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- § 1.1 "A Preview of Calculus"
Day 1: WORKSHEET: Exploration - Instantaneous Rates of Change of a Function.
- Read § 1.1 … NB … nota bena (note well!) … you are expected to read every section we cover. Materials from sections provide excellent foundations, terminology, and examples. Use this resource!
- Day 2: WORKSHEETS: Exploration - Introduction to Limits; Exploration - Introduction to Definite Integrals. HANDOUT: "Notes(T9) - A limit is …"
Probability Topics from Year 1 (not covered due to lack of time) Day 1: [NOTES: Probability Notes] WORKSHEET-Probability-1 (Simple Probabilities); WORKSHEET-Probability-2 (Probability, Set Language, and Venn Diagrams)
Day 2: WORKSHEET -Probability-3 (Cumulative Frequency and Probability with
Venn Diagrams)
Day 3: Probability, Steroid Testing, & Baseball: A Conditional Probability Exercise;
§ 11.5 (Combinatorics: Combinations and Permutations), p. 742 # 1-29 odd; WORKSHEET: Pascal's Triangle & Probability
Day 4: WORKSHEET-Probability-4 (Conditional Probability)
Day 5: NOTES: [Displaying Data Notes; Displaying Data Notes-Descriptive Stats & the TI83, WORKSHEET - Normal Distribution]; WORKSHEET-Probability-5-Calculating Standard Deviation and other Measures of Spread (including Cumulative Frequency)
Day 6: (1) Use data table 11.17 from your text (p. 767) to create a circle graph of the United States Budget, Net Receipts for Fiscal Year 1993. (2) Use data table 11.23 from your text (p. 778) to find the following information about the populations of South American nations (use only the LAST column and present your answers with 3-significant figure accuracy): mean; standard deviation (s x); 5-number summary (min, Q1, med, Q3, and max). Also, create a modified box-and-whisker plot of the data. Name any countries found to be "outliers."
Day 7: WORKSHEET: Cumulative Frequency for IB Exams; Begin PORTFOLIO: Transforming Data [Due one week after start of project.]
Day 8: TEST
- § 1.2 "Finding Limits Graphically and Numerically"
Day 3: Worksheet: "§ 1.2 Limits Evaluated Numerically and Graphically" (this worksheet is tied to text
- p. 53 #3-10) AND p. 53 # 11-20 all.
- Day 4: QUIZ - § 1.2: Evaluating Limits Graphically and Numerically
- § 1.3 "Evaluating Limits Analytically"
Day 5: p. 64 # 5-27 odd, 29-37 all, & 39
Day 6: p. 65 # 41-55 odd
Day 7: p. 65 # 57-67 odd, 68-72 all, & 77
Day 8: QUIZ - § 1.3: Squeeze Thm & Special Trig Limits (no calculators allowed)- § 1.4 "Continuity and One-Sided Limits"
Day 9: p. 76 # 5-10 all, 11-25 odd
Day 10: p. 76 # 27-51 odd
Day 11: p. 77 # 55, 57, 59-62 all, 67-70 all
Day 12: QUIZ - § 1.3 & 1.4- § 1.5 "Infinite Limits"
Day 13: p. 84 # 1-23 odd, 25-28 all
Day 14: p. 84 # 29-43 odd
Day 15: Supplemental Topic: Formal Definition of Limits - the epsilon-delta Definition of Limits- Day 16: TEST: CHAPTER 1 - LIMITS: Test will be in two parts (one class period allowed).
- Part I = no calculators allowed, Part II = calculators permitted.
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- § 2.1 "The Derivative and the Tangent Line Problem"
Objectives: (1) Find the slope of a line to a curve at a point; (2) Use limit definition to find the derivative of a function; (3) Understand the relationship between differentiability and continuity
Day 1: p. 98 # 1 & 5 - 15 odds only.
Day 2: p. 99 # 23, 25, 27 - 32 all.- § 2.2 "Basic Differentiation Rules and Rates of Change"
- Objectives: (1) Find derivatives using the Constant Rule, Power Rule, Constant Multiple Rule, and the Sum and Differences Rules; (2) Find the derivatives of the sine function and cosine function; (3) Use derivatives to find rates of change (velocity)
Day 3: p. 110 # 1 -21 odd.
