Monday Tuesday 1C Calculus AB First Six Weeks Week 1 8/27/07 to 8/31/07 Wednesday 1D Pre - Cal CA L 1A Learner Expectations T.L.W: Orientation Class rules Course expectations and requirements. Suggested Resources Text Pages 1A Learner Expectations T.L.W: Sketch the graph of an equation. Find the intercepts of a graph. Find the points of intersection of two graphs. Interpret mathematical models for real –life data. Suggested Resources Text Pages 17 – 22 Vocabulary Strategies Assessment Vocabulary Functions. Intercepts Strategies Analyze graph sketched both manually and with calculator. Finding points of intersection by solving equations algebraically, and graphically. Assessment 23 1 – 16 27 – 30 52 - 66 Scaffolding Questions Pages Problems Scaffolding Questions Learner Expectations T.L.W: Find the slope of a line passing through two points. Write the equation of a line with a given point and slope. Interpret slope as a ratio or as a rate of change in real –life application. Write equations of lines that are parallel or perpendicular to a given line. Thursday 1A,B 2A,B 1A 1A Learner Expectations T.L.W: Use function notation to represent and evaluate a function. Find domain and range of a function. Sketch the graph of a function. Identify different types of transformations of functions. Suggested Resources Text Pages 25 – 30 Suggested Resources Text Pages 34 – 41 Vocabulary Slope, Rate of change, Parallel, Perpendicular. Vocabulary Parent Graph, Domain, Range, Interval notation. Strategies Find slope of a line when given two points. Find equation of a line from two points or one point and a slope. Discuss slope-intercept, and standard form of an equation for a line. Relate slope to a rate of change and its applications. Strategies Identify domain and range of a function in both interval form and set notation form. Sketch parent graphs and perform transformations. Assessment Pages 23 – 24 Problems 53 – 56 Pages 31 Problems 1 – 54 Scaffolding Questions Friday 1A,B 2A,B Pages Problems Assessment 42 1 – 42 Scaffolding Questions Learner Expectations T.L.W: Classify functions and recognize combinations of functions. Test a graph for symmetry with respect to an axis and the origin. Suggested Resources Text Pages 20 – 21 40 – 41 Vocabulary Symmetry, Odd and Even function Strategies Find composite and inverse functions. Recognize Even and Odd functions. Discuss tests for symmetry with respect to axis and Origin. Use properties of Odd, Even, and Inverse function to complete the graph of a function. Assessment Pages 23 Problems 17 – 26 Pages 43 Problems 53 – 56 Scaffolding Questions Monday 2C, 3A Tuesday 2C, 3A Calculus AB First Six Weeks Week 2 9/3/07 to 9/7/07 Wednesday 1A,B,C,D Pre Cal 1A 1A 1A Thursday 1A,B,C,D 2A,B,C, 3A 1A Friday 1A,B,C,D 2A,B,C, 3A 1A CA LC Learner Expectations T.L.W: Review trigonometric identities. Solve special right triangles. Learner Expectations T.L.W: Graph trig. Functions. Solve trig. Functions. Learner Expectations T.L.W: Quiz over algebra review Suggested Resources Text Pages 45 – 52 Suggested Resources Text Pages 45 – 52 Suggested Resources Text Pages Hand outs Vocabulary Standard position, Co terminal, Special right triangles, Identities, Period, Amplitude. Strategies Review basic trigonometric identities including sum, difference, double, and half angles. Review graphing of trig. functions including reciprocal, quotient, and Pythagoras. Evaluate exact value of a trig. Function using special right triangle. Solving trigonometric functions algebraically and graphically. Assessment Page 53 Problems 13 – 46 Scaffolding Questions Vocabulary Strategies Sketch all six trig. Function in [ – 2 , 2 Use graphing calculator to graph trig. Functions. Use special right triangle to solve trig. Function. Use graphing calculator to find zeros of trig. Functions. Assessment Page 55 Problems 51 – 77 Scaffolding Questions Vocabulary Strategies Answer student’s questions. Learner Expectations T.L.W: Review last two weeks objectives Suggested Resources Text Pages Hand outs Vocabulary Strategies Answer student’s questions. Assessment Assessment Scaffolding Questions Scaffolding Questions Learner Expectations T.L.W: