (by 10-27): Law of Sines Worksheet
SAT/ACT practice
Lesson 2: 6.2: Law of Cosines: pp. 639-646.
Obj. To use the identity to solve problems; to find area using Heron’s formula.
Assign: pp.643-646: 2-8 even, 14, 18, 26,28,37, 38-52 even
Mid-Chapter Check Point: p. 668: 1-11
Quiz: 6.1-6.2 Assign: Study 6.3; p. 655: 1-20
Lesson 3: 6.3: Polar Coordinates: pp. 647-657.
Obj. To plot points in the polar coordinate system, find multiple sets of points for a given point, convert polar to rectangular & vice versa, convert equations from polar to rectangular & vice versa.
Assign: pp.655-657: 27-32,33-73 odd,83,84,88-95
Lesson 3: 6.4: Graphs of Polar Equations: pp. 657-688.
Obj. To use point plotting to graph polar equations, to use symmetry to plot polar equations.
Assign: pp. 666-668: 1-6, 7-33 odd, 52-56, 83-88
Hand in : pp.666-668: 58-74 even (use graph paper)
Mid-Chapter Check Point: p. 668: 12,14,16, 18-25, 28-32 even
Lesson 3: 6.5: Complex Numbers in Polar Form: pp. 669-680.
Obj. To plot complex numbers, find the absolute value, write complex numbers in polar form, find products, quotients, powers and roots of complex numbers in polar form.
Assign: pp.678-679: 1-39 odd, 43, 45,47,51,53,57,61,65-73 odd, 74,
Hand in ( ): p. 679-680: 81, 96-101,107
Quiz: 6.4-6.5 Assign: Study 6.6; pp. 690-691: 1,9,13-17 odd, 21,25
Note: Students may work together on all vector problems.
Lesson 3: 6.6: Vectors: pp. 680-693.
Obj. To use magnitude & direction to show vectors are equal, use scalar multiplication, addition & subraction, represent vectors in the rectangular coordinate system, use vectors i and j, find unit vectors, write vector in terms of magnitude and direction, solve problems.
Assign: pp.690-691:31,35,41,47,49,61,63,
Hand in ( ) pp.691-692: 66,69,71,75,77,79,83,85
Lesson 3: 6.7: Dot Product: pp. 693-702.
Obj. To find the dot product, find the angle between vectors, determine if vectors are orthogonal, find the projection of a vector, express a vector as the sum of two orthogonal vectors, compute work.
Assign: pp.700-701: 1,3,9,11,17,19,23-29 odd, 33,35,45-49 odd
Hand in ( ) pp. 701-702 51,55,63,68-70, 78
For review: pp. 702-707: Summary, Ch. Review, Ch. Test: 1-22; CHAPTER PROJECT DUE
TEST Assign: Study pp. 239-241 (Circles); pp. 239-241: 2-8 even, 20-26 even,32-38 even, 42-48 even
CHAPTER 9: CONIC SECTIONS & ANALYTIC GEOMETRY pp. 849-923 Assignment guide (4 weeks)
“The path to success is traveled by those who believe in themselves.” Unknown
NOTE: CHAPTER PROJECT DUE: PORTFOLIO DUE:
Lesson 1: 1.9: Distance & Midpoint Formulas; Circles: pp.233-241.
Obj. To find the distance between 2 pts., to find the midpoint of a segment, to write the standard form and general form of a circle, to find the center and radius of a circle.
Assign: pp.239-241: 2-8 even, 20-26 even, 32-38 even, 42-56 even, 63,80
Lesson 2: 9.1: The Ellipse: pp. 850-861.
Obj. To graph ellipses, write equations of ellipses, solve problems.
Assign: pp.859-861: 2-8 even, 14-28 even, 31-45 odd, 51-57 odd,65,72,73
Lesson 3: 9.2: The Hyperbola: pp. 862-875.
Obj. To find vertices and foci, write equation in standard form, graph hyperbolas, solve problems.
Assign: pp.873-875: 1-4,5-23 odd,27,29,33-39 odd, 43,45,47,63, 68,69,70,79
Lesson 3: 9.3: The Parabola: pp. 876-887.
Obj. To graph parabolas, write equations, solve problems.
Assign: pp. 885-887: 1-4, 5-29 odd, 31-34, 35-47 odd, 63,6572,73.81
Mid-Chapter Check Point: p. 888: 1-21, 23-31 odd
Quiz: 1.9, 9.1-9.3
*Lesson 3: 9.4: Rotation of Axes: pp. 889-900.
Obj. To identify conics, use rotation of axes formulas, write equations of rotated conics.
