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AP CALCULUS B Spring 2010 April 26, 1010 U-Substitution pg 338 53 - 66 April 13, 2010 #17 Calculus Review 2007 A #1 Read article on How To Survive AP Exam Copy and Answer Review Quesions April 9, 2010 Optimization Problems April 8, 2010 2006 A #6 2006 B 3,5,&6 April 6, 2010 2009 B 1,2,3 April 5, 2010 2009 4,5,6 March 24,2010 March 22, 2010 #16 Displacement & Area I. D&S Exam 1 M. C II. Section 7.1 1 - 16 March 19 #15 Differential Equations I. AP 2006 #2 March 9, 2010 #14 Graphs and Derivatives Worksheet March 8, 2010 #13 Review I. Practice Test: Find the volume of the solid when the region bounded by y = x3 , x = 2 and the x-axis is revolved around 1. y = 0 2. y = 12 3. x = 0 4. x = 2 5. x = 4 II. Slope fields Matching III.AP Exam 2006 # 6 IV. Chapter 7 Review 2-26 Even March 4, 2010 #12 Integration Patterns I. AP Exam 2006 # 3 II. Matching Slope fields III. Integration Patterns Barron’s IV. Chapter 7 Review 1-25 odd March 3, 2010 #11 Slope Fields and Fund. Th of Calc Review I. AP Exam 2006 #4 II. Slope field worksheet 2 III. 5.4 2 – 48 E March 1, 2010 #10 Slope Fields I. Warm-Up Slope Fields Introduction Sheet II. Worksheet 1 on Slope Fields III. 5.4 Fundamental Th or Calc pg 302: QR 1-10. 1-49 odd February 26, 2010 #9 Fundamental Theorem of Calculus Part 1!!!!!!!!! I. WS 4.4: 47,51-57 odd II. FTOC P1 III. WS 4.3 2 – 48 even February 24, 2010 #8 The Area So Far I.Warm-Up Discovery Project II. AP Exam 2006 Question 1 IV. Larson 4.3 Worksheet 1-47 odd February 23, 2010 #7 Area & Volume Review I.Warm-Up AP Exam 2007 Question 1 II. Area: Princeton Review pg 200 2 – 10 Even III. Volume: Princeton Review pg 218 1,3,5,11 IV. WS 4.4 2-46 E February 19, 2010 #6 Area & Volume Review I. Mean Value Theorem for Integrals WS 4.4: 36, 38,40, 42 II. Volumes of Solids of Revolution WS(6.2) 7,13,15,17 III. AP Exam 2007 B Question 1 IV. 4.4 worksheet 1 – 45 odd February 18, 2010 #5Volumes of Solids of Revolution: Washer Method I. Warm-Up: 12 minutes ( ) 1. 4 – x2/2 2 = 2. Graph and find the pts of intersection of a. y = x + 6 and y = 6 – 2x – x2 b. y = x2 and y = √x 3. Find the volume of a 6 in tire whose outer radius is 15 in and inner radius is 10 in. II. Volume by Washer Method. The washer method is used when the axis of rotation is not a boundary of the revolved region. V = П ∫(R2 – r2) dx or V = П ∫(R2 – r2) dy Where R is the outer radius and r is the inner radius. Larson 6.2 Worksheet 7, 8, 14, 16 III. Larson 4.2 WS 2-48 Even February 12010 #4 Properties of Definite Integrals I. AP Exam 2007 Form B Question 4 II. Volume by Disk Method 1-6,8,9-12 III. Larsen 4.2 WS 1 – 47 odd February 12, 2010 #3 Volumes of Solids of Revolution: Disk Method I. Volume by Disk Method: Used when the Axis or Rotation is a Boundary of the region. Graph the regions in 1 and 2 below Bh = Πr2dx or Πr2dy 1.y = x2 , y = 0, x = 4 Vol of region revolved around x -axis 2. y = x2 , x = 0, y = 9 Vol of region revolved around y-axis 3. y = 2x + 4, y = 0, x = 2 Reg revolved around x – axis 4. y = 2x + 4, x = 0, y = 8 Reg revolved around y-axis 5. y= -x2 + 8, y = 4 revolved around y = 4 III. Definite Integral Practice 2 – 30 Even, 31-38 February 10, 2010 #2 Definite Integrals I. AP Exam 2007 From B Question 2 II. Warm-Up: Find the volume of a solid whose base is bounded by y = x2, y = -1, x = 0, and x = 3 with the indicated cross sections │ to the x-axis a. squares b. equilateral triangles c. semicircles III. Finding Definite Integrals Signed Areas pg. 279 Exp 1 IV. Definite Integral Practice WS Q1-Q10 & 1 – 29 odd February 9, 2010 #1 Volume of Solids: Known Cross-sections I. AP EXAM 2007 #6 II. Warm-Up: 1. On the same coordinate plane, graph f(x) = 1 – x , g(x) = - 1 + x 2 2 2. Find the points of intersection of f(x) and g(x) analytically. 3.Find the volume of the solid bounded by f, g and the y-axis with the indicated cross-sections perpendicular to the x-axis. a. squares, b. rectangles with h = 2b c. equilateral triangles d. semi-circles, e. iso rt. Δ. hyp on base, f. iso. rt. Δ. leg on base III. Indefinite Integral Review Wk Sh 1(Foerster) 1-25 IV.Find the volume of the solid bounded by y = x2 , x = 4, y = 0. a. squares, b. rectangles with h = 2b c. equilateral triangles d. semi-circles, e. iso rt. Δ. hyp on base, f. iso. rt. Δ. leg on base February 5, 2010 I. Warm-Up 1. Describe a Riemann Sum and what it is used for. 2. Write the formulas for: Area: Circle, Right Triangle, Equilateral Triangle, Square, Rectangle Volume: Rectangular Solid, Cylinder, Cone, Pyramid