1 Calculus AB Priority Keys Aligned with Nevada Standards MA I MI L S MA represents a Major content area. Any concept labeled MA is something of central importance to the entire class/curriculum; it is a foundation or cornerstone of the course. Mastery of MA concepts is required for a student to succeed in a course. I represents Important content area. A little smaller than MA, I concepts must be Mastered but are not necessarily cornerstones of a course or required in order to succeed throughout the course. MI represents a Minor content area. Minor content areas are those that must be touched on briefly, introduced, but not thoroughly covered or mastered in order for students to achieve success in a course or completion of state and national standards. Nevada Academic Standards that are assessable at the local level only. Nevada Academic Standards that are assessable at the state and local levels. Interdisciplinary Links Key HI History LA Language Arts FL Foreign Language T Theology M Mathematics FA Fine Arts H Health/Physical Education TE Technology GV Government GE Geography SC Science WR Writing
2 Standards Keys Nevada/National Standards NCTM Content Standards Key NCTM Process Standards Key 1 Numbers and Operations 6 Problem Solving 2 Algebra 7 Reasoning and Proof 3 Geometry 8 Communication 4 Measurement 9 Connections 5 Data Analysis 10 Representation Common Core State Standard-ELA Link Key Reading Standards for Literature RL Reading Standards for Literacy in History/Social Studies RH Reading Standards for Informational Text RI Reading Standards for Literacy in Science/Technical RST Writing Standards W Writing Standards for Literacy in Social Studies/Sci/Tech WHST Speaking and Listening Standards SL Language Standards L Assessment Key Problems of the Week will be assigned, reviewed and assessed every class. An assignment representing or Proficiency style questions and spiraled review over previous or current areas of study. Assigned and assessed weekly. An essay style question requiring creative analytical written response; included with each Problem of the Week assignment. includes (but is not limited to): white board response questions, in-class practice worksheets, teacher/student group questioning, exit tickets and solving problems using manipulative resources.
3 Week Objective State/National Standard Common Core ELA Standard Assessment 1 Chapter 1 Sections Find increments, slope, and equations for parallel and perpendicular lines Find linear regression equations Review interval analysis and solving quadratic inequalities Solve quadratic inequalities by a calculator NCTM 2,3,4,9, NCTM 2,3,4,5, RST 2,4,7 NCTM 2,8,9, NCTM 2,8,9, WST 2c, 4 Review functions, function notation, domain, range (no calculator), even and odd functions Find function compositions NCTM 2,6, NCTM 2,6, Chapter 1 Sections Review piecewise functions Review exponents Review exponential growth and decay NCTM 2,3,7, , NCTM 1,2,4,6, , NCTM 2,4,5,6,8, RST 2, 4, 7 Graph using parametric mode with and without calculator NCTM 2,6,9 Change from parametric mode to Cartesian mode and vice versa NCTM 2,6,9 WST 2c, 4 3 Chapter 1 Section Find inverses NCTM 1,2,7 Identify 1 1 functions NCTM 1,2,7 Review logarithms NCTM 1,2,7
4 Review log properties NCTM 1,2,7 Review trigonometry NCTM 2,3,7,8 Convert from radians to degrees and vice versa NCTM 2,3,4,9 Graph trig functions NCTM 2,3,7,9,10 Review inverse trigonometry NCTM 2,7 Translate trig graphs NCTM 2,3,7,8 Finish trig review NCTM 2,3,7,8 Develop an intuitive understanding of limits 4 Chapter 1 Sections 1.6 & 1.7 Chapter 2 Section Chapter 2 Section Compare and contrast average and instantaneous rates of change Find limits by: a graph, substitution, algebra, numerical Evaluate limits involving sin x lim x0 x Prerequisites for Calculus Assessment Lines Functions and Graphs Exponential Functions Parametric Equations Functions and Logarithms Trigonometric Functions Find, horizontal, vertical and slant asymptotes Identify end behavior Prerequisites for Calculus Mastery Assessment: The test will be free response over material from Chapter 1. One page of the test will be takehome.
