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MCV 4U - Calculus and Vectors (Spring 2009)

Page history last edited by Peter Kim 14 years, 10 months ago

This Grade 12 course was developed in 2007 to marry the abstract spatial concepts of vector algebra and the more concrete analytical tools of differential calculus. It will provide students with the fundamental tools necessary to be successful in math intensive university programs such as engineering, architecture and economics.

See the course outline MCV 4U Outline

Prerequisite: MHF 4U (can be taken concurrently)

For additional information regarding this course, visit the Ontario Ministry of Education website:

Ontario Curriculum MCV 4U (p. 99)

All Materials presented below are links to MS-Word documents.

NOTABLES:

02/03	Zap-a-Graph (1987 version) is available in the Handouts folder on the school server.
02/04	Textbook (Geometry & Discrete Mathematics) CD available fromMr. Kim
02/05	*Basic Vector Operations* *Interactive* website
04/05	MATH HELP with VECTORS! (Very Useful)
05/11	Derivative Calculator

Calendar of Topics:

Date	Session Name	Materials	Assignment
02/02	Intro to MCV 4U	Student Info; Course Expectations; Calendar Opening Exercise	Complete the Opening Exercise
02/03	Intro to Vectors (Geometric)	Textbooks, or textbook CD Grid Paper	p. 8 #2,5,8,9,10,11*
02/04	Addition/Subtraction of Vectors Zero Vector	Geometric Vectors Worksheet I	Complete Wksht Q's @ bottom of page Add: p. 22 #4,5 Geometric Vectors II Due: Mon. 02/09
02/05	Scalar Multiplication		pp. 29-31 #2,5,6,9 (on grid paper), 12, 13 or 14
02/06	Resolving Vectors	Resolving Vectors Video Notes for CAST method Resolving Forces into V & H Components Wksht	Complete Worksheet Solution for Set D Solution for Set D (CAST)
02/09	Forces as Vectors - Resultant & Equilibrant (zero vector)	Handout: Forces as Vectors	H/O: #2,7,9,12,15-18, 20,21 Geo. Vectors WKSHT II Due
02/10	Snow Day - Catch Up
02/11	QUIZ - Adding/Subtracting Vectors Using Components Velocity Vectors - Relative Velocity	Handout: Velocity as Vectors	H/O: #1,3 (1-D only), 4,5,8,9,10,13,14
02/12	Relative Velocity	V: 1-D Relative Velocity	#1,3,4,5,8
02/13	ARGGH! Jason's coming!!! Relative Velocity		#9,10,13,14 p. 51 #11,12,13*
02/17	Linear Combinations Exercise Review of Vectors	Linear Combinations Review of Geometric Vectors (slight correction to #4)
02/18	Algebraic (Cartesian) Vectors	Complete worksheets	p. 40 #2,5-8,10,12,15a,c,23
02/19	*Geometric Vectors Test*
02/20	Short Period - WINTER CARNIVAL 11:00 - 11:40	Algebraic/Cartesian Vectors (see 02/18)	Read pp. 34 - 39
02/23	Geometric TIPS #1	Properties of Vectors: 3-space	Read pp. 74 - 80 Do p. 81 #2a-d;3a;6 (length)
02/24	Vectors in 3-Space	3-Space Exercise (see 02/24)	Complete Exercise Do p. 81 #7,10,11,12a,19 p. 89 #7,9,10
02/25	Discuss 3-Space Vectors	Linear Combinations and Basis Vectors Exercise	Complete the exercise
02/26	Quiz 1 - Cartesian Vectors	Collinear Vectors and Coplanar Vectors	Read pp. 84 - 88 p. 88 #4,6,7a,d;9,10a,c