Major assessment. Chapter review test. Suggested Resources Text Pages Hand outs Vocabulary Strategies Assessment Scaffolding Questions Monday Holiday Tuesday 1D Calculus AB First Six Weeks Week 3 9/10/07 to 9/14/07 Wednesday 1D Thursday Friday 1D, 1E Pre -Cal I–B–1 I–B–2 I–B–2 I–B–3 CA LC Learner Expectations Holiday Learner Expectations T.L.W: Estimate a limit using a numerical or graphical approach Learner Expectations T.L.W: Evaluate a limit using properties of limits Learn different ways that a limit can fail to exist I – B – 1, 2, 3 Learner Expectations T.L.W: Develop and use a strategy for finding limits Learner Expectations T.L.W: Evaluate a limit using properties of limits Evaluate a limit using dividing out and rationalizing techniques Develop and use a strategy for finding limits Evaluate a limit using dividing out and rationalizing techniques Suggested Resources Text Pages Suggested Resources Text Pages 61-65 Vocabulary Vocabulary Limit Strategies Strategies Find limits of functions through table (as x approaches a value) and graphically Suggested Resources Text Pages 70-74 Suggested Resources Text Pages 76-79 Vocabulary Scalar multiple Vocabulary Rationalization Strategies Find limits of function by direct substitution Strategies Find limits by using algebra to get equivalent expressions for which limits are defined Assessment Assessment p. 68: 1-18, 35, 36 Assessment p.74: 1-34 Assessment p. 82: 1-24 Scaffolding Questions Scaffolding Questions Scaffolding Questions Scaffolding Questions Suggested Resources Text Pages Various AP questions from past tests and other resources. Vocabulary Strategies Quiz students over objectives covered up to date over limits Assessment Teacher made quiz Scaffolding Questions Monday Pre Cal CALC Tuesday 1–D 1–D I–B–1 I–B–2 I – B – 1, 2 Learner Expectations T.L.W: Evaluate a limit using properties of limits Calculus AB First Six Weeks Week 4 9/17/07 to 9/21/07 Wednesday 1–D I – B – 1, 2 Learner Expectations T.L.W: Evaluate a limit using the squeeze theorem Learner Expectations T.L.W: Evaluate a limit using properties of limits Develop and use a strategy for finding limits Develop and use a strategy for finding limits Evaluate a limit using dividing out and rationalizing techniques Evaluate a limit using dividing out and rationalizing techniques Thursday 1–D E B–2 C–3 I – B – 1, 2 Friday 1-D I–D–3 Learner Expectations T.L.W: Review all objectives covered to date Learner Expectations T.L.W: Determine one-sided limits and continuity on a closed interval Suggested Resources Text Pages Various AP questions from tests Suggested Resources Text Pages 86-87 Evaluate a limit using the squeeze theorem Suggested Resources Text Pages Vocabulary Strategies Correct Friday’s quiz, review concepts of limits that were not mastered Suggested Resources Text Pages 80-81 Vocabulary Squeeze theorem Strategies Find limit as x approaches 0 of sin x/x by applying squeeze theorem Suggested Resources Text Pages 81-83 Vocabulary Strategies Review more trig concepts to help find limits involving trig functions. Vocabulary Strategies Test students on objectives covered up to this point Vocabulary One sided limits Strategies Find one sided limits using previous objectives Find all limits of a piece-wise. Assessment Oral evaluation Assessment p.82: 25-40 Scaffolding Questions Scaffolding Questions Review all function objectives on limits covered to date. Assessment p.83: 43-48, 51-52 Scaffolding Questions Assessment Teacher made test Scaffolding Questions Assessment p.92: 1-13 Scaffolding Questions Monday 1–E Tuesday 1–E Pre Cal CALC I–B–1 I–B–2 Calculus AB First Six Weeks Week 5 9/24/07 to 9/28/07 Wednesday 1–E 2–B I – D – 1, 2 Learner Expectations T.L.W: Determine continuity at a point and continuity on an open interval I – D – 1, 2 Learner Expectations T.L.W: Use properties of continuity Determine one-sided limits and continuity on a closed interval Learner Expectations T.L.W: Determine continuity at a point and continuity on an open interval Thursday Friday 1–E 2–B 1–E 3–C I–D–3 I – D – 1, 2, 3 Learner Expectations T.L.W: Understand and use the intermediate value theorem Learner Expectations T.L.W: Determine continuity at a point and continuity on an open interval Determine one-sided limits and continuity on a closed interval Determine one-sided limits and continuity on a closed interval Use properties of continuity Use properties of continuity Understand and use the intermediate value theorem Suggested Resources Text Pages 84-85 Suggested Resources Text Pages 86-88 Suggested Resources Text Pages 89-90 Vocabulary Removable and non removable discontinuities Vocabulary Removable and non removable discontinuities Vocabulary Removable and non removable discontinuities Strategies Discuss limits of functions by examining functions graphically Strategies Discuss continuity of functions by examining functions graphically Strategies Use various methods to find limits of functions including onesided and non-existent. Suggested Resources Text Pages 91-92 Vocabulary Mean value theorem Strategies Discuss intermediate value theorem and give applications Assessment p.93: 14-26 Assessment p.93: 27-46 Assessment p.93: 49-50 Assessment p.93: 67-74 Scaffolding Questions Scaffolding Questions Scaffolding Questions Scaffolding Questions Suggested Resources Text Pages Quiz Vocabulary Strategies Give quiz over concepts covered up to this point. Assessment Quiz Scaffolding Questions Monday 1–E Tuesday 1–E Calculus AB First Six Weeks Week 6 10/1/07 to 10/5/07 Wednesday 1–E Thursday 1–E Pre Cal I – C – 1, 2 I – C – 1, 2 I–B I – C – 1, 2 CALC Learner Expectations T.L.W: Determine infinite limits from the left and from the right Find and sketch the vertical asymptotes of the graph of a function Learner Expectations T.L.W: Determine finite limits at infinity Determine the horizontal asymptotes, if any, of the graph of a function Vocabulary Vertical asymptote Strategies Relate infinite limits to vertical asymptote Suggested Resources Text Pages 198-201 Vocabulary Horizontal asymptote Strategies Find limits as x approaches infinity and relate to horizontal asymptote I–B I – C – 1, 2 I – B, C, D Learner Expectations T.L.W: Determine infinite limits from the left and from the right Learner Expectations T.L.W: Determine infinite limits from the left and from the right Learner Expectations T.L.W: Determine infinite limits from the left and from the right Find and sketch the vertical asymptotes of the graph of a function Find and sketch the vertical asymptotes of the graph of a function Find and sketch the vertical asymptotes of the graph of a function Determine finite limits at infinity Determine finite limits at infinity Determine finite limits at infinity Determine the horizontal asymptotes, if any, of the graph of a function Suggested Resources Text Pages 96-100 Friday 1–E 1–D Suggested Resources Text Pages 102-103 Vocabulary Strategies Review all methods of finding limits discussing continuity, finding vertical and horizontal asymptotes Determine the horizontal asymptotes, if any, of the graph of a function Suggested Resources Text Pages Test Determine the horizontal asymptotes, if any, of the graph of a function Suggested Resources Text Pages Test Vocabulary Strategies 6 week test Assessment p.101: 9-42 Assessment p.203: 1-30 Assessment p.102: 1-40 Assessment Test Scaffolding Questions Scaffolding Questions Scaffolding Questions Scaffolding Questions Vocabulary Strategies 6 week test Assessment Test Scaffolding Questions Monday Pre Cal CALC Tuesday Calculus AB Second Six Weeks Week 7 10/8/07 to 10/12/07 Wednesday 1–E Thursday 1–E II – A – 1 II – A – 3 II – A – 2 II – A – 4 Learner Expectations T.L.W: Find the slope of the tangent line to a curve at a point Learner Expectations T.L.W: Find the slope of the tangent line to a curve at a point Learner Expectations T.L.W: Find the slope of the tangent line to a curve at a point Learner Expectations T.L.W: Find the slope of the tangent line to a curve at a point Learner Expectations T.L.W: Find the derivative of a function using the constant rule. Use the limit definition to find the derivative of a function Use the limit definition to find the derivative of a function Use the limit definition to find the derivative of a function Use the limit definition to find the derivative of a function