CanterburyHigh School Calculus and Vectors, Grade 12 University Preparation MCV4U

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.

Prerequisite: MCR3U

The Term work will be worth 70% . The methods of evaluation will include tests, quizzes, and in class tasks.

The topics to be studied and evaluated in this course are: A. RATE OF CHANGE 1. demonstrate an understanding of rate of change by making connections between average rate of change over an interval and instantaneous rate of change at a point, using the slopes of secants and tangents and the concept of the limit; 2. graph the derivatives of polynomial, sinusoidal, and exponential functions, and make connections between the numeric, graphical, and algebraic representations of a function and its derivative; 3. verify graphically and algebraically the rules for determining derivatives; apply these rules to determine the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions, and simple combinations of functions; and solve related problems.

B. DERIVATIVES AND THEIR APPLICATIONS 1. make connections, graphically and algebraically, between the key features of a function and its first and second derivatives, and use the connections in curve sketching; 2. solve problems, including optimization problems, that require the use of the concepts and procedures associated with the derivative, including problems arising from real-world applications and involving the development of mathematical models.

C. GEOMETRY AND ALGEBRA OF VECTORS 1. demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by recognizing their applications; 2. perform operations on vectors in two-space and three-space, and use the properties of these operations to solve problems, including those arising from real-world applications; 3. distinguish between the geometric representations of a single linear equation or a system of two linear equations in two-space and three-space, and determine different geometric configurations of lines and planes in three-space; 4. represent lines and planes using scalar, vector, and parametric equations, and solve problems involving distances and intersections.

The Final Evaluation will be worth 30% of the course. This evaluation will be composed of a summative task done in class (15 %), and an exam (15 %). Both of these are required components for a credit in this course.

Required materials

All students are required to have a scientific calculator, pencils, pens, an eraser, paper, graph paper, and a ruler for each class. Borrowing from other students in class during tests, exams, and quizzes is not permitted. Please come to class prepared.

Textbook

Nelson Calculus and Vectors ( $75 if lost or damaged)

Page 299 #'s 1 to 5,7,11,14,15,18
Page 306 #'s 3,4,7,8,9

Monday, February 08, 2010

Page 316 #'s 3,5,6,9,15

Tuesday, February 09, 2010

Page 324 #'s 3,4,5,6,7,9,10,11,12,15

Wednesday, February 10, 2010

Page 332 #'s 1,2,4,5,7,8,11,13,14,15

Thursday, February 11, 2010

Ch 6 Quiz Tuesday

Friday, February 12, 2010

Monday, February 15, 2010

Tuesday, February 16, 2010

Ch 6 Quiz

Wednesday, February 17, 2010

Page 362 #'s 1 to 8.

Thursday, February 18, 2010

Page 364 #'s 12,13,15,16,17,19

Friday, February 19, 2010

Read Page 365 to 368,
Do #'s 1 to 3 on page 369

Monday, February 22, 2010

Page 369 #'s 4 to 11

Tuesday, February 23, 2010

Wednesday, February 24, 2010

Page 375 Read ex 4.
Page 377 #'s 1 to 14

Thursday, February 25, 2010

Page 386 #'s 4,5,6

Friday, February 26, 2010

Page 386 #'s 7,8,10,11,12,16,17,18

Monday, March 01, 2010

Tuesday, March 02, 2010

Wednesday, March 03, 2010

Thursday, March 04, 2010

Friday, March 05, 2010

Page 399 #'s 6,7,11,13,15
Page 405 #'s 1 to 10

Monday, March 08, 2010

Page 414 #'s 3,5a,6,7

Tuesday, March 09, 2010

Page 9 #'s 1,2,3.

Wednesday, March 10, 2010

Test is moved to Tuesday March 23rd.
Thursday will be an in-class assignment based on the following two questions.
1. A 4 kg mass is hanging from the end of a string. If a 10 N force pulls the mass at a direction of 30˚ down from the horizontal then find the tension in the string relative to the mass. (Give the direction relative to [up].) 2. Find the work done by a 30 N force acting in the direction of the vector (-2, 1, 5), which moves an object from A(2, 1, 5) to B(3, -1, 2). The distance is in metres.
(Hint. (-2, 1, 5) does not have a magnitude of 30.)