Day 4: Worksheet: §2.2 Differentiation Rules for Powers, Constant Multiples, and Sums
Day 5: p. 110 # 23 - 41 odd.
Day 6: p. 111 # 43 & 45 (with graphs using computer software), 47 - 52 all, 56 (with graph).
Day 7: p. 111 # 65, 67, 71, 73, 83, & 91.
Day 8: Handouts: § 2.2 Position, Velocity, Acceleration, the Graph of a Falling Object,
- and The Moving Particle; Derivatives - Calculator and Non-Calculator AP Exam style Questions;
- § 2.2 BASIC DIFFERENTIATION AND RATES OF CHANGE: Approximating Rates of Change by Difference Quotients
- Day 9: QUIZ: § 2.1-2.2. Quiz in two parts (one class period). HW From § 2.1-2.2 due by test date.
- Part I = no calculators, Part II = calculators permitted.
- § 2.3 "The Product and Quotient Rules and Higher-Order Derivatives"
Objectives: (1) Find the derivative of a function using the Product Rule and Quotient Rule; (2) Find the derivative of a trigonometric function; (3) Find a higher-order derivative of a function (i.e., the second derivative, the third derivative, etc).
Day 10: p. 121 # 1 - 25 odd.
Day 11: Use the derivatives of sine and cosine and the quotient rule to show that the derivatives
- of the cotangent, secant, and cosecant are true. [Use the proof on p. 118 for tan x as a guide.] Note, this process is known as "deriving" a formula, as opposed to simply using a given formula. In this case, you are deriving the derivative of the trig functions. ALSO: Do p. 121 # 27 - 41 odd.
- Day 12: p. 121-122, # 51 (use "Draw, Tangent" features of TI-83) plus include a "careful" sketch,
- # 57 (include a "careful" sketch of the graph with horizontal tangent lines), # 59 - 64 (all), & 67.
- Day 13: p 122 # 70, 71 - 83 odd, 89, and 90.
- [Hint for # 89, the average velocity during each interval refers to work we did on p. 108, and you are to find Ds/Dt for the intervals (0,1) seconds, (1,2) seconds, (2,3) seconds, and (3,4) seconds.]
- Day 14: QUIZ: § 2.3 HW From § 2.3 due by test date.
- Day 15: Handout: § 2.3 Exploration: Differentiability and Continuity at a Point
- § 2.4 "The Chain Rule"
Objectives: (1) Find the derivative of a composite function using the Chain rule; (2) Find the derivative of a function using the General Power Rule; (3) Simplify the derivative of a function using algebra; (4) Find the derivative of a trigonometric function using the Chain Rule.
Day 16: Worksheet: § 2.4 Exploration: Derivative of Sin f(x); p. 130 # 1 - 6 all, 7 - 29 odd.
Day 17: § 2.4, p. 131 #31 - 40 all, using worksheet.
Day 18: p. 131-2 # 41, 42, 43 - 59 odd, 63, 69, & 71.
Day 19: TEST § 2.1-2.4 HW From § 2.4 due by test date.- § 2.5 "Implicit Differentiation"
Objectives: (1) Distinguish between functions written in implicit form and explicit form; (2) Use implicit differentiation to find the derivative of a function
Day 20: p. 139 # 1 - 15 odd
Day 21: p. 139 # 17 - 29 odd
Day 22: p. 139 # 31 - 37 odd
Day 23: p. 139 # 41 - 45 odd- § 2.6 "Related Rates"
Objectives: (1) Find a related rate; (2) Use related rates to solve real-life problems
Day 24: p. 146 # 1 - 7 odd
Day 25: p. 146 #11, 13, 15, & 19 [Skip part (a) of #15]
Day 26: p. 146 # 17 & 21
Day 27: p. 147 # 25 & 33- Day 28: QUIZ § 2.5-2.6 HW From § 2.5-§ 2.6 due by quiz date.