Find the derivative of a function using the power rule. Understand the relationship between differentiability and continuity Understand the relationship between differentiability and continuity Understand the relationship between differentiability and continuity Find the derivative of a function using the sum and difference rule. Suggested Resources Text Pages 110-112 Suggested Resources Text Pages Suggested Resources Text Pages Teacher made test Suggested Resources Text Pages 105-110 Vocabulary Secant line Tangent line Derivative Rate of change Strategies Find slopes of secant lines then relate to slope of tangent line using limits II – A – 1, 2, 3, 4 Vocabulary Differentiability Differentiable Differentiation Strategies Discuss derivatives of functions with sharp turns, vertical tangent lines, and discontinuities Vocabulary Instantaneous rate of change Strategies Answer questions. 1–E Friday 1–E 1–E II – A – 1, 2, 3, 4 Vocabulary Strategies Administer test over intro to derivatives Incorporate calculators to discuss continuity and differentiability Define the derivative of a function II – A – 1 Suggested Resources Text Pages 115-117 Vocabulary Constant rule Power rule Sum and difference rules Strategies Demonstrate constant rule, basic power rule, and sum/difference rules. Have students relate back to definition of a limit with limits to compare answers with rules. Assessment p.112: 1-16 Assessment p.113: 17-32 Assessment p.114: 39-65 Assessment Test Scaffolding Questions Scaffolding Questions Scaffolding Questions Scaffolding Questions Assessment p.123: 1-12, 17-28 Scaffolding Questions Pre Cal Monday Professional Development Day Tuesday 2–B Calculus AB Second Six Weeks Week 8 10/15/07 to 10/19/07 Wednesday 2 – B, 2 – C II – A – 1 II – F – 1, 2 CALC Learner Expectations Professional development day Learner Expectations T.L.W: Find the derivatives of the sine and cosine function II – A – 2 II – B – 1, 2 II – F – 1, 2 Learner Expectations T.L.W: Use derivatives to find rates of change Thursday 2 – B, 2 – C II – A – 2 II – B – 1, 2 II – F – 1, 2 Learner Expectations T.L.W: Use derivatives to find rates of change Friday 2 – B, 2 - C II – A – 2 II – B – 1, 2 II – F – 1, 2 Learner Expectations T.L.W: Find the slope of the tangent line to a curve at a point Use the limit definition to find the derivative of a function Understand the relationship between differentiability and continuity Find the derivatives of the sine and cosine functions Suggested Resources Text Pages Vocabulary Suggested Resources Text Pages p. 120 Vocabulary Strategies Strategies Derive formulas for derivatives of sine and cosine and apply to various functions Assessment Assessment p.123: 13-16, 29, 30, 41, 47 Scaffolding Questions Scaffolding Questions Suggested Resources Text Pages p. 121 Vocabulary Linear approximations Strategies Find equation of tangent and normal lines, points with horizontal tangent lines, apply linear approximations Assessment p.124:43-59 Scaffolding Questions Suggested Resources Text Pages p. 121 Vocabulary Average rate of change Strategies Compare average rate of change to instantaneous rate of change Assessment p.124: 61-70 p.126: 81-88 Scaffolding Questions Use derivatives to find rates of change Suggested Resources Text Pages Quiz Vocabulary Strategies Administer quiz Assessment Quiz Scaffolding Questions Monday Pre Cal 1–D 1–E II – E – 5 CALC Learner Expectations T.L.W: Use derivatives to find rates of change Suggested Resources Text Pages p.122 Vocabulary Calculus AB Second Six Weeks Week 9 10/22/07 to 10/26/07 Tuesday Wednesday 1–D 1–D 1–E 1–E 2–B 2–B II – A – 2 II – A – 2 II – B – 1 II – B – 1 II – C – 2 II – C – 2 II – E – 5 II – E – 5 II – F – 1, 2 II – F – 1, 2 Learner Expectations Learner Expectations T.L.W: T.L.W: Find the slope of the tangent line Find the slope of the tangent line to a curve at a point to a curve at a point Use the limit definition to find the derivative of a function Use the limit definition to find the derivative of a function Understand the relationship between differentiability and continuity Understand the relationship between differentiability and continuity Find the derivatives of the