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MCV4U - 2016-2017 Semester 2

Page history last edited by Steve Sweeney 6 years, 10 months ago

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

Date	Topic / Lesson	Resources	Assigned Work
	Review: Final Exam	Review Questions & Unit Summaries	suggested textbook questions
J06	Test: Lines & Planes
J05	Review Lines & Planes		p.552 # 1, 3, 4, 5a, 6, 9, 10b, 11, 12ab, 13, 14, 15, 19, 20, 24, 26, 27
J01	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
M31	Intersection of Three Planes	video lesson (error in Ex1(d), first equation should be z, not y) note (error corrected)	p.532 # 9, 10, 13
M30	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
M29	Intersection of Two Planes	video lesson note	p.516 # 1, 2, 3, 6, 8, 10
M26	Intersection of Lines & Planes	video lesson note	p.496 # 3, 4, 5, 6, 7, 13
M25	Intersection of Lines in R3	video lesson note	p.497 # 8, 9, 11, 12
M24	Cartesian Equation of a Plane	video lesson note	p.468 # 1, 2, 3, 4b, 6, 8,10, 11, 13, 14
M18	Vector Equations of Planes	video lesson note Geogebra demo	p.459 #1, 2, 3, 4, 6, 8a, 9, 10, 11, 12b
M17	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
M16	Cartesian Equation & Normal Vector	video lesson note	p.443 # 1, 3cd, 4, 5, 6, 7, 9b, 10acef, 11
M15	Vectors & Parametric Equations of Lines in R2	video lesson note	p.433 # 1, 2, 3, 4, 5, 6, 7, 9b, 10
	Unit 7: Lines & Planes
M23	Test Unit 6: Applications of Vectors
M19	Review Unit 6	note	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
M12	Applications of Dot & Cross Product	video lesson note Handout - Application Problems	p.414 # 1, 3, 5, 6, 8, 10 + handout (optional)
M11	Cross Product	video lesson note	p.407 # 1, 2, 3, 4abc, 5, 7, 9a, 13 p.415 # 5b, 7
M10	Scalar & Vector Projections Direction Angles & Direction Cosines	video lesson note	p.398 # 1, 6, 7b, 8, 11, 13, 15, 17
M09	Retest: Introduction to Vectors
M08	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
M05	Dot Product of Geometric Vectors	video lesson note	p.377 #2, 5, 6abe, 7acd, 9, 11, 12
M04	Velocity Vectors	video lesson note	p.369 # 3, 4, 6, 7, 9, 10, 11, 14
M03	Vectors as Forces	video lesson video lesson - exercises (probably don't watch this) note	p.362 # 3, 5, 6, 8, 10, 11, 12, 16, 17
	Unit 6: Applications of Vectors
M02	Test - Vectors
M01	Review - Vectors	blank isometric graph paper	p.344 - 347 # 1, 2a, 3, 5, 6a, 7, 8, 11, 12b, 15ab, 16c(also find direction), 19a, 21, 23
A28	Linear Combinations & Spanning Sets	video lesson note	p.340 # 6, 7b, 9, 8, 10, 11, 13, 14
A27 A26 A25	Algebraic Vectors in R3	video lesson (too short, sorry) note	p.332 # 1, 2, 3, 4, 5ac, 6bd,, 8, 10, 11, 12, 14, 15
A27 A26 A25	Algebraic Vectors in R2	video lesson (too long, sorry) note	p.325 # 3, 4, 5b, 6ac, 7c, 8c, 10, 11, 12, 13a
A24	Vectors in R2 and R3	video lesson: vectors in R2 video lesson: vectors in R3 R2_note R3_note Visualize Vectors in R3 blank isometric graph paper	p. 316 # 1, 4, 5, 6, 7ab, 8, 12a, 15
A21	Properties of Vectors Quiz - Lessons 1-3	no video necessary note	p.306 # 5, 7, 8, 10, 11 p.308 # 2, 6, 11, 12, 15
A20	Scaling Multiplication of Vectors	video lesson note	p.299 # 1, 5, 7, 12, 14, 15, 21*
A19	Addition & Subtraction of Vectors	video lesson note	p.290 # 1 to 5, 7, 9, 11, 13, 15
A18	Introduction to Vectors	video lesson note	p.279 # 4 to 7, 9, 11
	Unit 5 - Vectors
	AM Class: April 13 PM Class April 12 Test: Exponential & Trigonometric Functions
A11	Review		p.263 # 1-9, 11-16, 23
A10	Derivatives of Tangent	video lesson note Trig Identities Sheet	p.259 # 1-8, 10, 11
