MCV4U Semester 2:  2017-2018

# Unit 1: Limits and Derivatives

 Date Topic/Learning Goals Daily Work/Assignments Monday, February  5, 2018 Introduction and Review   We will review prerequisite skills for this course. Review Sheet:  Are you ready for Calculus and Vectors? Tuesday, February  6, 2018 Rationalizing Denominators   We will simplify expressions that contain radicals. Page 9   # 1, 2ac, 3abdf, 4bc, 6abdef, 7 Wednesday,  February 7, 2018 Slope of a Tangent   We will learn various methods of calculating the slope of a tangent line Page 18   # 3,6,8b,9c,10b,11, 17, 19-23 Thursday,  February  8, 2018 Rates of Change   We will learn average and instantaneous rate of change. Page 29 # 4, 7, 8, 10-13, 15bc,20, 22 Friday,  February 9, 2018 Limit of a Function   We will define a limit of a function. Page 38 # 4, 6-11,14, 15 Monday,  February  12, 2018 Properties of Limits   We will evaluate limits by using properties of limits including indeterminate forms. Page 45 # 4-10,12, 15, 16, Tuesday,  February 13, 2018 Continuity   We will examine continuous functions at particular points and define continuity. Page 51  # 4,5, 7, 8, 10,11, 13, 14,16 Wednesday,  February 14, 2018 Quiz #1 Infinite Limits We will learn how to evaluate limits at infinity. Handout Thursday  February  15, 2018 Infinite Limits Handout Friday  February 16, 2018 Definition of the Derivative   We will formally define a derivative using a limit. Page 74 #5-8, 10, 11, 15, 19 Monday, February 19, 2018 Family Day Tuesday,  February 20, 2018 Derivatives of Polynomial Functions.    We will learn how to find the derivative of various functions using specific properties. Page 73    # 1   Page 82 #2-4, 6, 7cd,8a,9bef, 10, 13, 14, 17a, 21, 25a(iii) Wednesday,  February 21, 2018 Product Rule   We will differentiate a product of two or more functions using the product rule. Page 90   # 1d-f, 2cd, 5cdf, 6, 7a, 8a, 9, 10, 12 Thursday,  February  22, 2018 Quotient Rule   We will differentiate a quotient of functions using the quotient rule. Page 97 #4bcef, 5-7, 9, 10,12,14,15 Friday, February 23, 2018 Quiz#2 Derivative of Composite Functions (The Chain Rule) Page 105  #1bdef, 4-5. 7-17 Monday,  February  26, 2018 Implicit Differentiation Page 564 #2, 3cd, 4-10, 12, 13 Tuesday,  February  27, 2018 Review Day 1 Page 92 #2, 6-9, 11,12,14,15, 17 Page 110 # 2-5 Wednesday,  February 28, 2018 Review Day 2 Page 110 # 7ab, 8, 10a,  11-13, 15 Page 112 # 17-19, 24, 26, 28-30 Thursday, March 1, 2018 Unit 1 Test

# Unit 2: Related Rates and Derivatives of Functions

 Date Topic/Learning Goals Daily Work/Assignments Friday, March 2, 2018 Introduction to Related Rates   We will learn how to work with related rates in word problems. Page 569 # 1ab, 3-7, 12, 13, 15-17, 20 Monday, March 5, 2018 Related Rates –Day 2 Page 569 # 1cde, 2,8-11, 18, 21 Tuesday, March 6,  2018 Higher Order Derivatives Velocity and Acceleration We will learn how to apply higher derivatives. Page 127 # 2- 4, 6bc, 8, 10-12, 14, 15, 17 Wednesday, March 7, 2018 The Natural Exponential Number “e” and Derivatives of Exponential Functions Page 232   # 2-13, 15 Thursday, March 8, 2018 The derivative of the Natural Logarithmic Function “ln x” Page 575 #3,4,5ab,6, 7a,8,9a 10-13 Friday, March 9, 2018 Quiz #3 Monday March 12, 2018  to Friday March 16, 2018 March Break Monday, March 19, 2018 Derivative of General Exponential Functions   Derivatives of General Logarithmic Functions Page 240 #1-6, 7ab, 8 Page 578 #1, 2, 3a, 4acef, 5, 7, 9a Tuesday,  March 20, 2018 Logarithmic Differentiation   We will learn how to find derivatives using logarithms. Page 582 # 1-9, 12, 13 Wednesday, March 21, 2018 Exponential and Logarithmic Differentiation Handouts Thursday,  March  22, 2018 Derivative of Sine and Cosine Functions Page 256 # 1-5, 14 Friday, March 23, 2018 Derivative of the Tangent Function Page 260 # 1-5, 8, 10, 11 Monday, March 26, 2018 Applications of Trigonometric Functions (Day 1) Handout:  Applications of Trigonometric Functions (Part 2,  Questions 1-3)  Page 257   #7, 10 Page 260   # 7 Tuesday, March 27, 2018 Quiz #4   Applications of Trigonometric Functions (Day 2) Handout:  Applications of Trigonometric Functions (Part 2,  Questions 4-10) Wednesday,  March  28, 2018 Review –Day  1 Page 156 # 3, 4, 7, 12, 27-30 Thursday, March 29, 2018 Review –Day  2 Page 263 # 1, 2, 4-8, 11,13, 14 Page 248 # 1-5, 6abc Friday, March 30, 2018 Good Friday Monday, April 2, 2018 Easter Monday Tuesday, April 3, 2018 Review –Day  3 Page 263 # 3, 9,  10, 15-17, 23