sine and cosine functions Find the derivatives of the sine and cosine functions Use derivatives to find rates of change Suggested Resources Text Pages p.161 Use derivatives to find rates of change Suggested Resources Text Pages Vocabulary Vocabulary Free fall Strategies Discuss free fall formula and apply to various situations (metric and customary) Assessment p.125: 71-79 Scaffolding Questions Strategies Review all concepts of differentiation up to this point Assessment Oral evaluation Scaffolding Questions Strategies Administer test Assessment Teacher made test Scaffolding Questions Thursday Friday 2–B 1 II – F – 2 II – F – 1, 2 Learner Expectations T.L.W: Find the derivative of functions using the product and quotient rules Learner Expectations T.L.W: Find the derivative of functions using the product and quotient rules Find the derivative of trigonometric functions Suggested Resources Text Pages p.127-130 Suggested Resources Text Pages p.131-132 Vocabulary Product and quotient rules Vocabulary Secant, cosecant, tangent, cotangent Strategies Use rules to find derivatives of trig functions other than sine and cosine with product and quotient rules Strategies Use quotient and product rule to find derivatives Assessment p.134: 1-20 Scaffolding Questions Assessment p.134: 21-56 Scaffolding Questions Monday Tuesday Calculus AB Second Six Weeks Week 10 10/29/07 to 11/2/07 Wednesday Thursday Friday Pre Cal II – F – 1 II – F – 3 Learner Expectations T.L.W: Find the derivative using the general power rule Learner Expectations T.L.W: Find the derivative of a function using the chain rule Simplify the derivative of a function using algebra Simplify the derivative of a function using algebra II – F – 1, 3 II – F – 1, 3 II – F – 1, 3 CALC Suggested Resources Text Pages 139-141 Vocabulary General power rule Strategies Find the derivative of functions of the form y = (f(x))n Suggested Resources Text Pages 137-138 Vocabulary Chain rule Strategies Find the derivative of functions using the chain rule Learner Expectations T.L.W: Find the derivative of trigonometric functions using the chain rule Simplify the derivative of a function using algebra Suggested Resources Text Pages 142 Vocabulary Strategies Find the derivatives of functions of higher power trig functions Learner Expectations T.L.W: Find the derivative using the general power rule Learner Expectations T.L.W: Find the derivative using the general power rule Simplify the derivative of a function using algebra Simplify the derivative of a function using algebra Find the derivative of a function using the chain rule Find the derivative of a function using the chain rule Find the derivative of trigonometric functions using the chain rule Find the derivative of trigonometric functions using the chain rule Suggested Resources Text Pages 137-142 Suggested Resources Text Pages 137-142 Vocabulary Strategies Use the chain to find rate of change in application problems Vocabulary Strategies Teacher made quiz on general power rule, chain rule, and trig rules Quiz on product and quotient rules and trig derivatives Assessment p.143: 7-30 Quiz Scaffolding Questions Assessment p.144: 53-62 Scaffolding Questions Assessment p.143: 1-6 p.144: 39-52 Scaffolding Questions Assessment p.145: 79-91 Scaffolding Questions Assessment Quiz Scaffolding Questions Monday Tuesday Calculus AB Second Six Weeks Week 11 11/5/07 to 11/9/07 Wednesday Thursday Friday Pre Cal II – F – 3 II – F – 1, 2, 3 Learner Expectations T.L.W: Distinguish between functions written in implicit form and explicit form Learner Expectations T.L.W: Distinguish between functions written in implicit form and explicit form Use implicit differentiation for find the derivative of a function Use implicit differentiation for find the derivative of a function Suggested Resources Text Pages 146-149 Suggested Resources Text Pages 150 II – F – 1, 2, 3 II – F – 1, 2, 3 CALC Vocabulary Implicit functions Strategies Discuss differences between implicit and explicit functions Vocabulary Strategies Find 2nd derivatives implicitly being sure to substitute y into the first derivative Learner Expectations T.L.W: Review all derivative rules covered