Assign: pp.889-00900: 1-17 odd, 24,27,29,36,39-44,49-53
Lesson 3: 9.5: Parametric Equations: pp901-909.
Obj. To graph plane curves, eliminate the parameter, find parametric equations for functions.
Assign: pp.907-909: 1-15 odd, 19, 21-29 odd, 41-44,45-57 odd, 69, 79,80
*Lesson 3: 9.6: Conic Sections in Polar Coordinates: pp. 910-918.
Obj. To define conics in terms of a focus & a directrix, graph polar equations of conics.
Assign: pp.917-918: 1-15 odd, 33-37,49
For review: pp. 918-923: Summary, Ch. Review, Ch. Test: 1-17; CHAPTER PROJECT DUE
TEST; PORTFOLIO DUE
SEMESTER 2
CHAPTER 10: SEQUENCES, INDUCTION, PROBABILITY pp. 925-1002 Assignment guide (4 weeks)
“The path to success is traveled by those who believe in themselves.” Unknown
NOTE: CHAPTER PROJECT DUE:
Lesson 1: 10.1: Sequences & Summation Notation: pp.926-936.
Obj. To find terms of sequences, write recursive form, use factorial and summation notation.
Assign: pp.933-936: 2-8 even, 2-10 even, 13-15,17,20,25-39 odd,43-51 odd,55,73,82,95
Continue 10.1
Lesson 2: 10.2: Arithmetic Sequences: pp. 936-945.
. Obj: To find common differences, write terms of sequences, use formula for general term, find sum.
Assign: pp.943-945: 2-10 even, 15-31 odd,35,38,45,64-68
Continue 10.2
Lesson 3: 10.3: Geometric Sequences: pp. 945-958.
Obj. To find common ration, write terms, use formula for general terms, find sum.
Assign: pp.955-958: 2-8 even,9,11,17,19,23,25,27,31,34,37,41,45,47,51,53,55,68,73,77,97
Continue 10.3
Mid-Chapter Check Point: pp. 958-959: 1-19; Chapter Project assigned
Quiz: 10-1-10.3
Lesson 4: 10.4: Mathematical Induction: pp. 959-966.
Obj. To understand the principles of mathematical induction, prove statements.
Assign: pp. 965-966: 1-15 odd
Continue 10.4
Lesson 5: 10.5: Binomial Theorem: pp. 967-973.
Obj. To evaluate binomial coefficients, expand binomials, use Pascal’s triangle, find terms.
Assign: pp.972-973: 2-8 even,12-20 even,25,33,40,43,48,73
Lesson 6: 10.6: Counting Principles, Permutations: pp. 974-983.
Obj. To use the fundamental counting principle, use permutations and combinations, solve problems.
Assign: pp.981-983: 2-16 even,17,19,29-37 odd,41-55 odd,57,59,65,66,77
Continue 10.6;
Lesson 7: 10.7: Probability: pp. 984-997.
Obj. To compute empirical & theoretical probability, find probability of events.
Assign: pp.994-997: 11-25 odd, 31-36,43,44,45,47,51,53,67
Continue 10.6;
For review: Summary, Ch. Review, Ch. Test: p. 1002: 1-30
TEST; CHAPTER PROJECT DUE
CHAPTER 1: FUNCTIONS & GRAPHS Assignment Guide (4weeks)
Mathematics is a science, an art, a way of thinking. Appearing in nature, art, music, architecture, history, science, literature – its influence is present in every facet of the universe.
NOTE: CHAPTER PROJECT DUE: PORTFOLIO DUE:
Lesson 1: 1.2 Basics of Functions & Their Graphs pp. 138-154
Obj: To find domain and range, distinguish between a relation & a function, evaluate & graph functions.
Assign: pp. 149-154: 1-37 odd, 42.44,55-76,78-94 even, 105,106,112,114,116,121
Lesson 1: continued
Lesson 2: 1.3 More on Functions & Their Graphs pp. 154-168
Obj: To find & simplify a difference quotient, use piecewise functions, identify properties of functions (increasing, decreasing, constant, maxima, minima, even, odd, symmetries), graph step functions.
Assign: pp, 163-168: 3,7,23,27,29-44,45,47,49,57,58,61,64,85-88, 98-100,104,106
Lesson 2: continued
Mid Chapter Check Point: pp. 193-194: 1-24, 36, 37, 38
Quiz: 1.2-1.3 Chapter project assigned
Lesson 3: 1.6 Transformations of Functions pp. 194-208
Obj: To recognize common functions, use rigid and nonrigid transformations, graph functions using transformations.
