INSTRUCTOR: MR.SHUM AND MR. DOERKSEN

The final exam for this course is scheduled for

THURSDAY JUNE 6TH.

It begins at 8:30AM.

Students will have exactlytwo and a half hours (2.5 hrs) to complete the exam.

This final exam serves as a summative evaluation towards the end of the course and is worth 30% of the final mark.

FORMAT• Draws upon material from the entire

course• NO multiple-choice• Algebraic solutions are required unless

explicitly told to rely on graphing technology

• NO guess & check solutions; show your reasoning for full mark

• Similar to most tests, all Categories will be represented (see page 2)

Exam Outl ineSummative Evaluation

Final Exam

EQUIPMENTHERE’S WHAT YOU’LL NEED...

• Graphing Calculator

• Pencil

• Eraser

• Ruler

YOU MAY ALSO BRING...

• Water bottle

DO NOT BRING...

• Laptop

• Formula sheet*

• Cell phone

*only those students whose Individual Education Plan (IEP) designates the use of this memory aid will be allowed to bring a formula sheet**students who own a TI-89 or Nspire CAS may reserve a “loaner” TI-83/84; email your teacher well ahead of the exam.

Students on IEP should also consult with the Learning Centre as they may be entitled to other accommodations, e.g., extra time, quiet space, etc.

MCV4U CALCULUS & VECTORS WINTER-SRING 2013

Mini-Tests15%

Tests30%

Final Exam30%

Assignments25%

INSTRUCTOR: MR.SHUM AND MR. DOERKSEN

Topics from textbookby Chapter.Section

1.1 Radical Expressions: Rationalizing Denominators

1.2 The Slope of a Tangent

1.3 Rates of Change

1.4 Limit of a Function

1.5 Properties of Limits

1.6 Continuity

2.1 The Derivative Function

2.2 The Derivatives of Polynomial Functions

2.4 The Quotient Rule

2.5 The Derivatives of Composite Functions

3.1 Higher Order Derivatives, Velocity and Acceleration

3.2 Minimum and Maximum on an Interval (Extreme Values)

3.3 Optimization Problems

3.4 Optimization Problems in Economics and Science

4.1 Increasing and Decreasing Functions

4.2 Critical Points, Local Maxima, and Local Minima

4.3 Vertical and Horizontal Asymptotes*

4.4 Concavity and Points of Inflection

4.5 An Algorithm for Graph Sketching

5.1 Derivatives of Exponential Functions

5.2 The Derivative of the General Exponential Function

5.3 Optimization Problems Involving Exponential Functions

5.4 The Derivatives of sine and cosine

5.5 The Derivative of tangent

6.1 An Introduction to Vectors

6.2 Vector Addition

6.3 Multiplication of a Vector by a Scalar

6.4 Properties of Vectors

6.5 Vectors in R2 and R3

6.6 Operations with Algebraic Vectors

6.7 Operations with Vectors

6.8 Linear Combinations and Spanning Sets

7.1 Vectors as Forces

7.2 Velocity

7.3 The Dot Product of Two Geometric Vectors

7.4 The Dot Product of Two Algebraic Vectors

7.5 Scalar and Vector Projections

7.6 The Cross Product of Two Vectors

7.7 Applications of the Dot and Cross Product

8.1 Vector and Parametric Equations of a Line in R2

8.2 Cartesian Equation of a Line

8.3 Vector, Parametric, and Symmetric Equations of a Line in R3

8.4 Vector and Parametric Equations of a Plane

8.5 The Cartesian Equation of a Plane

9.1 The Intersection of a Line with a Plane and the Intersection of Two Lines

9.2 Systems of Equations

9.3 The Intersection of Two Planes9.4 The Intersection of Three Planes

*also Oblique Asymptotes and behaviour as well as Removable Discontinuities

For students enrolled in AP...Topics shown in RED are not part of the College Board’s AP curriculum BUT are included in the Ontario curriculum and MUST be evaluated for students to earn the MCV4U credit.

MCV4USTRANDS

• Rate of Change• Derivatives and their Applications• Geometry and Algebra of VectorsMathematics - The Ontario Curriculum Grades 11 and 12 (revised 2007)

MCV4U CALCULUS & VECTORS WINTER-SRING 2013

CATEGORIES

• Knowledge

• Application

• Communication

• ThinkingProblem-Solving

INSTRUCTOR: MR.SHUM AND MR. DOERKSEN

Suggestionspreparing for your final examUSE YOUR PORTFOLIO

Over the course of the year, your teacher has encouraged you to copy corrections onto their marked tests, mini-tests and assignments and store them in a portfolio. You can now use these questions to test your knowledge. As you’ve copied the correct solutions in class, they can serve as a more robust resource than your textbook as it only provides answers (not solutions).