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- § 3.1 Extrema on an Interval
Objectives: (1) Definition of relative and absolute extrema; (2) Definition of critical numbers; (3) Finding extrema on a closed interval
Day 1: p. 160 # 7 - 25 odd
Day 2: p. 160 # 27, 29 - 32 all, 33, 35- § 3.2 Rolle's Theorem and the Mean Value Theorem
Objectives: (1) Definition of Rolle's Thm and the MVT
Day 3: p. 167 # 1, 2, 3 - 15 odd, & 19
Day 4: p. 168 # 27 - 37 odd, & 44- § 3.3 Increasing and Decreasing Functions and the First Derivative Test
Objectives: (1) The first derivative test; (2) Sign charts
Day 5: p. 176 # 7 - 19 odd
Day 6: p. 176 # 29 - 32 all (include sketches of trig graphs)
Day 7: p. 176 # 37 - 41 odd, 43 - 48 all, & 49- QUIZ: Sections 3.1 - 3.3
- § 3.4 Concavity and the Second Derivative Test
Objectives: (1) Connection between concavity and the second derivative; (2) Points of Inflection; (3) Second derivative test
Day 8: HANDOUTS: § 3.4 Exploration: Concavity and the 2nd Derivative; § 3.4 Exploration:
- Maxima, Minima & Pts of Inflection; Additional HW: p. 184 # 7 - 19 odd
- Day 9: p. 184 # 21 - 29, 31, & 35 odd
- [Must do complete analysis with sign chart, graphing may be done in the calculator with rough sketches satisfactory.]
- Day 10: p. 185 # 45 - 50 All
- § 3.5 Limits at Infinity
Objectives: (1) Finding limits at infinity; (2) Horizontal asymptotes
Day 11: HANDOUT: § 3.5 Exploration: Limits Involving Infinity; HW: p. 193 # 11 - 25 odd
Day 12: p. 193 # 27, 29, 61, & 63- § 3.6 A Summary of Curve Sketching
Objectives: (1) Geometric connection between the tangent line and concavity; (2) Graphing a function based on its derivative
Day 13: p. 204 # 57-64 all, 71-74 all- WORKSHEETS:
Day 14: Exploration - Derivative of an Exponential Function; Differentiation of Exponential Functions
Day 15: Differentiation of Logarithmic Functions
Day 16: Applications of Differentiation with Exponential Functions (Worksheet # 3)- § 3.7 Optimization Problems
Objectives: (1) Applied minimum and maximum problems
Day 17: p. 210 # 3, 5, 7 - 10 all, & 11
Day 18: p. 211-12 # 16, 22, & 35- § 3.8 The Newton-Raphson Method [Possible Portfolio Project topic]
Objectives: (1) Algebraic solutions (approximations) of polynomial equations; (2) Iterative processes
Day 19: Notes and discussion of the process
- §3.8 The NR Method of Approximating Zeros wit the GDC
§3.8 Example of Using the Newton-Raphson Method with the Graphing Calculator
An Example of Using NR and Sketching Tangent Lines
WORKSHEET: §3.8 The Newton-Raphson Method - WORKSHEET # 1- Day 20: §3.8 The Newton-Raphson Method - WORKSHEET # 2
Day 21: Begin Portfolio on Newton-Raphson Method.
Day 22: Fixed Point Iteration - Notes and Worksheet
Day 23: WORKSHEET: Derivatives & Linear Approximations
- Day 24: TEST: All of Chapter 3
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- § 4.1 Antidifferentiation and Indefinite Integration
Objectives: (1) Write the general solution of a differential equation (2) Use definite integral notation for antiderivatives; (3) Use basic integration rules to find antiderivatives; (4) Find a particular solution of a differential equation
HANDOUTS: § 4.1 Differential Equations; Notes: Differential Equations & Slope Fields; To Sketch a Slope Field Using WinPlot
Day 1: WORKSHEET: Intro to Riemann sums & Integral Calculus; p. 248 #1 - 13 odd
Day 2: p. 248 # 15 - 37 odd
Day 3: § 4.1 WORKSHEET: Differential Equations & Slope Fields p. 249 # 41 - 47 odd, 51 - 55 all, 57, & 61- § 4.2 Area
Objectives: (1) Use sigma notation to write and evaluate a sum; (2) Understand the concept of area; (3) Approximate the area of a plane region; (4) Find the area of a plane region using limits.