# Unit 3: Curve Sketching and Optimization

 Date Topic/Learning Goals Daily Work/Assignments Wednesday, April 4, 2018 Increasing and Decreasing Functions Local Extremum We will determine intervals of increase and decrease and discuss local extremum Page 169 #1,3,5, 7, 8           Page  178 # 5, 7-9, 11, 15 Thursday, April 5, 2018 Unit Test 2 Friday, April 6, 2018 Increasing and Decreasing Functions,  Local Extremum (Day2) Page 246  #10, 12 Page 260 #6 Monday, April 9, 2018 Vertical, Horizontal and Oblique Asymptotes We will learn how to determine equations of various asymptotes Page 193 # 1, 5, 7, 9, 10, 12,14, 17 Tuesday,  April  10, 2018 OSSLT Wednesday,  April 11, 2018 Concavity and Points of Inflection We will define points of inflection and examine concavity in graphs. Page 205  # 2, 4, 8-11 Thursday,   April  12, 2018 Curve Sketching (Day 1)   We will develop an algorithm for sketching functions Page 212  # 3, 4abefgh, 6 Friday,  April 13, 2018 Curve Sketching (Day 2) Page 213  # 4cdij, 7        Page 257  #8 Monday,  April  16,  2018 Inclement Weather Day Page 217  #1,3,5,7,12,14,17 Tuesday,   April  17, 2018 Optimization Word Problems   (Measurement) Page 145  # 1, 3-5, 7-9, 11,    13-14, 20, 21 Wednesday, April 18, 2018 Quiz #5   Optimization Word Problems Page 145  # 1, 3-5, 7-9, 11,    13-14, 20, 21                  Page 145  # 15, 16  Page 151, # 1, 4,  6-9, 11ab, 12, 14 Thursday,  April 19, 2018 Optimization Word Problems Page 151, # 1, 4,  6-9, 11ab, 12, 14 Friday,  April 20, 2018 Optimization Word Problems (Trigonometric and Exponential Functions) Page 257  # 6, 12,  13     Page 260   # 6 Page 245   # 4-6 Monday,  April  23, 2018 Optimization Problems Page 257  # 7, 11-13 Page 245 # 8, 9, 11, 14 Tuesday,  April  24, 2018 Unit 3 Review (Day 1) Page 156  # 9-11, 14-26  Page 219  #18-20 Wednesday, April 25, 2018 Unit 3 Review (Day 2) Page 156  # 9-11, 14-26  Page 219  #18-20 Thursday, April 26, 2018 Unit 3 Test