up to this point Learner Expectations T.L.W: Administer test II – E – 3 II – E – 5 Learner Expectations T.L.W: Find a related rate Use related rates to solve real life problems Suggested Resources Text Pages Suggested Resources Text Pages Vocabulary Strategies Review all derivative rules covered up to this point Vocabulary Strategies Administer test Suggested Resources Text Pages 153-156 Vocabulary Related rate Strategies Find rate of change of functions with 2 or more variables Find derivatives implicitly Assessment p.151: 1-34 Scaffolding Questions Assessment p.151: 35-52 Scaffolding Questions Assessment Assessment Test Scaffolding Questions Scaffolding Questions Assessment p.158: 11-21 Scaffolding Questions Monday Tuesday Calculus AB Second Six Weeks Week 12 11/12/07 to 11/16/07 Wednesday Thursday Friday Pre Cal CALC II – E – 3 II – E – 5 II – F – 1, 2 I–D–3 Learner Expectations T.L.W: Find a related rate Learner Expectations T.L.W: Develop and use properties of the natural logarithmic function Learner Expectations T.L.W: Develop properties of the natural exponential function Find derivatives of functions involving the natural logarithmic function Differentiate natural exponential functions Use related rates to solve real life problems Suggested Resources Text Pages 153-156 Vocabulary Strategies Find rate of change of functions with 2 or more variables Assessment p.159: 22-46 Scaffolding Questions Suggested Resources Text Pages 317-323 Vocabulary Natural logarithm II – F – 1, 2 I–D–3 Suggested Resources Text Pages 344-347 Learner Expectations T.L.W: Answer questions and review related rates and natural logarithmic and exponential functions Suggested Resources Text Pages Vocabulary Natural exponential Strategies Review properties of natural logs Strategies Review properties of exponents Find derivative of functions involving natural logarithm Find derivative of functions involving eu Assessment p.324: 13-66, 77-85 Assessment p.350: 1-52 Scaffolding Questions II – E – 3 II – F – 1,2 Scaffolding Questions II – E – 3 II – F – 1, 2 Learner Expectations T.L.W: Review and administer quiz Suggested Resources Text Pages Vocabulary Strategies Vocabulary Review Strategies Review and administer quiz Assessment Oral evaluation Quiz Scaffolding Questions Assessment Scaffolding Questions Monday Tuesday Calculus AB Second Six Weeks Week 13 11/19/07 to 11/23/07 Wednesday Thursday Friday Pre Cal Benchmark Benchmark Learner Expectations T.L.W: Benchmark Learner Expectations T.L.W: Benchmark II – C – 2 II – C – 2 CALC Suggested Resources Text Pages Vocabulary Strategies Benchmark Assessment Benchmark Scaffolding Questions Suggested Resources Text Pages Vocabulary Strategies Benchmark Assessment Benchmark Scaffolding Questions Learner Expectations T.L.W: Understand the definition of extrema of a function on an interval Learner Expectations T.L.W: Understand the definition of extrema of a function on an interval Understand the definition of relative extrema of a function on an open interval Understand the definition of relative extrema of a function on an open interval Find the extrema on a clased interval Find the extrema on a clased interval Determine intervals on which a function is increasing or decreasing Determine intervals on which a function is increasing or decreasing Apply the first derivative test Apply the first derivative test to find relative extrema of a to find relative extrema of a function function Suggested Resources Suggested Resources Text Pages Text Pages 165-169 165-16179-185 179-185 Vocabulary Vocabulary Extrema Increasing Absolute minimum Decreasing Absolute maximum Critical values Relative minimum First derivative test Relative maximum Strategies Find maximum and minimum (absolute and relative) on open and closed intervals via the first derivative Assessment p.170: 1-38 Scaffolding Questions Strategies Find maximum and minimum (absolute and relative) on open and closed intervals via the first derivative Assessment p.186: 1-56 Scaffolding Questions II – D – 2,3 II – E – 1 Learner Expectations T.L.W: Determine intervals on which a function is concave upward or concave downward Find any points of inflection of