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§ 1.1 "A Preview of Calculus"
Day 1: Worksheet "1.1 Introduction to the Calculus - Tangent Lines & Limits." Read § 1.1 … NB … nota bena (note well!) … that you are expected to read every section we cover. Materials from sections provide excellent foundations, terminology, and examples. You are to use this resource.
Day 2: Worksheet "1.1 Introduction to the Calculus - The Area Problem."§ 1.2 "Finding Limits Graphically and Numerically"
Day 1: 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 2: QUIZ - § 1.2: Evaluating Limits Graphically and Numerically§ 1.3 "Evaluating Limits Analytically"
Day 1: p. 64 # 5-27 odd, 29-37 all, & 39
Day 2: p. 65 # 41-55 odd
Day 3: p. 65 # 57-67 odd, 68-72 all, & 77
Day 4: QUIZ - § 1.3: Squeeze Thm & Special Trig Limits (no calculators allowed)§ 1.4 "Continuity and One-Sided Limits"
Day 1: p. 76 # 5-10 all, 11-25 odd
Day 2: p. 76 # 27-51 odd
Day 3: p. 77 # 55, 57, 59-62 all, 67-70 all
DAY 4: QUIZ - § 1.3 & 1.4§ 1.5 "Infinite Limits"
Day 1: p. 84 # 1-23 odd, 25-28 all
Day 2: p. 84 # 29-43 oddSupplemental Topic: Formal Definition of Limits - the epsilon-delta Definition of Limits
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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Portfolio Project: Population Growth
1 class period to begin. Approximately 2-weeks to complete.
§ 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 1: p. 110 # 1 -21 odd.
Day 2: Worksheet: §2.2 Differentiation Rules for Powers, Constant Multiples, and Sums
Day 3: p. 110 # 23 - 41 odd.
Day 4: p. 111 # 43 & 45 (with graphs using computer software), 47 - 52 all, 56 (with graph).
Day 5: p. 111 # 65, 67, 71, 73, 83, & 91.
Day 6: 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 7: QUIZ: § 2.1-2.2. Quiz in two parts (one class period). 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 1: p. 121 # 1 - 25 odd.
Day 2: 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 3: 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 4: 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 5: QUIZ: § 2.3- 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 1: Worksheet: § 2.4 Exploration: Derivative of Sin f(x); p. 130 # 1 - 6 all, 7 - 29 odd.
Day 2: In pairs, do p. 131 #31 - 40. Each pair will do only 2 (to be assigned) using MathPert.
Day 3: p. 131-2 # 41, 42, 43 - 59 odd, 63, 69, & 71.
Day 4: TEST § 2.1-2.4
HW From § 2.1-2.4 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 1: p. 139 # 1 - 15 odd
Day 2: p. 139 # 17 - 29 odd
Day 3: p. 139 # 31 - 37 odd
Day 4: 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 1: p. 146 # 1 - 7 odd
Day 2: p. 146 #11, 13, 15, & 19 (for part a of #15 you need the Trig Double-angle Identity)
Day 3: p. 146 # 17, 21, & 23
Day 4: p. 147 # 25 & 33Day 5: QUIZ § 2.5-2.6
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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 1: p. 167 # 1, 2, 3 - 15 odd, & 19
Day 2: 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 1: p. 176 # 7 - 19 odd
Day 2: p. 176 # 29 - 32 all (include sketches of trig graphs)
Day 3: p. 176 # 37 - 41 odd, 43 - 48 all, & 49QUIZ: 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 1: 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 2: 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 3: p. 185 # 45 - 50 All§ 3.5 Limits at Infinity
Objectives: (1) Finding limits at infinity; (2) Horizontal asymptotes
Day 1: HANDOUT: § 3.5 Exploration: Limits Involving Infinity; HW: p. 193 # 11 - 25 odd
Day 2: 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 1: p. 204 # 57-64 all, 71-74 allWORKSHEETS:
Exploration - Derivative of an Exponential Function
Differentiation of Exponential Functions
Differentiation of Logarithmic Functions
Applications of Differentiation with Exponential Functions (Worksheet # 3)§ 3.7 Optimization Problems
Objectives: (1) Applied minimum and maximum problems
Day 1: p. 210 # 3, 5, 7 - 10 all, & 11
Day 2: 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 1: Program calculators to run "Newton" and "Newton2." Review steps in using calculator to do iterations using the "Home Screen." HW: p. 219 # 5 - 15 odd, 21 - 24 allQUIZ: Sections 3.7 & 3.8
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: 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 1: Sigma Notation. p. 260 #1 - 13 odd [Use #s 2, 8 as examples.]
Day 2: Summation formulas. p. 261 # 15 - 33 odd [Use #s 18, 26, 32 as examples.]
Day 3: Worksheet packet: § 4.2 Rectangular Approximations of Area
Day 4: Finding the area by the limit definition. p. 261-2 # 35, 37, & 43§ 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 1: p. 271-272 #1 - 10 all, 21 - 24 all, 43-44 (on handout)
- § 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 1: The Fundamental Thm of Calculus: p. 276. Do: p. 283 # 5 - 23 odd.
Day 2: p. 283 # 25 - 29, 33 - 41 odd.
Day 3: Mean Value of an Integral & Avg Value (pp. 277-78). Do: p. 284 # 43 - 49 odd, 51 - 56 All, & 61.
Day 4: The 2nd Fundamental Thm of Calculus: Exploration: The 2nd Fundamental Thm of Calculus;
- p. 285 # 67 - 83 odd.
- Day 5: Exploration - Finding Displacement from Acceleration Data;
- § 4.4 Practice Worksheet - The Derivative as an Accumulator Function
- Day 6: Worksheet: Speed of Download … Total Download An Application of Integration
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 1: p. 296 # 1 - 15 odd.
Day 2: p. 296 # 17 - 29 odd.
Day 3: p. 296 # 33 - 45 odd.
Day 4: 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 1: HANDOUT: § 4.6 Numerical Integration - WS #1TEST - Ch 4 Integration
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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 1: p. 327 # 1 - 25 odd (skip # 15).
Day 2: 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 1: 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 1: p. 345-346 # 49, 51, 75 - 91 odd
Day 2: p. 347 # 97 - 101 odd, 104 (a) [omit Simpson's Rule and use n = 4]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 1: 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 1: p. 363 # 1 - 9 odd, & 57 [HANDOUTS: § 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 1: 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 1: p. 383 # 23 - 30 all, 43 - 55 oddTEST: § 5.1-5.8
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§ 6.1 Area of a Region Between Two Curves
Day 1: p. 414 # 1 - 6 all, 37 - 45 odd.§ 6.2 Volume: The Disc Method
Day 1: p. 423 # 1 - 6 all, 23 - 28 all.
Day 2: Worksheet: An Application of Integration - Volume with the Trapezoidal Rule.[ Back to TOP ]
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