# Unit 4: Introduction and Application of Vectors

 Date Topic/Learning Goals Daily Work/Assignments Friday, April 27, 2018 Introduction to Vectors Page 279 # 1, 4-8, 10, 11 Monday,  April 30, 2018 Vector Laws   We will learn how to add and subtract vectors. Page 290 # 1-7, 12, 15 Tuesday May 1, 2018 Multiplication of a Vector by a Scalar We will learn how to create a linear combination of vectors. Page 291  # 9, 11 Page 299  #2bd, 4cde, 5, 6bde, 13-15, 21 Wednesday,  May 2, 2018 Properties of Vectors Page 306  # 5-10, 12 Thursday,  May 3, 2018 Algebraic Vectors in 2-D and 3-D Page 317  # 5, 9, 10ade, 16adf Page 324  #2, 4, 6-8 Page 332  # 1-3, 5 Friday,  May  4, 2018 P.A. Day Monday,  May  7, 2018 Operations of algebraic vectors in 2-D and 3-D Page 324  #1, 5, 9, 10, 12-14  Page 332  # 4, 6, 7, 10, 12, 14 Tuesday,  May  8,  2018 Linear Combinations of Vectors We will learn how to apply vector concepts to do linear combinations Page 341  # 2, 7, 9-13, 16 Wednesday, May 9, 2018 Quiz #7   Velocity as a Vector Page 369  # 1- 12 Thursday, May 10, 2018 Vectors as Forces Page 362  # 3,  5, 6, 8, 10-17 Friday, May 11, 2018 Vectors as Forces (Day 2) Monday May 14, 2018 Dot Product of Vectors We will learn the dot product of vectors Page 377  # 6abef,  7abdf, 8, 9, 12, 13, 17   Page 385  # 2, 4, 6, 7, 10, 13, 16, 17 Tuesday, May 15, 2018 Scalar and Vector Projections Page 398  # 1, 5-8, 11, 12, 14, 15a Wednesday, May 16, 2018 Cross Product of Vectors We will learn the cross product of two vectors. Page 407  # 3,  4abc, 5, 7, 8b, 11 Thursday, May 17, 2018 Review  (Day 1) -Prom Page 418  #  1-18 Friday, May 18, 2018 Review – Day 2 Page 419  #  19-37 Monday May 21, 2018 Victoria Day Tuesday, May  22, 2018 Application of the Dot and Cross Product Page 414  # 1,  2a, 3, 5b, 7a, 8, 9 Wednesday, May 23, 2018 Begin Final Unit   Equations of Lines in 2-D Page 434  # 6, 7, 9, 10 Page 443   # 1, 3, 5-11 Friday, May 25, 2018 Unit 4 Test

# Unit 5: Lines and Planes

 Date Topic/Learning Goals Daily Work/Assignments Monday, May 28, 2018 Equations of Lines in  3-D      We will determine vector, scalar and parametric  equation of a line in three  dimensions Page 449   # 1acef, 3-6, 9, 10 bd, 11, 13 Tuesday, May 29, 2018 Equations of Planes   We will learn to write vector and parametric equations  of planes. Page 459  #1, 3, 4, 6-8, 11, 13ab Wednesday, May 30, 2018 Scalar Equations of Planes   We will determine Cartesian (Scalar) equation of a plane. Page 468  # 1, 5, 7, 9b, 11- 13, 15 Thursday, May 31, 2018 Sketching Planes in Space   We sketch planes in space. Page 476  # 1, 4-6, 8-10 Friday, June 1, 2018 Intersection of Lines in 2-D and 3-D Page 497  #  8-12, 14, 15 Monday, June 4, 2018 Intersection of a Line with a Plane Page 496  #  3-5,  7, 13, 17 Tuesday, June 5, 2018 Quiz #8 Wednesday, June 6, 2018 Systems of Equations          (Gauss-Jordan Elimination) Page 507  # 1, 3, 8, 9, 12  Page 595  # 3 Thursday, June  6, 2018 Intersection of 2 Planes Page 516  #  1-4,  6,  10 Friday, June 8, 2018 Intersection of 3 Planes   Carnival Day Page 531  #  8, 10, 12, 13, 15 Monday, June 11, 2018 Distance from a Point to a Line in 2-D and 3-D Page 540 # 1b,2b, 3b, 4b, 5, 6b, 8, 10 Tuesday, June 12, 2018 Distance from a Point to a Plane in 2-D and 3D Page 549  # 2-7 Wednesday, June 13, 2018 Review –Chapter 8 Page 480  # 1, 3ab, 4-15, 17, 19, 20ad, 21a, 23, 29, 30, 33, 34 Thursday, June 14, 2018 Review – Chapter 9 Page 552  # 1-3, 5-8, 9a, 10, 12, 13b, 16, 19, 23, 26 Friday, June 15, 2018 Course Review  (Calculus)   Course Review  (Vectors)   Course Review Page 267, All questions except 1d. Page 557, All questions   Page 160 # 1-8 Page 220 # 1-7 Tuesday, June 19, 2018 Period 5 Calculus Exam Wednesday, June 20, 2018 Period 1 Calculus Exam