5 Use sandwich theorem to prove sin x lim x x Find holes More practice finding limits Prove continuity at a point WST 1c,e Types of discontinuity Introduce the Intermediate value theorem, IVT WST 1c,e Draw functions from clues Find the slope of the secant and average rate of change Find the slope of the tangent line Find the instantaneous rate of change 6 Chapter 2 Sections 2.4 Find the slope of the normal line Write equations for tangent lines Find the derivative from the limit of a difference quotient Find vertical tangents Limits and Continuity Mastery Assessment: The test will be free response over material from Chapter 2. One page of the test will be takehome.
6 7 Chapter 3 Sections 3.1 & Chapter 3 Section 3.3 Limits and Continuity Assessment Rates of Change and Limits Limits Involving Infinity Continuity Rates of Change and Tangent Lines Find the derivative from both versions of the definition Notice and find when a continuous function is not differentiable WST 1c,e Find one sided derivatives Find derivatives on a calculator Know differentiation rules Apply power, product and negative exponent rules Find higher derivatives Apply derivatives to free-fall problems RST 2,7 Find instantaneous rates of change and average rates of change RST 2,7 9 Chapter 3 Sections Find and explain particle movement RST 2, 7 Apply derivatives to economics marginal cost and marginal revenue RST 2.7 Prove the derivatives of y = sinx and y = cosx WST 1c,e Find jerk Use the chain rule to find the derivatives of composite functions Differentiate parametric equations
7 10 Chapter 3 Section 3.7 Solve word problems using derivatives SEMESTER 1 MIDTERM ASSESSMENT Prerequisites for Calculus (Ch 1) Limits and Continuity (Ch 2) Derivatives (Ch 3) o Derivative of a function o Differentiability o Rules for Differentiation o Velocity and Other Rates of Change o Derivatives of Trigonometric Functions RST 2, 7 Find the derivative by implicit differentiation Find 2 nd derivative using implicit differentiation Find the equations for tangent to circles Find the derivative of inverse functions SEMESTER 1 MIDTERM Mastery Assessment: The test will be free-response over material from the weeks 1-9 of school. 11 Chapter 3 Sections 3.8 & 3.9 Find the derivatives of trig functions Start take home problems RST 2,7 Find the derivative of inverse trig functions Find the derivatives of exponential and logarithmic functions 12 Chapter 3 Section 3.9 Chapter 4 Section 4.1 Practice logarithmic differentiation Prove the Arbitrary Power Rule
8 Identify absolute extreme values Find critical points and relative extreme Apply the Mean Value Theorem RST 2,7 Find where functions are increasing and decreasing 13 Chapter 4 Sections Explore functions having the same derivative that differ only by a constant Review interval analysis and use it in graphing AMC Apply 1 st derivative test for local extema Find inflection points and concavity 14 Chapter 4 Derivatives and Applications of Derivatives Assessment Chain Rule Implicit Differentiation Derivatives of Inverse Trigonometric Functions Derivatives of Exponential and Logarithmic Functions Extreme Values of Functions Mean Value Theorem AMC Derivatives and Applications of Derivatives Mastery Assessment: The test will be free response over material from Chapter 3.6, 3.7, 3.8, 4.1 and 4.2. One page of the test will be take-home.
9 15 Chapter 4 Sections 4.3 & 4.4 Use the 2 nd derivative test for local extreme Use a calculator to find extreme and concavity Optimize problems from geometry, algebra, business, and economics RST 2, 7 AMC Continue optimizing especially from business RST 2,7 Minimize average cost RST 2,7 16 Chapter 4 Sections 4.4 & 4.5 Find the linearization at a point AMC Find roots using Newton s method Estimate change by differentials RST 2,4,7
10 17 Chapter 4 Section 4.6 Solve related rates RST 2,4,7 Estimate area using RAM s Estimate volume using RAM s 18 Chapter 5 Sections 5.1 & 5.2 Review IVT, MVT, and linearization Find Riemann sums Find the area of a nonnegative curve Use numerical integration--calculator Use geometry to integrate 19 Chapter 5 Sections What are bounded functions? When can discontinuous functions be integrated?