HANDOUT: Area by Summation and Limits; Summation Proof of the Harmonic Series
Day 4: Sigma Notation. p. 260 #1 - 13 odd [Use #s 2, 8 as examples.]
Day 5: Summation formulas. p. 261 # 15 - 33 odd [Use #s 18, 26, 32 as examples.]
Day 6: WORKSHEET: § 4.2 Rectangular Approximations of Area
Day 7: Finding the area by the limit definition. p. 261-2 # 35 & 37
- [For Discussion only … solutions will be provided.]
- § 4.3 Riemann Sums and Definite Integrals
Objectives: (1) Understand the definition of a Riemann Sum; (2) Evaluate a definite integral using limits; (3) Evaluate a definite integral using properties of definite integrals.
Day 8: p. 271-272 #1 - 10 all, 21 - 24 all, 43-44 (on handout)HW Due from § 4.1- § 4.3
- § 4.4 The Fundamental Theorem of Calculus
Objectives: (1) Evaluate a definite integral using the Fundamental Theorem of Calculus; (2) Understand and use the Mean Value Theorem for Integrals; (3) Find the average value of a function over a closed interval; (4) Understand and use the Second Fundamental Theorem of Calculus.
HANDOUTS: Exploration - Finding Displacement from Acceleration Data; The Derivative as an Accumulator Function; Speed of Download
Day 9: The Fundamental Thm of Calculus: p. 276. Do: p. 283 # 5 - 23 odd.
- NOTES: Integral versus Area Caution
- Day 10: p. 283 # 25 - 29, 33 - 41 odd.
Day 11: Mean Value of an Integral & Avg Value (pp. 277-78). Do: p. 284 # 43 - 49 odd, 51 - 56 ALL.
Day 12: EXPLORATION: The 2nd Fundamental Thm of Calculus- Day 13: EXPLORATION: Finding Displacement from Acceleration Data
- Day 14: p. 285 # 67 - 81 odd.
HW Due from § 4.4
- QUIZ: § 4.1 - 4.4 Integration
- § 4.5 Integration by Substitution
Objectives: (1) Use pattern recognition to evaluate an indefinite integral; (2) Use a change of variables to evaluate an indefinite integral; (3) Use the General Power Rule for Integration to evaluate an indefinite integral; (4) Use a change of variables to evaluate a definite integral; (5) Evaluate a definite integral involving an odd or even function.
Day 15: p. 296 # 1 - 15 odd. WORKSHEET: Change of Variables and AP Style Questions
Day 16: p. 296 # 17 - 29 odd.
Day 17: p. 296 # 33 - 45 odd.
Day 18: p. 297-8 # 47, 49, 55 - 63 odd.- § 4.6 Numerical Integration
Objectives: (1) Approximate a definite integral by the Trapezoidal Rule (Trapezium Rule).
Day 19: WORKSHEET: § 4.6 The Trapezoidal Rule- Day 20: TEST - Ch 4 Integration - [Part I without calculator, Part II with calculator.]
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- § 5.1 The Natural Logarithmic Function and Differentiation
Objectives: (1) Develop and use properties of the natural logarithmic function; (2) Understand the definition of the number e; (3) Use basic integration rules to find antiderivatives; (4) Find derivatives of functions involving the natural logarithmic function
Day 1: p. 318-19 # 37, 53, 69, 71, 72, & 83- § 5.2 The Natural Logarithmic Function and Integration
Objectives: (1) Use the Log rule for Integration to integrate a rational function; (2) Integrate trigonometric functions.
Day 2: p. 327 # 1 - 25 odd (skip # 15).
Day 3: p. 327 # 27 - 39 odd- § 5.3 Inverse Functions
Objectives: (1) Verify that one function is the inverse of another function; (2) Determine whether a function has an inverse function; (3) Find the derivative of an inverse function.