Thursday, March 11, 2010

Friday, March 12, 2010

Page 9 #'s 1 to 7 odd
Page 19 #'s 4,7

Monday, March 15, 2010

Break

Tuesday, March 16, 2010

Break

Wednesday, March 17, 2010

Break

Thursday, March 18, 2010

Break

Friday, March 19, 2010

Break

Monday, March 22, 2010

Tuesday, March 23, 2010

Read through section 1.3 and make notes
Page 29 #'s 1 to 6

Wednesday, March 24, 2010

Test

Thursday, March 25, 2010

Cancelled

Friday, March 26, 2010

Monday, March 29, 2010

Limits

Tuesday, March 30, 2010

Page 37 #'s 2 to 10

Wednesday, March 31, 2010

Copy out examples 2 to 9 and do questions 1 to 9
on Page 45

Thursday, April 01, 2010

Friday, April 02, 2010

Monday, April 05, 2010

Tuesday, April 06, 2010

Page 53 #'s 12,13,14,15
Page 73 #'s 1,2,5,6

Wednesday, April 07, 2010

Thursday, April 08, 2010

Page 74 #'s 7 to 11, 13, 14

Friday, April 09, 2010

Monday, April 12, 2010

Page 82 #'s 1 to 9, 11,13,15,16

Tuesday, April 13, 2010

Wednesday, April 14, 2010

Page 90 #'s 1 to 8

Thursday, April 15, 2010

Page 91 #'s 9, 10, 13,14

Friday, April 16, 2010

Page 96 #'s 4 to 9

Monday, April 19, 2010

Page 105 #'s 1,2,7,13

Tuesday, April 20, 2010

Wednesday, April 21, 2010

Page 122 ex 3, Page ex 5,
Page 127 < #'s 2 odd, 3 odd, 8 (add (c) when is the object speeding up), 10, 11

Thursday, April 22, 2010

Page 135
#'s 1 to 7, 11

Friday, April 23, 2010

Page 145 #'s 1 to 15

Monday, April 26, 2010

Work period

Tuesday, April 27, 2010

Calc Test

Wednesday, April 28, 2010

1. A chocolate manufacturer uses an equilateral triangular prism package. If the volume of chocolate to be contained in the package is 400 cm3, what dimensions of the package will use the minimum amount of materials? (clearly label your diagram)
2. Find the dimensions of the inverted cone with maximum volume inscribed in a cone with base radius 10 cm and height 12 cm.
3. Find the dimensions of the cone with maximum volume inscribed in a sphere with radius 10 cm.
Page 152 #'s 4,5,9,12

Thursday, April 29, 2010

In class assignment

Friday, April 30, 2010

Page 443 #????5,6,??, 10

Monday, May 03, 2010

Page 449 #'s 1 to 10

Tuesday, May 04, 2010

Ch 3 quiz

Wednesday, May 05, 2010

Page 443 #'s 4 to 9

Thursday, May 06, 2010

Page 459 #'s 1 to 5

Friday, May 07, 2010

Page 444 #'s 10 to 12
Page 459 #'s 6 to 14
Read examples from section 8.5

Monday, May 10, 2010

Page 468 #'s 1 to 11, 13,14

Tuesday, May 11, 2010

Page 476 #'s 1 to 3,5,6,8,10
Page 497 #'s 4 to 7

Wednesday, May 12, 2010

Read examples 4 to 6 on Page 492 and do questions 8 to 15 on Page 497.

Thursday, May 13, 2010

Friday, May 14, 2010

Monday, May 17, 2010

Page 516 #'s 1 to 4, 6 to 10
Analyze 3 planes

Tuesday, May 18, 2010

Wednesday, May 19, 2010

Page 531 (Make sure you understand #'s 1 to 7) Do #'s 8 to 10, 12, 13

MCV4UCanterburyHigh SchoolCalculus and Vectors, Grade 12University Preparation MCV4UThis 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.