11 Study rules for integration Start the geometry proof of the Fundamental Theorem of Calculus What is the difference between integration and area? Find the average value of a function 20 SEMESTER 1 FINAL ASSESSMENT Prerequisites for Calculus (Ch 1) Limits and Continuity (Ch 2) Derivatives (Ch 3) Applications of Derivatives (Ch 4) SEMESTER 1 FINAL Mastery Assessment: The test will be free-response over material from the weeks 1-19 of school. Review conclusions from the Fundamental Theorem of Calculus 21 Chapter 5 Sections 5.4 & 5.5 Solve word problems using integration RST 2, 7 Decide when to differentiate and when to integrate Find area using finint
12 22 Chapter 6 Section 6.1 Use the trapezoid rule to find area Begin indefinite and definite integration Apply the Fundamental Theorem of Calculus Review direct and indirect variation The Definite Integral Assessment: Estimating with Finite Sums Definite Integrals Definite Integrals and Antiderivatives Fundamental Theorem of Calculus Trapezoid Rule The Definite Integral Mastery Assessment: The test will be free response over material from Chapter 5. One page of the test will be takehome. Draw slope fields 23 Chapter 6 Sections 6.1 & 6.2 Start integration by substitution Find total distance traveled from velocity RST 2,7 24 Chapter 6 Sections 6.3 & 6.4 Integrate secx, tanx, cotx Continue separable differential equations Solve problems using exponential growth and decay WST 2c.4 RST 2,7 25 Chapter 6 Continue exponential growth and decay RST 2, 7 Find % remaining, half-life, and doubling time RST 2,7
13 Sections 6.4 & 6.5 Chapter 7 Section 7.1 Continue particle movement RST 2,7 Analyze logistic growth RST 2,4,7 What is the difference between displacement and total distance traveled? RST 2,7 26 Chapter 7 Sections 7.1 & 7.2 Find the area between 2 curves Find the area between 2 curves across the y axis Make a choice whether to integrate across the RST 5 x or y axis Differential Equations and Mathematical Differential Equations and Mathematical Modeling Mastery Assessment: Modeling: The test will be free response over material from Antiderivatives and Slope Fields Chapter 6. One page of the test will be takehome. Integration by Substitution Exponential Growth and Decay Population Growth 27 Chapter 7 Section 7.3 Find volume from a known cross section RST 2,7 28 Chapter 7 Section 7.3 Continue finding volume from a known cross section Find volume of revolution using disk method, revolving around the x and y axis.
14 29 Chapter 9 Section 9.4 SEMESTER 2 MIDTERM ASSESSMENT: The Definite Integral (Ch 5) Differential Equations and Mathematical Modeling (Ch 6) Applications of Definite Integrals (Ch 7) o Integral as Net Change o Areas in the Plane o Volumes Find the volume of revolution using the washer method RST 2,4,7 SEMESTER 2 MIDTERM Mastery Assessment: The test will be free-response over material from the weeks of school. 30 Chapter 8 Section 8.1 Find the volume of revolution, revolving around lines other than the x and y axes RST 2,4,7 Apply L Hopital s Rule to limits Compare rates of growth Begin packet (review) RST 2,7 31 Review Packets (review) Applications of Definite Integrals and L Hopital s Rule Take Home Assessment Areas in the Plane Volumes L Hopital s Rule Relative Rates of Growth RST 2,7 Applications of Definite Integrals and L Hopitals Rule Take Home Mastery Assessment: The test will be free response over material from Chapter 7 and 8.1
15 32 Review Packets (review) RST 2,7 33, 34 Review Packets (review RST 2,7 35 Trig Star Review RST 2, Polar Review RST 2,7 Integrate by parts
16 38 SEMESTER 2 FINAL ASSESSMENT Prerequisites for Calculus (Ch 1) Limits and Continuity (Ch 2) Derivatives (Ch 3) Applications of Derivatives (Ch 4) The Definite Integral (Ch 5) Differential Equations and Mathematical Modeling (Ch 6) Applications of Definite Integrals (Ch 7) L Hopital s Rule (Ch 8.1) SEMESTER 2 FINAL Mastery Assessment: The test consists of free response and multiple choice questions. The format will be similar to an actual exam.