Assign: pp. 206-209: (Use graph paper for graphs.) 17-32,67-80,129-134,137,140
Lesson 3: continued
Lesson 4: 1.7: Combinations of Functions pp. 209-222
Obj: To use the algebra of functions; to write the composition of functions; to find domain of functions.
Asgn: pp.219-222: 7,9,11,17,19,31,35,39,51,57,59,81,82,90,92,99,100,110,111,116
Lesson 4: continued
Lesson 5: 1.8: Inverse Functions pp. 222-233.
Obj: To find, graph, verify existence of inverse functions., to use the horizontal line test
Assign: pp. 231-233: 15,29-38,41,53-58,7-74,87
Lesson 5: continued
Lesson 7: 1.10: Modeling with Functions pp. 242-255
Obj: To use functions to model real-life situations.
Assign: pp. 250-255: 1,9,15,22,24,35,37,53
For Review: pp. 255-264: Summary, Ch. Review, Ch. Test p. 263-264: 1-3,9,11,1517,18,22,23,30,37; CHAPTER PROJECT DUE
TEST; PORTFOLIO DUE; PI DAY PROJECT ASSIGNED: DUE
SECTIONS FROM CHAPTERS 2,3,7: FUNCTIONS & GRAPHS CONTINUED Assignment Guide (4weeks)
Mathematics is a science, an art, a way of thinking. Appearing in nature, art, music, architecture, history, science, literature – its influence is present in every facet of the universe.
NOTE: PI DAY Project DUE ; CHAPTER PROJECT DUE:
Lesson 1: 2.3: Polynomial Functions pp. 287-301
Obj:To recognize characteristics of polynomial functions, to factor and find zeros, to graph functions.
Assign: pp. 297-301: 1-18, 19-53 odd, 82-89103,104
Lesson 1: continued
2.5: Zeros
Lesson 2: 2.6: Rational Functions pp. 326-346
Obj: To find domain, identify asymptotes, use transformations, graph.
Assign: pp.324-346: 1-7 odd, 9-20, 21-53 odd, 57-63 odd. 71, 89,105-109, 114, 116,117
Lesson 2: continued PI DAY project due
2.7: Inequalities
Quiz; PI DAY; Chapter project assigned
Lesson 3: 3.1: Exponential Functions pp. 376-387
Obj: To evaluate and graph exponential functions; to use compound interest formulas.
Assign: pp. 384-387: 11,15,20-24,25-33 odd, 35-41 odd, 53,55,66,67,73,86,87
Lesson 3: continued
Lesson 4: 3.2: Logarithmic Functions pp. 388-400
Obj: To change from log to exp form, change from exp to log form, to evaluate and use properties of common and natural logs, to graph.
Assign: pp. 397-400: 1-45 odd, 47-52,53,55,57,65,71,81-97 odd, 124,135
Lesson 4: continued
Lesson 5: 3.3: Properties pp. 400-407
Obj: To use the product, quotient, power rules to expand and condense expressions; to use the change-of-base formula.
Assign: pp. 407-409: 1-35 odd,41-65 odd,71,79,103,121
Lesson 5: continued
Mid-Chapter check point: p. 409: 1,2,4,6.7,9,10-26
Quiz; Study 3.4
Lesson 6: 3.4: Equations pp. 410-418
Obj: To solve exponential and logarithmic equations; to solve problems.
Assign: pp. 418-421: 1-35 odd,41-47 odd, 49-81 odd,105-111 odd, 135,136
Lesson 6: continued
Lesson 7: 3.5: Growth and Decay pp. 422-433
Obj: To model exponential growth and decay; to use logistic models and Newton’s Law of Cooling; to model data.
Assign: pp. 433-437: 1-6, 9-12,, 19,21,31,33,36,38,62
For Review: pp. 437-442: Summary, Ch. Review, Ch. Test p. 443: 1=18, 20-39;
CHAPTER PROJECT DUE
Test; Study 7.3 Partial Fractions pp. 737-741
Lesson 8: 7.3: Partial Fractions pp.737-741
Obj:To decompose P/Q, where Q has a variety of factors.
Assign: pp. 745-746: 9,13,15,17,21,25, 53
Lesson 8: continued
Review
Quiz; Study 11.1: pp. 1006-1013
CHAPTER 11: INTRODUCTION TO CALCULUS Assignment Guide (4weeks)
Mathematics is a science, an art, a way of thinking. Appearing in nature, art, music, architecture, history, science, literature – its influence is present in every facet of the universe.
