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MCV4U Master Schedule

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MCV4U - Calculus & Vectors (University Preparation)

This course builds on students' previous experience with functions and their developing understanding of rates of change. Students will solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in three dimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions; and apply these concepts and skills to the modelling of real-world relationships. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended for students who choose to pursue careers in fields such as science, engineering, economics, and some areas of business, including those students who will be required to take a university-level calculus, linear algebra, or physics course.

Prerequisites:

Functions, Grade 11, University Preparation
Advanced Functions, Grade 12, University Preparation (can be taken concurrently, but generally not recommended)

This page will have a daily breakdown of the course. Most recent classes are at the top of the page, while the older classes get pushed to the bottom.

The beginning of each unit will be marked in blue.

Evaluations (e.g., tests, assignments, quizzes) will be marked in red.

Returned evaluations with be marked in purple.

Nelson Calculus & Vectors Textbook Answers (Updated) Chapters 1-3 Chapters 4-6 Chapters 7-9

Day	Topic / Lesson	Resources	Assigned Work
	Unit 1 - Limits & Derivatives
1	Rationalizing note video lesson		p.9 # 1, 2 (basics) p.9 # 3bdf, 4, 6ef, 7
2	Slope of a Tangent Line note video lesson		p.19 # 4, 5 (basics) p.20 # 8c, 9ac, 10b, 11ef, 16, 20, 25*
3	Rates of Change note video lesson	[VT - Pascal's Triangle & Binomial Expansion]	p.30 # 7, 9 (use Ex.1 as template) (basics) p.30 # 10, 11, 12, 13, 16, 21*
4	Defining Limits note video lesson	handout: Defining the Limit	p.38 # 5, 6, 7, 10def, 11bc, 12a
5	Properties of Limits note video lesson	[VT - KA - Properties of Limits] [VT - KA - Example - Taking a Limit] [VT - KA - Example - Cubic Limit & Factoring]	p.45 # 4, 7bce, 8cef, 9, 10ad
6	Continuity of Functions note video lesson	[VT Series - KA - Continuity]	p.52 # 4ace, 5bcdf, 7, 8, 12, 14, 15
7	Power Rule note video lesson	[VT - SS - Power Rule]	summarize table on p.81 into your notes read proofs on p.76, p.77 p.82 # 2, 3def, 4cef, 8ab, 9bf, 14, 15, 16
8	Product Rule note video lesson		p. 90 #1abcde, 5abc, 6, 7, 9, 12
9	Quotient Rule note video lesson		p. 97 # 4, 5cd, 6, 7, 8, 9, 13, 17*
10	Chain Rule note video lesson	[VT - SS - Chain Rule]	p.105 # 4, 5, 11, 15,16, try 8
11	Combining Rules for Derivatives	Worksheet (see video for 2 solutions) [VT - SS - Combination of Rules]	complete worksheet
12	Review		p.56 # 2ab (use 1st principles), 9, 10,11, 17,18abf p.110 # 3, 4, 8, 10a, 11a, 16, 17, 19, 21, 24
13	Test - Limits & Derivatives	Real-world Application of Calculus (not at all, but interesting... to me)

Day	Topic / Lesson	Resources	Assigned Work
	Unit 2 - Applications of Derivatives
1	Higher-Order Derivatives video lesson note		review "Need to Know" on p.126 p.127 #4, 5, 6ac, 8, 9, 10, 11, 12, 13b, 16
2	Extreme Values video lesson note		p.117 # 7, 8 (interval notation, optional) p.136 # 2ab, 3d, 4ab, 6, 7, 8, 9
3	Optimization video lesson note		p.145 # 1, 3-12
4	Optimization of Distance video lesson note	more examples	p.147 # 15, 16, 20 Handout # 15, 8, 9
5	Optimization of Time video lesson note Quiz - Optimization of Dimensions		WS # 11-15
6	Optimization of Economics & Science video lesson note		p.152 # 5, 6, 8, 10, 12, 15, 17*
7	Work Period Quiz - Optimization
9	Review - Applications & Optimization		p.156-159 #3, 5, 6, 7ab, 8, 9, 14, 15, 17, 19 to 24, 26d
10	Test - Applications & Optimization

Day	Topic / Lesson	Resources	Assigned Work
	Unit 3 - Curve Sketching
1	Intervals of Increase & Decrease note video lesson		p.169 # 1ab, 3, 4abcd (algebraically), 8, 9, 10, 11
2	Critical Points & First Derivatives note video lesson		p.178 # 3, 4ab, 5bcd, 7cdef
3	Vertical & Horizontal Asymptotes note video lesson		p.193 # (3, 4, 5)(ignore d) p.193 # 6, 9abc, 11, 12, 13, 15*
4	Oblique Asymptotes Quiz - Inc/Dec, Critical Points, HA/VA note video lesson		p.193 # 3d, 4d, 5d, 6c, 7, 9d, 10, 14
5 6	Concavity & Points of Inflection note video lesson	video tutorial - supplemental	p.205 # 2, 3, 5, 10, 11, 12, 13a
7	Algorithm for Curve Sketching note	WS - Determining Graphs from Equations recommended questions: Part A # 1-6, Part B # 1, 2, 3, 6
8	Review - Curve Sketching	p. 216 #?1, 2, 3, 4, 5, 8, 10, 19, 20
9	Test - Curve Sketching

