AP Calculus AB - Fall 2005 Summer Homework is not a written assignment. It's a practice test for a trig/precalc test on our 1st day back! So if you can do all those problems and have already memorized the graphs, you don't need to actually 'do' anything! On the other hand, it won't help you much if you just 'write' out the homework and don't really 'know' the material. email: mrryono@hotmail.com for questions/help Day 1(8/25) - Go over Precalculus Practice Test Establishing a mental 'math dictionary' of graphs Absolute Value Functions, Cubic Curves, Square Root Function, log & exponential functions - Increasing vs Decreasing functions - Trig Graphs (including principal trig functions) y = sin(x) vs y = Sin(x) Graphing ellipses & hyperbolas (also y = 1/x) Solving trig equations & log and exponential equations Domain & Range Hwk: Study for the 1st Precalculus Review Test Day 2(8/29) - Go over graphs of inverse trig functions Precalc Test Notation: Symbols & Greek alphabet Set & Logic symbols Neighborhoods (interval notation ex/ (a,b) vs [a,b] Hwk: p.10 #1-45(5k+1) Day 3(8/31) - FUNCTIONS - Relations vs Functions (D & R) - Inverse Functions - functions that are one-to-one (1-1) have inverse functions /y=x line symmetry / restricting domains to get 1-1 functions / Domain of a function equals the Range of its inverse. Slope of a 'secant' line: f(x+h)-f(x) divided by h??? Limits? Trick #1 - Simplifying Complex Fractions Trick #2 - Hole-in-the-graph Trick Piecewise Functions KINEMATICS - in one-dimension distance traveled vs displacement avg speed vs avg velocity Differentiation - practice quiz Hwk: p.10 #1-45(5k+2) Extra Hwk: Solving Trig Equations and graphing y=|x| Day 4(9/2) - Function Catalog (linear(y=mx+b,m not zero), constant functions, square function, square root function, cubic function, polynomial, trig functions, principal trig functions(y=Sin(x), y=Cos(x), y=Tan(x), y=Cot(x)) Absolute Value, Step, signum function (piecewise) KINEMATICS - position-time graphs(functions) and instantaneous velocity vs avg velocity (practice quiz) more differentiation Hwk: p.10 #1-45(5k+3) Day 5(9/7) - Function Theory - Equal Functions? ex/ y=x vs y=(x^(1/2))^2 vs y=(x^2)^(1/2) Increasing vs Decreasing Functions Relative Maximum/Minimum Points Even Functions - y-axis symmetry Odd Functions - point symmetry w.r.t. (0,0) Step Function ex/ y = [2sin(x)] ex/ y=2[x] ex/ y=[2x] Trick #3 - Using the 'radical conjugate' Practice Quiz - Position-Time Graph Hwk: p.10 #1-45(5k+4) Day 6(9/9) - Average Rate of Change (slope of secant line) vs Instantaneous Rate of Change (slope of tangent line) Position-Time Graph - Quiz KINEMATICS - acceleration (avg vs instantaneous) acceleration direction vs "deceleration" Trig Function Values (practice quiz) Solving Trig Equations (vs working with Inverse Trig Functions) Log and Exponential Functions (graphs, D&R) Hwk: p.10 #1-45(5k) Day 7(9/13) - Laws of Exponents /Laws of Logs Derivative of the Square Root Function Solving Trig Equations (practice quiz) Quiz - Trig Function Values Relative Maximum Point (x,y) vs Relative Maximum Value relative vs absolute maxima "local" vs "global" maxima Extreme Points (relative or absolute maximum or minimum points) Trig Equations Practice Quiz KINEMATICS - velocity-time graph(practice quiz) negative acceleration (force is left) vs positive acceleration (force is to the right) Hwk: p.20 #1-50(4k+1) Day 8(9/15) - Composite Functions Derivative of the Square Root Function at (9,3) Trig Equations Quiz Go over position-time quizzes x-t graphs Hwk: p.20 #1-50(4k+2) Day 9(9/19) - Laws of Exponents & Logs Solving logarithmic and exponential equations (surprise) quiz - graphing y=x^2 or y=|x| Requiz - position-time graphs Hwk: p.20 #1-50(4k+3) Day 10(9/21) - Quiz - Velocity-Time Translation & Change of Scale - Practice Quiz More Derivatives (chain rule, derivative of y=sin(x)) Hwk: p.20 #1-50(4k) Day 11(9/23) - Polynomical Functions Inequalities - "Number Line Trick" practice quiz - graphing polynomials & inequalities Limits - as x goes to infinity /as x goes approaches 2 /as x approaches 2 from the right Hwk: p.51 #1-24,31-43(4k+1) Day 12(9/27) - Rational Functions -introduction Asymptotes and intercepts Limits 'as x goes to infinity' left- and right-hand limits Trick #7 - factoring the... Sum or Difference of 2 cubes Hwk: p.51 #1-24,31-43(4k+2) Day 13(9/29) - Rational Functions - formal notes Oblique Asymptotes too! + practice quiz (used with the hole-in-the-graph trick) velocity-time - Requiz Hwk: p.51 #1-24,31-43(4k+3) /p.70 #35-44(4k+3) Day 14(10/3) - Translation & Change of Scale Rational Functions - Quiz Graph y=f(|x|) even function! vs y=|f(x)|nonnegative! Limits - practice quiz Hwk: p.57 #1-21(4k+1) /p.70 #35-44(4k+1) Day 15(10/5) - Continuity Continuity at (1)a point (2)over an open interval and (3)over a closed interval "Removable Discontinuities" Limits - Quiz Translation/Change of Scale - Quiz 2 Hwk: p.57 #1-21(4k+2) /p.70 #35-44(4k+2) p.80 #1-28(4k+2) Day 16(10/7) - Translation/Change of Scale Problem #2 Rational Functions - Quiz Hwk: p.57 #1-21(4k) /p.70 #35-44(4k) p.80 #1-28(4k) /p.71 #45 Day 17(10/12) - Derivatives of sine and cosine Chain Rule Translation/Change of Scale Problem #3 Surprise Precalc Quiz - Functions (composites/inverses) Hwk: p.80 #1-28(4k+1) /p.116 #1-16(4k+1) p.117 #21-48(4k+1) /p.71 #46 Day 18(10/14) - Product Rule - Quotient Rule Derivatives of tangent, cotanget, secant, cosecant Tangent Lines and Normal Lines Point-Slope Form for the Equation of a Line Precalc Quiz - composite & inverse functions Hwk: p.116 #1-16(4k+2) /p.117 #21-48(4k+2) p.141 #1-36,41-51(4k+2) Day 19(10/18) - Differentiation - Practice Quiz Derivative Drill Limits - practice quiz L'Hopital's Rule Rational Functions Requiz Precalc Quiz - exponential & log equations Hwk: p.116 #1-16(4k+3) /p.117 #21-48(4k+3) p.141 #1-36,41-51(4k+3) Day 20(10/20) - Law of Falling Bodies constant acceleration problems - practice quiz Translation/Change of Scale - finish practice quiz Hwk: p.116 #1-16(4k) /p.117 #21-48(4k) p.141 #1-36,41-51(4k) /p.152 #1 Day 21(10/24) - Calculator Practice Area Problems (with calculator!) TI-83 Graphing Calculator - (8)nDer, (9)nInt, (0)solver - (5)intersect (6)derivative (7)integral - function list with to buttons also quadratic formula program, graphing & windows Differentiation Practice Quiz Limits Practice Quiz Hwk: p.141 #1-36,41-51(4k+1) p.152 #3,5,7 /p.170 #3-41(4k+1) Day 22(10/26) - finish Constant Acceleration (practice) Increasing/Decreasing at a point, over an interval (and the derivative f'(x)>0 or f'(x)<0 or f'(x)=0) Thm/ Differentiable implies Continuity (contrapositive vs converse (latter not true) graph and solve inequalities(number line trick) Translation/Change of Scale Hwk: p.125 #1-20(a and d only)(4k+2) /p.152 #2,4 p.170 #3-41(4k+2) /p.181 #1-24(4k+2) Day 23(10/28) - Review Limits practice quiz Translation/Change of Scale Differentiation - xc quiz Hwk: p.152 #6,8,17 /p.170 #3-41(4k+3) p.181 #1-24(4k+3) Day 24(10/?) - 1st Derivative Test(number line) ex 5(p.241) /Given g'(x) graph, is g continuous or not? Differentiation - Quiz Hwk: p.153 #9,12,18 /p.170 #3-41(4k) p.181 #1-24(4k) /p.242 #1-18(4k) Day 25(11/1) - Product Rule (practice quiz) Quotient Rule (practice quiz) Limits Quiz Extra Credit Lunch Film - The Derivative Hwk: p.153 #10,13,20 /p.181 #1-24(4k+1) p.242 #1-18(4k+1) Day 26(11/3) - 1st Derivative Test(number line) for (1) increasing/decreasing