02/27	Collinear & Coplanar	(see 02/26)	p. 89 #11,13,14,15,17,18
03/02	Dot Product	The Dot Product
03/03	Dot Product Properties & Projections	Properties & Projections Dot Product Applications	p. 64 #1,2,5 p. 98 #18, 19 wksht: #7
03/04	Quiz 2 - Cartesian Vectors Discuss HW	(see 03/03)	wksht: #1-6
03/05	Cross Product	The Cross Product	p. 106 #2,6,10 p. 108 #11,13,14,16
03/06	Torque & Applications of X-Product	Cross Product Exercise	p. 115 #4,5,7,9,10,16 Exercise Wksht
03/09	Practice Test = Review
03/10	Cartesian Vectors Test
03/11	Cartesian TIPS #2 (Postponed) Parent-Teacher Interviews Class 1:00 - 1:45 p.m. Lines & Planes Introduction Recall	Eq'ns of Lines in 2 & 3-space Lines in 2-Space scalar vector parametric symmetric	p. 131 #2,4,5,9,11,18,23
03/12	Lines in 3-Space	Lines in 3-Space intersection parallel coincident skew	p. 141 #2,3,5,8,11,18,28
03/13	Discuss HW
03/23	Parallel, Coincident, Intersecting & Skew	H: Line Types	p. 133 # 15,16 p. 142 # 14,15,22,23
03/24	Equations of a Plane	H: Plane Equations	p. 152 #1,2,5-7,10,11,17a,b
03/25	Cartesian TIPS #2		XTRA: Lines Practice
03/26	Equations of a Plane II	H: Plane Equations II
03/27	Lines Quiz Planar Pot-Pourri	H: Pot-Pourri
03/30	Intersection of a Line & Plane	H: Line & Plane Intersection	p.160 #1;6all;8,12,14 p.161 #10
03/31	Intersection of 2 Planes	H: Intersection of 2 Planes	W: Int of 2 Planes
04/01	*Planes Quiz* Intersection of 3 Planes	H: Intersection of 3 Planes
04/02	Lines & Planes Review		W: Lines & Planes Rvw (Requires textbook)
04/03	Lines & Planes Test
04/06	Matrices	W: Intersection of Planes W: Matrices
04/07	TIPS #3 - Lines & Planes
04/08	Intro to Calculus "Rates of Change"	H: Acty 3.1a - Rates of Chg	Complete Activity 3.1a & b
04/09	Term I Test
04/10	Good Friday
04/13	Easter Monday
04/14	Rates of Change	H: Acty 3.2 Spreadsheet for 3.2	Complete Activity 3.2
04/15	The Derivative!	H: Acty 3.3
04/16	More of the derivative	H: Acty 3.3b	Complete 3.3b
04/17	Limits of Secant to Tangent		p. 137 #2,3,5,7
04/20	Concavity	H: Acty 3.4	See Handout
04/21	Quiz on Limits of Secants		Complete Activity 3.4 (Concavity)
04/22	Graphing Assignment	W: Activity 3.5 Begin Review (+ see 04/23)	p. 128 #4,7 p. 168 #4,9,11,16 p. 173 #4
04/23	Review		p. 174 #5a,b,c,e; 6d,e; 8; 21 p. 399 #1a,c,d,f; 2,3,5; 7a-d,f,g; 8alt
04/24	Concepts of Calculus Test
04/27	Differentiable Functions	H: To "Differentiate"	p. 194 #2,4,5b,f,g; 6a,b,g; #10 by first principles;13
04/28	Rules of Derivatives	W: Derivatives 1	p. 205 #10,13,15,18,20 Begin worksheet
04/29	Product and Quotient Rules	www.analyzemath.com/calculus/Differentiation/rules.html	p.212 #1alt; 4a,c;6b,c;7;9;10 p.218 #1alt; 2; 4; 7; 8; 10
04/30	Quiz Work Period		Continue from yesterday
05/01	Motion & Derivatives	W: Motion & Derivatives	p. 205 #14,16,17,31* p. 237 #2,3,7
05/04	*Quiz* Derivative Rules Business Problems	W: Business & Derivatives	p. 205 #22,24 p. 237 #9,11,17 p. 249 #1,4,10
05/05	Review of Differentiation		p. 250 #6,15,16 p. 254 #4a,c,e; 8b,d,e,f,[g (by 1st principles)],h; 9a,c; 14 alt; 15;18a,c,e,f; 19b p. 256 #26-29,31
