Unit Quarter Week Topics Assessments 1 Functions & Trig. Review 1 13 Function Representations (Graphical, Verbal, Numerical, Analytical) Functions and Models (Linear, Quadratic, Power, Root, Rational, Trigonometric, Exponential, Logarithmic, Piecewise, Absolute Value, Step, Composite) Function Properties (Odd, Even, Symmetry, Increasing/Decreasing, One) Transformations of Functions Reflect, Stretch, Compress) Trigonometry Review (Unit Circle, Trigonometric Identities) Graphing Calculator Activities (graph a function within an arbitrary viewing window, find zeros of functions) Daily Five Question Quizzes Test (Functions & Trig. Review) consists of: Multiple Choice, Constructed Response, Extended Constructed Response 2 Limits and Continuity 1 47 Formal Definition of Limit Limit Laws Infinite Limits (Indeterminate Forms) Horizontal & Vertical Asymptotes on communicating limit justifications) Continuity (3 Conditions) Discontinuity (Removable, Jump, Infinite) Intermediate Value Theorem (Existence Theorem) Sketch graphs of functions using limit properties Daily Five Question Quizzes Weekly AP Free Response Sets Test (Limits & Continuity) consists of: Multiple Choice, Brief Constructed Response, Extended 8
Constructed Response 3 Derivatives 1 & 2 814 Activity one Slope as a rate of change Instantaneous rate of change vs. Average rate of change Activity two Tangent & Normal Lines Limit Definitions of Derivatives (as h →0 and x→a) The Derivative as a Function (focus on communicating the importance of notation) Differentiability implies Continuity (not reverse) ---------------------------------------- Derivative (Constant, Power, Sum, Difference, Product, Quotient) Higher Order Derivatives Particle Motion (Position, Velocity, Acceleration, Jerk) (focus on communicating the importance of notation & drawing conclusions) ---------------------------------------- Trigonometric Derivatives Chain Rule Derivatives tables ---------------------------------------- Implicit Derivatives Exponential & Logarithmic Derivatives Derivative of an Inverse Function Derivatives of Inverse Trigonometric Functions (sin1x, cos1x, tan1x only) Daily Five Question Quizzes Weekly AP Free Response Sets Quiz (Rates of Change, Limit Definition of Derivatives) consists of: Brief Constructed Response Quiz (Derivative & Particle Motion) consists of: Brief Constructed Response Test (Derivative Rules) consists of: Multiple Choice, Brief Constructed Response, Extended Constructed Response Test (All Differentiation) consists of: Multiple Choice, Brief Constructed Response, Extended Constructed Response 4 of Derivatives 2 1520 Extrema (Critical Numbers, Absolute Max/Min, Relative Max/Min) Activity 3 Increasing/Decreasing Intervals Concavity Test Points of Inflection 1st & 2nd Derivative Tests (Max/Min) (focus on writing and Five Question Quizzes Weekly AP Free Response Sets Test (Apps. Of 9
drawing conclusions from sign charts) Graphing Calculator Activities (numerically calculate the derivative of a function) Mean Value Theorem & Rolle’s Theorem ---------------------------------------- Revisit sketching graphs of f, f ’, f ” L’Hopital’s Rule (revisit vertical asymptotes, horizontal asymptotes, limits at infinity) (focus on communicating limit justifications Using Derivatives to find Functions ---------------------------------------- Optimization (focus on writing and drawing conclusions) Related (focus on writing and drawing conclusions) Linearization Graphing Calculator Activities (store values without rounding and retrieve these stored values) Derivatives) consists of: Multiple Choice, Brief Constructed Response, Extended Constructed Response Quiz (Curve Sketching, L’Hopital’s Rule) consists of: Multiple Choice, Brief Constructed Response Quiz (Optimization, Related Rates, Linearization) consists of: Multiple Choice, Brief Constructed Response, Extended Constructed Response COMPREHENSIVE SEMESTER EXAM (timed exam – 90 minutes) consists of: Multiple Choice & 3 Free Response Questions (graded using AP College Board scale) 5 Integrals 3 2225 Activity 4 Finding of regions Riemann Sums (Left, Right, Midpoint) Trapezoidal Rule ---------------------------------------- Definite Integrals (focus on communicating the importance of notation) Indefinite Integral Rules (Power, Sum, Difference, Five Question Quizzes Weekly AP Free Response Sets Quiz (Finding areas, Riemann Sums, Trapezoidal Rule) consists of: Brief Constructed Response Quiz (Integration 10
Trigonometric, Exponential) Properties of Integrals ---------------------------------------- Fundamental Theorem of Calculus (Parts 1 & 2) Graphing Calculator Activities (numerically calculate the of a definite integral) Activity 5 Net Change Revisit Particle Motion (with integrals) (focus on communicating the importance of notation & drawing conclusions) ---------------------------------------- U-Substitution consists of: Multiple Choice, Brief Constructed Response Quiz (FTC, Net Change, Particle Motion) consists of: Constructed Response Test (All Integration) consists of: Multiple Choice, Brief Constructed Response, Extended Constructed Response 6 of Integrals 3 & 4 2630 Areas between curves Graphing Calculator Activities (find the intersection(s) of two functions, store values without rounding and retrieve these stored values, numerically calculate the value of a definite integral) Volumes (using disks and washers) ---------------------------------------- Cross Sections Arc Length Average Mean Value Theorem for Integrals Daily Five Question Quizzes Weekly AP Free Response Sets Quiz (Areas & Volume) consists of: Brief Constructed Response Test (Applications of Integrals) consists of: Multiple Choice, Brief Constructed Response, Extended Constructed Response 7 with Differential Equations 4 3132 Modeling with Differential Equations (Growth & Decay) (focus on writing and drawing conclusions) Separable Differential Equations Activity 6 Slope Fields Activity 7 Daily Five Question Quizzes Weekly AP Free Response Sets Test (Apps. with Diff. Eqs.) consists of: Multiple Choice, Brief Constructed Response, Extended Constructed Response Time! 4 33-36 Grade student samples & discuss grading techniques Practice timed multiple choice & free response questions AP Exam – Wednesday, May , 20 at 8:00 a.m. 11