Day 4: p. 336 # 47 - 52 all, 61 - 64 all.- § 5.4 Exponential Functions: Differentiation and Integration
Objectives: (1) Develop properties of the natural exponential function; (2) Differentiate natural exponential functions; (3) Integrate natural exponential functions.
Day 5: p. 345-346 # 49, 51, 75 - 91 odd
Day 6: p. 347 # 97 - 101 odd, 104 (a) [omit Simpson's Rule and use n = 4]- Day 7: QUIZ: § 5.1-5.4
- § 5.5 Bases Other than e and Applications
Objectives: (1) Define exponential functions that have bases other than e; (2) Differentiate and integrate exponential functions that have bases other than e; (3) Use exponential functions to model compound interest and exponential growth.
Day 8: p. 354 # 29 - 45 odd, 69 - 75 odd.- § 5.6 Differential Equations: Growth and Decay
Objectives: (1) Use separation of variables to solve a simple differential equation; (2) Use exponential functions to model growth and decay in applied problems.
Day 9: p. 363 # 1 - 9 odd, & 57 [HANDOUT: § 5.6 Newton's Law of Cooling; Solutions to DiffEQs Involving Population Growth]- § 5.7 Differential Equations: Separation of Variables
Objectives: (1) Use initial conditions to find particular solutions to differential equations; (2) Recognize and solve differential equations that can be solved by separation of variables; (3) Recognize and solve homogeneous differential equations; (4) Use a differential equation to model and solve an applied problem.
Day 10: p. 375 # 79 - 82 all [Use HANDOUT]- § 5.8 Inverse Trigonometric Functions: Differentiation
Objectives: (1) Develop properties of the six inverse trigonometric functions; (2) Differentiate an inverse trigonometric function; (3) Review the basic differentiation formulas for elementary functions.
Day 11: p. 383 # 23 - 30 all, 43 - 55 odd- Day 12: TEST: § 5.1-5.8
- § 5.9 Inverse Trigonometric Functions: Integration
Objectives: (1) Integrate Functions whose antiderivatives involve inverse trigonometric functions; (2) Use the method of completing the square to integrate a function; (3) Review the basic integration formulas involving elementary functions.
Day 13: p. 390 # 1 - 31 odd, 39, & 40
Day 14: time to complete assignment.- Day 15: QUIZ: § 5.7-5.8
- [This is a no calculator quiz for the entire quiz. Students will be allowed one 3x5 inch note card of notes (one side only).]
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- § 6.1 Area of a Region Between Two Curves
Objectives: (1) Find the area of a region between two curves using integration; (2) Find the area of a region between intersecting curves using integration; (3) Describe integration as an accumulation process.
Day 1: p. 414 # 1 - 6 all, 37 - 45 odd.- § 6.2 Volume: The Disc Method
Objectives: (1) Find the volume of a solid of revolution using the disc method; (2) Find the volume of a solid of revolution using the washer method; (3) Find the volume of a solid with known cross sections.
Day 2: p. 423 # 1 - 6 all, 23 - 28 all.
Day 3: Worksheet: An Application of Integration - Volume with the Trapezoidal Rule.
Day 4: Worksheet: Volume of a Solid with a Known Cross Section.- If Time Permits ... the following are not on the IB Math Methods nor AP Calculus (AB) curriculums:
- § 6.3 Volume: The Shell Method
Objectives: (1) Find the volume of a solid of revolution using the shell method; (2) Compare the uses of the disk method and the shell method.
Day 5: p. 432 # 1 - 12 all
Day 6: p. 432 # 13 - 23 all- § 6.4 Arc Length and Surfaces of Revolution
Objectives: (1) Find the arc length of a smooth curve; (2) Find the area of a surface of revolution.
Day 7: p. 442 # 3, 7, 9 - 17 odd
Day 8: p. 443 # 31 & 33- Day 9: TEST: § 6.1-6.4 Test will have a calculator and non-calculator part.
- Students are allowed one 3x5 inch card of notes (one-side only).
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