05/06	Test Derivatives
05/07	Composite Functions & the Chain Rule		Read pp. 277 - 281 Do p. 274 #5a,b,d,g; #6 p. 282 #1 (deriv only); 2,3
05/08	TIPS #4 - Derivatives		p. 282 #7, 12
05/11	Ass't - Derivatives Practice *(Due Thursday)* Combining Chain & Product Consolidate Derivative Rules	W: Derivatives Practice (w/ Answers revised May 14) H: Simple Derivative Rules	Assignment due Thursday SEE: Derivatives Calculator Shows you "How to do it..."
05/12	Derivatives Calculator Derivatives Problems	H: Derivatives Problem Sheet	#6, 7, 8, 15, 20, 22, 23
05/13	Implicit Differentiation	Discuss previous differentiation involving factoring Complete "Simple Derivative Rules" - Implicit	p. 289 #2 b-h
05/14	Implicit Differentiation Eq'ns of Tangent Lines	W: Implicit Differentiation N: Example 2 p1 N: Example 2 p2	Derivatives Practice Due p. 289 #3;4i,ii;5a Complete Worksheet
05/15	PD Day
05/18	Victoria Day
05/19	Related Rates	W: Area & Volume Rate Problems Solutions: Q#1 Q#2a Q#2b Q#5 Q#7&12	Wksht: #1,2,5,7 + 4,8,10
05/20	Related Rates	Discuss Problems from yesterday W: One Object Moving	#1,2,3,5,7
05/21	*Quiz Implicit Different'n*	W: Two Objects Moving	Do 3 problems
05/22	Review	Prepare for the test	p. 255 #14alt; #15a,d #18a,e,f p. 258 #3b p. 301 #7b; #8a,c,d (using Leibniz) #12a,b,d,f; #13c p. 302 #15 - 18
05/25 D1	*Differentiation Test 2*
05/26 D2	Review of Trig Functions Derivatives of Trig F'ns	H: Exploring Trig Derivatives	Complete investigation Practice: #2,3,4 (alternating)
05/27	TIPS #5 - Related Rates
05/28	Trigonometric Derivatives Rules	H: Trigonometric Derivatives Rules	Practice: #5-8,12
05/29	Trig Derivatives and Tangents to the Curve	Work Period	p. 518 #4; 5a,c; 6a,b; 9 Practice: Last page of H/O: #2 on
06/01 D2	Quiz - Trig Derivatives Modelling with Trig		p. 530 #3, 4, 5, 7, 11
06/02 D1	Intro to 'e' Derivative of y=e^x	H: Introducing 'e' Wksheet on reverse (not on e-copy) A: Background tutorial	Complete wksht: #1a,f,g,h,;#3;#13;#14 p. 458 #2f
06/03 D2	Natural Logaritms	Derivatives of ln: WS-2 WS-3	p. 459 #2, 4, 5 WS-3 #2alt; #7alt; #13alt
06/04	Quiz - Derivatives with e Expon'l & Logarithmic F'ns	N: Derivatives of Log & Expo F'ns WS-4 Answers	WS-4: #2,3,5b,c,e,g,j
06/05	MOGA Shortened Periods Review of Trig & Expo Deriv	H: Summary Sheet H: Review Sheet (pick up in class)	Side 1: #3;5a,b;6,7,9 Side 2: #12;16a,d,e,f,g;18a,b,c,f,h; 24 #2 Problems about bacteria
06/08	TEST - Trig & Exponents
06/09	Review Day 1 rates of change first principles derivatives of polynomials	H: Review Sheet (pick up in class)	#8,9,10,12,13,16,17,18,19,21
06/10	Review Day 2 curve sketching application problems trig & expon'l derivatives		#24,26,27,29,30,33,35,38,42
06/11	*End of Term Test*
06/12	Review Day 3 Geo Vectors Cart Vectors		#46,49,50,51,53 #55,56,58,60,61,62,64,66,67
06/15	Review Day 4 Cart Vectors Lines & planes		#70,73,75,77,79 #80,82,83,85,87,88,90,92,93
06/16	Return Textbooks	Summarize
06/17	*Exam A.M.*	H: Formula Sheet