the graph of a function Apply the second derivative test to find relative extrema of a function Suggested Resources Text Pages 189-193 Vocabulary Concavity Inflection point Second derivative test Strategies Find intervals of cancavity and points of inflection on open and closed intervals via the second derivative Assessment p.194: 1-66 Scaffolding Questions Monday Pre Cal CALC 1–D Tuesday Calculus AB Second Six Weeks Week 14 11/26/07 to 11/30/07 Wednesday Thursday Friday 1–D II – C – 1, 2 II – C – 1, 2 II – D – 1, 2, 3 II – D – 1, 2, 3 II – E – 1 II – E – 1 Learner Expectations Learner Expectations T.L.W: Understand the definition of extrema of a function on an interval Learner Expectations Thanksgiving Learner Expectations Thanksgiving Suggested Resources Text Pages Suggested Resources Text Pages Learner Expectations Thanksgiving Understand the definition of relative extrema of a function on an open interval Find the extrema on a clased interval Determine intervals on which a function is increasing or decreasing Apply the first derivative test to find relative extrema of a function Determine intervals on which a function is concave upward or concave downward Find any points of inflection of the graph of a function Apply the second derivative test to find relative extrema of a function Quiz on Tuesday Suggested Resources Text Pages AP released tests Vocabulary Strategies Use first and second derivative to analyze the graphs of f, f’. and f’’ Assessment AP released tests Scaffolding Questions Suggested Resources Text Pages AP released tests Vocabulary Strategies Use first and second derivative to analyze the graphs of f, f’. and f’’ Assessment AP released tests Quiz Scaffolding Questions Suggested Resources Text Pages Vocabulary Vocabulary Vocabulary Strategies Strategies Strategies Assessment Assessment Assessment Scaffolding Questions Scaffolding Questions Scaffolding Questions Monday PreCa l CALC 1–D II – C – 1, 2 II – D – 1, 2, 3 Learner Expectations T.L.W: Understand the definition of extrema of a function on an interval Understand the definition of relative extrema of a function on an open interval Tuesday 1–D II – C – 3 Calculus AB Second Six Weeks Week 15 12/3/07 to 12/7/07 Wednesday 1–D 1–D II – C – 3 Learner Expectations T.L.W: Understand and use Rolle’s Theorem Learner Expectations T.L.W: Understand and use Rolle’s Theorem Understand and use the Mean Value Theorem Understand and use the Mean Value Theorem Thursday II – E – 2 Learner Expectations T.L.W: Quiz Friday 1-D II – E – 2 Learner Expectations T.L.W: Solve applied minimum and maximum problems Solve applied minimum and maximum problems Find the extrema on a clased interval Determine intervals on which a function is increasing or decreasing Apply the first derivative test to find relative extrema of a function Determine intervals on which a function is concave upward or concave downward Find any points of inflection of the graph of a function Apply the second derivative test to find relative extrema of a function Suggested Resources Text Pages AP released test Vocabulary Strategies Use graph of f’(x) to graph f(x) Use information about f’ and f’’ to graph f Assessment AP released test Scaffolding Questions Suggested Resources Text Pages 173-174 Vocabulary Rolle’s Theorem Strategies Understand and apply Rolle’s Theorem in application problems Assessment p.: 1-24 Scaffolding Questions Suggested Resources Text Pages 175-176 Vocabulary Mean Value Theorem Suggested Resources Text Pages 213-218 Vocabulary Optimization Strategies Understand and apply MVT in application problems Strategies Use 1st and 2nd derivative to find optimized value of a function Assessment p.177: 25, 57 Scaffolding Questions Assessment p. 218: 1, 17 Scaffolding Questions Suggested Resources Text Pages 213-218 Vocabulary Optimization Strategies Use 1st and 2nd derivative to find optimized value of a function Assessment Scaffolding Questions Monday Pre Cal 1–D Tuesday 1–D II – E – 2 Calculus AB Second Six Weeks Week 16 12/10/07 to 12/14/07 Wednesday 1–D 1–D III – A – 4 Thursday Friday 1–D III – E – 1 III – E - 1 CALC Learner Expectations T.L.W: Solve applied minimum and maximum problems