NOTE: PROJECT: p. 1029: 80, 81 DUE ; PORTFOLIL DUE:
Lesson 1: 11.1 Finding Limits Using Tables; AMSCO Section 1: The Meaning of Limit
Obj:To understand limit notation, find limits using tables, find limits using graphs, find one-sided limits and use them to determine if a limit exists.
Assign: Read and study introductory material. Exercises: AMSCO: p.7: 1-14; Text: p. 1013: 1-17 odd
Lesson 1: continued
Assign: AMSCO: p. 8: 15-20; Text: pp. 1013-1015: 19-53 odd
Lesson 1: continued
Assign: (Hand in) AMSCO: p. 9: 21-26; Text: 71
Lesson 2: 11.2: Finding Limits Using Properties of Limits; AMSCO Section 2: Properties of Limits
Obj: To find limits of constant functions and the identity function, limits using properties of limits, one-sided limits, limits of fractional expressions in which the limit of the denominator is zero.
Assign: Read and study introductory material. Exercises: AMSCO: p.14: 1-19
Lesson 2: continued; AMSCO Section 3 Evaluating Limits
Assign: Text: p. 1027: 1-25 odd; AMSCO: p. 18: 1-21
Lesson 2: continued
Assign: Text: p. 1027: 43-49 odd, (Hand in) AMSCO: p. 19: 22, 24, 27, 30, 32, 34-38
Quiz: Limits
Assign: p. 1029: 74, 76
Lesson 3: 11.3: Limits and Continuity; AMSCO Section 4: Continuity
Obj: To determine whether a function is continuous at a number, determine for what numbers a function is discontinuous.
Assign: Read and study introductory material. Exercises: AMSCO: p. 24: 1-16; Text: p. 1034: 1-11 odd
Lesson 3: continued
Assign: Text: p. 1034: 13-29 odd, 30, 45; (Hand in) AMSCO: p. 25: 18-28 even; Text: p. 1035: 44
Mid Chapter Check Point
Obj: To review limits and continuity.
Assign: pp. 1036-1037: 1-22
Test on Limits and Continuity; PROJECT DUE
Continue test if necessary.
Assign: Review for senior exam; pp: 1003-1004: 1-12,14-16,25-31,33-37,39-41; p. 1054: 18
Continue Review; PORTFOLIO DUE Good bye to Seniors
CHAPTER 11: INTRODUCTION TO CALCULUS CONTINUED Assignment Guide (4weeks)
Office hours: By appointment; Math Lab one a week after school
Mathematics is a science, an art, a way of thinking. Appearing in nature, art, music, architecture, history, science, literature – its influence is present in every facet of the universe.
Lesson 1: 11.4 Introduction to Derivatives; AMSCO Section 5: The Derivative
Obj:To find slopes and equations of tangent lines, find the derivative of a function, find average and instantaneous rates of change, find instantaneous velocity.
Assign: Read and study introductory material. Exercises: AMSCO: p.35: 1-2-18 even
Lesson 1: continued
Assign: Text: p. 1047: 1-13 odd
Lesson 1: continued
Assign: (Hand in) AMSCO: p. 36: 22, 24, 26, 27, 30, 32
Lesson 1: continued
Assign: Text: p. 1047-1050: 15-25 odd, 37, 43, 45, 58, 68-73
Lesson 2: AMSCO Section 6: Rules for Finding Derivatives
Obj: To use the linear function rule, sum rule, constant times a function rule, and power rule, to find velocity.
Assign: Read and study introductory material. Exercises: AMSCO: p.41: 1-12
Lesson 2: continued
Assign: AMSCO: p. 41: 13-19
Lesson 2: continued
Assign: AMSCO: 20-24
Quiz on beginning derivatives
Assign: Read and study AMSCO section 7: More Rules for Differentiation. Exercises:: p. 446: 1-4
Lesson 3: AMSCO Section 7: More Rules for Differentiation
Obj. To use the product and quotient rules for finding derivatives,
Assign: p. 46: 5-19 odd; (Hand in) AMSCO: p. 46: 22
Lesson 3: continued.
Assign: continue exercies on p. 46
Lesson 4: Applications of the Derivative
Obj. To apply derivatives to increasing and decreasing functions, critical points, maximum and minimum problems, velocity
Assign: p. 53: 1-9 odd
Lesson 4: continued
Assign: 11-21 odd
Review
Assign: p. 58-5929-47 odd: 1003-1004: 1-12,14-16,25-31,33-37,39-41; p. 1054: 18
Test on Derivatives
Continue Test if necessary
SAT practice; Review for exam: Text: pp. 1053-1054: 5,16,17,18,22,29,33,34,38
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