A07	Derivatives of Sine and Cosine AM+PM Questions	video lesson note Geogebra Applet - Derivative of Sine Trig Identities Sheet	p.256 #1, 2, 3, 5, 7, 9, 11, 12
A06	work period
A05	Optimization & Curve Sketching of Exponential Functions AM+PM Questions	video lesson note	p. 245 # 3, 4, 5, 6, 8, 9, 12bc
A04	work period
M31	Derivatives of Logarithmic Functions	video lesson note	p.575 # 3 to 13 (Omit 5c, 9bc) p.578 # 1 to 5, 7, 9, 11
M30	Derivatives of General Exponential Functions	video lesson note	p.240 # 1, 2, 4, 5, 6, 9
M29	Derivatives of the Natural Exponential Function	video lesson note	p. 232 # 1, 2aef, 3, 4bc, 5a, 7, 8, 12, 13
	Unit 4 - Exponential, Logarithmic and Trigonometric Functions
Mon A03	Test - Curve Sketching
M28	Review - Curve Sketching		p. 216 # 1, 2, 3, 4, 5, 8, 10, 19, 20
M27	Algorithm for Curve Sketching AM PM	WS (extra) - Determining Graphs from Equations recommended questions: Part A # 1-6, Part B # 1, 2, 3, 6	(start with) p.212 # 4abcde, 6, 7 (end with) p.212 # 4fghij, 9 extra worksheet
M24	Activity: Curve Sketching		start getting ready for test
M23	Concavity & Points of Inflection AM PM	video lesson note video tutorial - supplemental	p.205 # 2, 3, 5, 10, 11, 12, 13a
M22	work period
M21	Oblique Asymptotes AM PM Quiz - Inc/Dec, Critical Points, HA/VA	video lesson note	p.193 # 3d, 4d, 5d, 6c, 7, 9d, 10, 14
M20	Vertical & Horizontal Asymptotes AM PM	video lesson note	p.193 # (3, 4, 5)(ignore d) p.193 # 6, 9abc, 11, 12, 13, 15*
M09	Critical Points & First Derivatives AM PM	video lesson note	p.178 # 3, 4ab, 5bcd, 7cdef
M08	Intervals of Increase & Decrease AM PM	video lesson note	p.169 # 1ab, 3, 4abcd (algebraically), 8, 9, 10, 11
	Unit 3 - Curve Sketching
M07	Test: Applications of Derivatives
M06	Review		p.156-159 #3, 5, 6, 7ab, 8, 9, 14, 15, 17, 19 to 24, 26d
M03	Optimization of Money AM PM	video lesson (jump to Ex1 Ex2 Ex3)	p.152 # 5, 6, 8, 10, 12, 15, 17*
M02	Optimization of Time AM PM	video lesson	Handout # 11 to 15
F28	Optimization of Distance AM PM Quiz: Lessons 1-3	video lesson more examples	p.147 # 15, 16, 20 Handout # 1 to 5, 8, 9
F27	Optimization Problems AM PM	video lesson	p.145 # 1, 3 to 12
F24	Extreme Values AM PM	video lesson	p.117 # 7, 8 p.136 # 2ab, 3d, 4ab, 6 to 9
F21	Displacement Velocity Acceleration AM PM	video lesson	p.127 3acdf, 4, 5, 10, 17
F16	Higher-Order Derivatives AM PM		p.127 # 2 (all) + see handout
	Unit 2 - Applications of Derivatives (by Mr. Goobie)
F23	Test - Limits & Derivatives	Real-world Application of Calculus (not real at all, but interesting... to me)
F15	Review	WS - Combining Derivative Rules	p.56 # 2ab (use 1st principles), 9, 10,11, 17,18abf p.110 # 3, 4, 8, 10a, 11a, 16, 17, 19, 21, 24
F14	Chain Rule video lesson	[VT - SS - Chain Rule]	p.105 # 4, 5, 15,16
F13	Quotient Rule note video lesson		p. 97 # 4, 5cd, 6, 7, 8, 9, 13, 17*
F10	Product Rule note video lesson		p. 90 #1abcde, 5abc, 6, 7, 9, 12
F09	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
F08	Continuity of Functions note video lesson Quiz: Lessons 3-5	[VT Series - KA - Continuity]	p.52 # 4ace, 5bcdf, 7, 8, 12, 14, 15
F07	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
F06	Defining Limits note video lesson	handout: Defining the Limit	p.38 # 5, 6, 7, 10def, 11bc, 12a
F03	Rates of Change note video lesson Quiz: Lessons 1-2	[VT - Pascal's Triangle & Binomial Expansion]	p.30 # 7, 9 (use Ex.1 as template) (basics) p.30 # 10, 11, 12, 13, 16, 21*
F02	Slope of a Tangent Line note video lesson		p.19 # 4, 5 (basics) p.20 # 8c, 9ac, 10b, 11ef, 16, 20, 25*
F01	Rationalizing note video lesson		p.9 # 1, 2 (basics) p.9 # 3bdf, 4, 6ef, 7
	Unit 1 - Limits & Derivatives