functions and (2) maximum/minimum points(or function values) ex 1(p.239)/ y=x^3-6x^2+9x+1 ex/ y=x^(2/3) ex 3(p.240)/ f(x), a "piecewise" function ex 4(p.241)/ given the graph of f'(x)... review - constant acceleration problems Hwk: p.153 #11,14,21 p.242 #1-18(4k+2) Day 27(11/7) - Derivatives of logarithmic & exponential functions D(ln(x)) = 1/x p.447 ex/2,3,4 and D(e^x) = e^x p.463 ex/2,3 Change of Base Theorems for logs & exponents Limits Contest Hwk: p.242 #1-18(4k+3) p.449 #5-30(6k+1) /p.467 #5-20(6k+1) Day 28(11/9) - Implicit Differentiation (introduction) Constant Acceleration & Law of Falling Bodies Quiz Hwk: p.242 #19-38(4k) p.449 #5-30(6k+2) /p.467 #5-20(6k+2) Day 29(11/14) - Implicit Differentiation Limits - Requiz Log Equations precalc pop-quiz Hwk: p.190 #1-12,17-37(6k+3) /p.242 #19-38(4k+1) p.449 #5-30(6k+3) /p.467 #5-20(6k+3) Day 30(11/16) - 2nd Derivative Number Lines Concavity & Inflection Points The "real" 2nd Derivative Test Constant Acceleration - Requiz product rule quiz Hwk: p.190 #1-12,17-37(6k+4) /p.242 #19-38(4k+2) p.449 #5-30(6k+4) /p.467 #5-20(6k+4) Day 31(11/18) - Number Line Notes - Section 3.1 f' graphs - practice quiz Hwk: p.242 #19-38(4k+3) p.190 #1-12,17-37(6k+5) /p.254 #1-30(6k+5) p.449 #5-30(6k+5) /p.467 #5-20(6k+5) Day 32(11/22) - Related Rates 2.0 (Ex 1,2) f' graphs - quiz polynomials & inequalities - precalc pop-quiz (next?) Hwk: p.190 #1-12,17-37(6k) /p.197 #1-45(6k) p.254 #1-30(6k)/p.449 #5-30(6k) Day 33(11/28) - Related Rates 2.0 (Ex 3) Integration Theorems (Section 4.1) f' graphs - requiz Hwk: p.190 #1-12,17-37(6k+1) /p.197 #1-45(6k+1) p.254 #1-30(6k+1) /p.467 #5-20(6k) Day 34(11/30) - go over Log Equations quiz go over product rule quiz Constant Acceleration - re-requiz Hwk: p.190 #1-12,17-37(6k+2) /p.197 #1-45(6k+2) p.289 #1-24(6k+2) /p.324 #1-42(6k+2) Day 35(12/2) - f' graphs vs f graphs (see hwk) "Reverse Power Rule" Integration (Antiderivative or indefinite integral) (Area or Definite Integral) Max/Min - p.226 #21 Product Rule - Requiz Hwk: p.197 #1-45(6k+3) /p.254 #1-30(6k+3) p.289 #1-24(6k+3) /p.324 #1-42(6k+3) Day 36(12/6) - Max/Min Problems Max/Min - p.222 ex 3 Max/Min - p.224 ex 6 \Integration Technique "u-substitutions" (reverse chain rule) Quotient Rule - Quiz Hwk: p.197 #-45(6k+4) /p.289 #1-24(6k+4) p.324 #1-42(6k+4) Day 37(12/8) - Finding areas with integration Vertical Strips vs Horizontal Strips Related Rates - Quiz #1 Quotient Rule - Quiz Hwk: p.197 #1-45(6k+5) /p.289 #1-24(6k+5) p.324 #1-42(6k+5) /p.396 #1-48(6k+5) Day 38(12/12) - Max/Min - practice quiz 1.0 Area vs Integration Hwk: p.289 #1-24(6k) /p.324 #1-42(6k) p.396 #1-48(6k) Day 39(12/14) - Riemann Sums (rectangles) Max/Min - finish practice quiz Quotient Rule - Requiz Log Equations - Requiz(optional/no penalty) Hwk:p.289 #1-24(6k+1) /p.324 #1-42(6k+1) p.334 #1-44(6k+1) /p.396 #1-48(6k+1) *Get the Max/Min Take-Home Test (60pts) Day 40(12/16) - Area & Integration Horizontal Strips /Points of intersection Related Rates - Requiz Polynomial Graphs & Inequalities - Quiz Hwk: p.334 #1-44(6k+2) /p.396 #1-48(6k+2) Take Home - Max/Min Test (help each other!) email MrR before xmas for help/hints. ------------------------------------- Day 41 (1/4) - Max/Min Problems Integration - practice quiz Hwk: p.310 #85,88 p.334 #1-44(6k+3) /p.396 #1-48(6k+3) Day 42 (1/6) - Requiz Related Rates f' graphs - practice quiz Related Rates - Quiz #2 Translation/Change of Scale - precalc quiz Hwk: p.334 #1-44(6k+4) /p.368 #15-42(6k+4) p.396 #1-48(6k+4) Day 43(1/10) - Go Over Max/Min Quiz Integration - Areas & Volumes Hwk: p.334 #1-44(6k+5) /p.368 #15-42(6k+5) Day 44(1/12) - Final Review Go over Max/min Inverse Functions (and their reciprocal derivatives or slopes) Hwk: Study for Final