Suggested Resources Text Pages 213-218 Learner Expectations T.L.W: Test Suggested Resources Text Pages Vocabulary Strategies Optimize real world situation Assessment p.219: 18, 33 Scaffolding Questions Vocabulary Strategies Administer test Assessment Test Scaffolding Questions Learner Expectations T.L.W: Write the general solution of a differential equation Learner Expectations T.L.W: Write the general solution of a differential equation Learner Expectations T.L.W: Write the general solution of a differential equation Use the indefinite integral for antiderivatives Use the indefinite integral for antiderivatives Use the indefinite integral for antiderivatives Use the basic integration rules to find antiderivatives Use the basic integration rules to find antiderivatives Use the basic integration rules to find antiderivatives Find a particular solution of a differential equation Find a particular solution of a differential equation Suggested Resources Text Pages 249-253 Vocabulary Integration Antiderivative Constant of integration Indefinite integral Strategies Find the general solution of differential equations Assessment p.256: 1-26 Scaffolding Questions Suggested Resources Text Pages p.254-255 Vocabulary Strategies Use the given conditions to find the particular solution for a differential equation Assessment p.257: 41, 42, 44, 60 Scaffolding Questions Suggested Resources Text Pages p.251 Vocabulary Strategies Use integration formulas to find the solution of differential equations involving trig functions Assessment p.256: 27, 35, 43, 48 Scaffolding Questions Monday Tuesday Calculus AB Second Six Weeks Week 17 12/17/07 to 12/21/07 Wednesday Thursday Friday Pre Cal CALC III – A – 4 III – E – 1 III – E - 1 Learner Expectations T.L.W: Test II – E – 6 Learner Expectations T.L.W: Use differential equations to draw slope fields II – E – 6 II – E – 6 Learner Expectations T.L.W: Use initial conditions to find particular solutions of differential equations Learner Expectations T.L.W: Use initial conditions to find particular solutions of differential equations Suggested Resources Text Pages Teacher’s resources Suggested Resources Text Pages Teacher’s resources II – E – 6 Learner Expectations T.L.W: Quiz Review for final Use initial conditions to find particular solutions of differential equations Suggested Resources Text Pages Vocabulary Slope field Suggested Resources Text Pages Teacher’s resources Vocabulary Differential equation Vocabulary Vocabulary Suggested Resources Text Pages Teacher’s resources Vocabulary Separation of variables Strategies Administer test Strategies Use differential equations to draw slope fields Use initial conditions to find particular solutions of differential equations Assessment Test Scaffolding Questions Assessment Teacher’s resources Scaffolding Questions Strategies Solve differential equations by separating variables to determine a particular solution Strategies Solve differential equations by separating variables to determine a particular solution Assessment Teacher’s resources Assessment Teacher’s resources Scaffolding Questions Scaffolding Questions Strategies Solve differential equations by separating variables to determine a particular solution Assessment Teacher’s resources Scaffolding Questions Monday Tuesday Calculus AB Second Six Weeks Week 18 Wednesday Pre Cal CALC Thursday Teacher work day All topics covered this semester All topics covered this semester All topics covered this semester Learner Expectations T.L.W: Final exam Learner Expectations T.L.W: Final exam Learner Expectations T.L.W: Final exam Learner Expectations Suggested Resources Text Pages Suggested Resources Text Pages Suggested Resources Text Pages Suggested Resources Text Pages Vocabulary Vocabulary Vocabulary Strategies Administer final exam Strategies Administer final exam Strategies Administer final exam Assessment Final exam Assessment Final exam Assessment Final exam Scaffolding Questions Scaffolding Questions Scaffolding Questions Friday Holiday Learner Expectations Suggested Resources Text Pages Vocabulary Vocabulary Strategies Strategies Assessment Assessment Scaffolding Questions Scaffolding Questions