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 video lesson	[VT - SS - Chain Rule]	p.105 # 4, 5, 15,16
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		review "Need to Know" on p.126 p.127 #4, 5, 6ac, 8, 9, 10, 11, 12, 13b, 16
2	Extreme Values		p.117 # 7, 8 (interval notation, optional) p.136 # 2ab, 3d, 4ab, 6, 7, 8, 9
3	Optimization		p.145 # 1, 3-12
4	Optimization of Distance		p.147 # 15, 16, 20 Handout # 15, 8, 9
5	Optimization of Time Quiz - Optimization of Dimensions		WS # 11-15
6	Optimization of Economics & Science		p.152 # 5, 6, 8, 10, 12, 15, 17*
7	Work Period Quiz - Optimization
8	Finish Optimization of Econ & Science		p.152 # 5, 6, 8, 10, 12, 15, 17*
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	video lesson	p.169 # 1ab, 3, 4abcd (algebraically), 8, 9, 10, 11
2	Critical Points & First Derivatives	video lesson	p.178 # 3, 4ab, 5bcd, 7cdef
3	Vertical & Horizontal Asymptotes	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	video lesson	p.193 # 3d, 4d, 5d, 6c, 7, 9d, 10, 14
5 6	Concavity & Points of Inflection	video lesson video tutorial - supplemental	p.205 # 2, 3, 5, 10, 11, 12, 13a
7	Algorithm for Curve Sketching	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 note	p. 232 # 1, 2aef, 3, 4bc, 5a, 7, 8, 12, 13
2	Derivatives of General Exponential Functions	video lesson note	p.240 # 1, 2, 4, 5, 6, 9
3	Derivatives of Logarithmic Functions	video lesson note	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		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 note Geogebra Applet - Derivative of Sine	p.256 #1, 2, 3, 5, 7, 9, 11, 12
8	Derivatives of Tangent	video lesson note	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	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	old note Visualize Vectors in R3	p. 316 # 1, 4, 5, 6, 7ab, 8, 12a, 15
5	Algebraic Vectors in R2	old note	p.325 # 3, 4, 5b, 6ac, 7c, 8c, 10, 11, 12, 13a
6	Algebraic Vectors in R3	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

note

Intervals of Increase & Decrease

video lesson

p.169 # 1ab, 3, 4abcd (algebraically), 8, 9, 10, 11

p.433 # 1, 2, 3, 4, 5, 6, 7, 9b, 10

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MCV4U - 2016-2017 Semester 2

MCV4U - 2016-2017 Semester 2

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