Day	Topic / Lesson	Resources	Assigned Work
	Unit 4 - Exponential, Logarithmic and Trigonometric Functions
1	Derivatives of Natural Exponential Function	video lesson videoNote	p. 232 # 1, 2aef, 3, 4bc, 5a, 7, 8, 12, 13
2	Derivatives of General Exponential Functions	video lesson videoNote	p.240 # 1, 2, 4, 5, 6, 9
3	Derivatives of Logarithmic Functions	video lesson videoNote	p.575 # 3 to 13 (Omit 5c, 9bc) p.578 # 1 to 5, 7, 9, 11
4 5	Optimization of Exponential Functions Quiz - Derivatives of Exponential Functions	videoLesson videoNote	Read examples 1 & 2, p.241-244 p. 245 # 3, 4, 5, 6, 8, 9, 12bc
6	Thinking Task - Optimization
7	Derivatives of Sine and Cosine	video lesson videoNote Geogebra Applet - Derivative of Sine	p.256 #1, 2, 3, 5, 7, 9, 11, 12
8	Derivatives of Tangent	video lesson videoNote	p.259 # 1-8, 10, 11
9 10	Review		p.263 # 1-9, 11-16, 23
11	Test - Derivatives of Exponential & Trigonometric Functions

Day	Topic / Lesson	Resources	Assigned Work
	Unit 5 - Vectors
1	Introduction to Vectors	video lesson old note	p.279 # 4 to 7, 9, 11
2	Addition & Subtraction of Vectors	video lesson old note	p.290 # 1 to 5, 7, 9, 11, 13, 15
3	Scaling & Properties of Vectors	videoLesson old note	p.299 # 1, 5, 7, 12, 14, 15, 19, 21* p.306 # 5, 7, 8, 10, 11
4	Vectors in R2 and R3	videoLesson (R2) videoLesson (R3) old note Visualize Vectors in R3	p. 316 # 1, 4, 5, 6, 7ab, 8, 12a, 15
5	Algebraic Vectors in R2	videoLesson old note	p.325 # 3, 4, 5b, 6ac, 7c, 8c, 10, 11, 12, 13a
6	Algebraic Vectors in R3	videoLesson old note	p.332 # 1, 2, 3, 4, 5ac, 6bd,, 8, 10, 11, 12, 14, 15
7	Linear Combinations & Spanning Sets	old note video lesson	p.340 # 6, 7b, 8, 10, 11, 13, 14
8	Review - Vectors		p.344 - 347 # 1, 2a, 3, 5, 6a, 7, 8, 11, 12b, 15ab, 16c(also find direction), 19a, 21, 23
9	Test - Vectors

Day	Topic / Lesson	Resources	Assigned Work
	Unit 6 - Applications of Vectors
1	Vectors as Forces	video lesson video lesson - exercises note	p.362 # 3, 5, 6, 8, 10, 11, 12, 16, 17
2	Velocity Vectors	video lesson note	p.369 # 3, 4, 6, 7, 9, 10, 11, 14
3	Dot Product of Geometric Vectors	video lesson note	p.377 #2, 5, 6abe, 7acd, 9, 11, 12
4	Dot Product of Algebraic Vectors	video lesson note	p.385 # 2, 4, 6bd, 7b, 9b, 10a, 11, 12, 14 + Read Example 5 on page 384
5	Scalar & Vector Projections Direction Angles & Direction Cosines	video lesson note	p.398 # 1, 6, 7b, 8, 11, 13, 15, 17
6	Cross Product	video lesson note	p.407 # 1, 2, 3, 4abc, 5, 7, 9a, 13 p.415 # 5b, 7
7	Applications of Dot & Cross Product	video lesson note Handout - Application Problems	p.414 # 1, 3, 5, 6, 8, 10 + handout (optional)
8	Review - Applications of Vectors		p.418 # 1cd, 2f, 3, 4, 6, 7, 8b, 9, 10, 11, 14, 15, 16, 18bcd, 20c, 22, 23, 24, 25, 26, 29, 30, 31b, 32
9	Test - Applications of Vectors

Day	Topic / Lesson	Resources	Assigned Work
	Unit 7 - Lines & Planes
1	Vectors & Parametric Equations of Lines in R2	video lesson note	p.433 # 1, 2, 3, 4, 5, 6, 7, 9b, 10
2	Cartesian Equation & Normal Vector	video lesson note	p.443 # 1, 3cd, 4, 5, 6, 7, 9b, 10acef, 11
3	Equations of Lines in R3	video lesson note p.450 #14 Video Solution p.450 #14 Text Only Solution	p.449 # 3, 6, 7, 8, 9, 12, 14
4	Vector Equations of Planes	video lesson note Geogebra demo	p.459 #1, 2, 3, 4, 6, 8a, 9, 10, 11, 12b
5	Cartesian Equation of a Plane	video lesson note	p.468 # 1, 2, 3, 4b, 6, 8,10, 11, 13, 14
6	Intersection of Lines in R3	video lesson note	p.497 # 8, 9, 11, 12
7	Intersection of Lines & Planes	video lesson note	p.496 # 3, 4, 5, 6, 7, 13
8	Intersection of Two Planes	video lesson note	p.516 # 1, 2, 3, 6, 8, 10
9	Solving Systems of Equations using Matrices	video lesson note online matrix solver (check steps/answers)	p.588 # 4, 6b, 8b, 10ace p.594 # 1c, 3ace
10	Intersection of Three Planes	video lesson note	p.532 #9, 10, 13
11	Distances between Points, Lines, and Planes	video lesson note VT - Distance Between Point and Line in R3	p.540 # 2a, 3a, 5ac, 6b, 8 p.550 # 2a, 3a, 5, 6
12	Review Lines & Planes		p.552 # 1, 3, 4, 5a, 6, 9, 10b, 11, 12ab, 13, 14, 15, 19, 20, 24, 26, 27
13	Test - Lines & Planes

Review: Final Exam

Review Questions & Unit Summaries

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