Prerequisite: MCR3U

The

. The methods of evaluation will include tests, quizzes, and in class tasks.Term work will be worth 70%The topics to be studied and evaluated in this course are:

A.RATEOF CHANGE1.demonstrate an understanding of rate of change by making connections between average rate of change over an interval and instantaneous rate of change at a point, using the slopes of secants and tangents and the concept of the limit;2.graph the derivatives of polynomial, sinusoidal, and exponential functions, and make connections between the numeric, graphical, and algebraic representations of a function and its derivative;3.verify graphically and algebraically the rules for determining derivatives; apply these rules to determine the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions, and simple combinations of functions; and solve related problems.B. DERIVATIVESANDTHEIR APPLICATIONS1.make connections, graphically and algebraically, between the key features of a function and its first and second derivatives, and use the connections in curve sketching;2.solve problems, including optimization problems, that require the use of the concepts and procedures associated with the derivative, including problems arising from real-world applications and involving the development of mathematical models.C. GEOMETRYANDALGEBRA OF VECTORS1.demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by recognizing their applications;2.perform operations on vectors in two-space and three-space, and use the properties of these operations to solve problems, including those arising from real-world applications;3.distinguish between the geometric representations of a single linear equation or a system of two linear equations in two-space and three-space, and determine different geometric configurations of lines and planes in three-space;4.represent lines and planes using scalar, vector, and parametric equations, and solve problems involving distances and intersections.The

of the course. This evaluation will be composed of a summative task done in class (15 %), and an exam (15 %). Both of these are required components for a credit in this course.Final Evaluation will be worth 30%## Required materials

Borrowing from other students in class during tests, exams, and quizzes is not permitted. Please come to class prepared.## Textbook

Nelson Calculus and Vectors ( $75 if lost or damaged)

Teacher: Mr. Hughsone-mail: darrin.hughson@ocdsb.caWebsite:hughsonmath.wikispaces.comTextbook Homework

CalculusCh 1

24Ch 2

Ch 3

Ch 4 Curve Sketching

Ch 5 Exponential and Trig

VectorsCh 6

290

299

307

4,5,7,8,11,14

5,7,9,13,14,18

7,9,11

Ch 7

Ch 8

Ch 9

Some helpfull websites:University of Waterloo course video lessons and exercises with solutions: http://courseware.cemc.uwaterloo.ca/11?gid=106

Course notes: http://www.la-citadelle.com/courses/calculus/

Video lessons: http://www.yourepeat.com/g/MCV4U

OAME: http://www.oame.on.ca/main/staging9.php?code=grspecres&ph=12&sp=MCV4U

Dot Product Video: http://www.youtube.com/watch?v=KDHuWxy53uM

http://www.youtube.com/watch?v=PUK5PVMsXmg&feature=related

Cross Product Video: http://www.youtube.com/watch?v=zA0fvwtvgvA&feature=channel

http://www.youtube.com/watch?v=o_puKe_lTKk&feature=related

Dot Versus Cross Product http://www.youtube.com/watch?v=E34CftP455k&feature=channel

Page 290 #'s 1,4,6,7,8,12

Page 306 #'s 3,4,7,8,9

Do #'s 1 to 3 on page 369

Page 377 #'s 1 to 14

Page 405 #'s 1 to 10

Thursday will be an in-class assignment based on the following two questions.

1. A 4 kg mass is hanging from the end of a string. If a 10 N force pulls the mass at a direction of 30˚ down from the horizontal then find the tension in the string relative to the mass. (Give the direction relative to [up].)

2. Find the work done by a 30 N force acting in the direction of the vector (-2, 1, 5), which moves an object from A(2, 1, 5) to B(3, -1, 2). The distance is in metres.

(Hint. (-2, 1, 5) does not have a magnitude of 30.)

Page 19 #'s 4,7

Page 29 #'s 1 to 6

on Page 45

Page 73 #'s 1,2,5,6

Page 127 < #'s 2 odd, 3 odd, 8 (add (c) when is the object speeding up), 10, 11

#'s 1 to 7, 11

2. Find the dimensions of the inverted cone with maximum volume inscribed in a cone with base radius 10 cm and height 12 cm.

3. Find the dimensions of the cone with maximum volume inscribed in a sphere with radius 10 cm.

Page 152 #'s 4,5,9,12

Page 459 #'s 6 to 14

Read examples from section 8.5

Page 497 #'s 4 to 7

Analyze 3 planes

Page 549 #'s 1 to 7

Page 240 #'s 1,2,6