ACCESS OTHER RESOURCES

In addition to the explanations and examples in your test, your teacher also provides an electronic copy of notes that you can download. Access your class calendar and use this in conjunction with text to help you review key ideas. You can access this calendar at http://mail.rsgc.on.ca/~ashum/mcv4u

Your teacher has selected Review Questions for each chapter in the course and posted them on your class calendar for each test and mini-test (see right). Your textbook also provides several Cumulative Review sections. Each Cumulative Review section covers a trio of chapters (see next page).

You may also consider working with your peers to study together. Supplementary information is also available at http://pinterest.com/shumalex/

EXTRA HELP

Your teacher’s Extra Help schedule is updated each week and is always posted on the classroom door and online at: http://mail.rsgc.on.ca/~ashum/ExtraHelp Extra Help is NOT private one-to-one tutoring. Your teacher may be asked to help several students at the same time and may not be able dedicate an extended period of time exclusively to you, e.g., to re-teach an entire lesson. You are responsible for catching-up over the course of the academic year and addressing gaps in your understanding as each unit is covered. As suggested in class, you should identify your individual areas of weakness based on your performance on tests/mini-tests/assignments, and come early for Extra Help, i.e., do NOT procrastinate until right before the exam. Arrive with specific questions.

SUGGESTED REVIEW QUESTIONS BY UNIT

These suggested Review Questions have been copied from your online calendar for your convenience:

Intro to Calculus and Derivatives- p32 #1c, 3d, 4, 7acd, 10, 11b, 12- p30 #13, 14ab, 15bc- p92 #1, 2a, 4, 6acd, 7c, 8bc, 11, 13, 17- p110 #3acf, 4af, 5, 7a, 11, 12, 18, 23, 26, 27

Derivatives, Applications and Curve Sketching- p156 #6, 7- p160 #3, 4a- p196 #3, 8ad, 9, 16cd- p216 #1, 3c, 4, 10, 12, 15- p156 #9, 10b, 11, 14, 15, 16, 17, 22, 23, 25

Derivatives of Exponential and Trigonometric Functions- p256 #1abcde, 2abc, 3d, 4a, 5ad, 7ab- p260 #1; 3bde- * p263 #1, 2, 6, 13, 19

Introduction and Applications of Vectors- page 344 #2a, 3, 6a, 7abc, 15ab, 16b, 17, 23- page 388 #2, 4, 5, 11, 14, 18- p344 #9, 26- p348 #2, 3, 5b- p418 #1a,

*Equations of Lines and Planes- p480 #1, 3-13, 15, 16, 19-27, 29, 30, 33, 34

*Relationships between Points, Lines and Planes - p552 #3, 8, 10, 12abc, 14a, 19

*will be confirmed April-May

MCV4U CALCULUS & VECTORS WINTER-SRING 2013

INSTRUCTOR: MR.SHUM AND MR. DOERKSEN

FAQs Frequently asked questions

What formulas will be provided? Only these two formulas will appear on the exam

“vector projection a onto b”

projba= a⋅b

b 2 b

“scalar projection of a onto b”

compba

= a⋅b

b .

Will we review material in class before

the exam?

Your teacher has set aside several classes in late May for assisting you in your exam review. Each class is typically just over an hour. As such, relying solely on this time to prepare for the final exam will NOT be adequate preparation.

As suggested in class, you should begin your exam review througout the month of May, set your priorities targeting your weakest topics first, seeking extra help in a timely manner, using the online notes, suggested review questions for each unit and your portfolio to help you prepare.

Are there other review questions from

the text?

Here is a selection of suggested questions from the three Cumulative Review sections of your textbook.

Cumulative Review Calculus p267#1-32

Cumulative Review Vectors p557 #1-12, 17-25, 27, 28, 31, 33, 34

What mark do I need to pass the

course?

To earn the credit and “pass” the course, your final mark must be 50% or higher. Most university admissions requirements will require a significantly higher mark. Please check with the Director of University Admissions for recent historical and/or updated information on cut-offs.

Is my mark in June final?

What about the Advanced Functions course that I took in first semester? or

concurrently with Advanced Placement?

The Calculus & Vectors course ends with the final exam. Your final mark will appear on the Final Report Card. This is the final mark that will be submitted to universities. The Calculus & Vectors course is a separate course from the Advanced Functions course. Your performance in each course is graded separately.

Students taking the Advanced Placement (AP) course must be aware that there is a significant amount of material that is NOT within the College Board AP curriculum but is within the Ontario Calculus & Vectors course. These topics are highlighted in red on the page 2 and pertain mostly to vectors, their applications, lines and planes.

I don’t know if I’m entitled to a

formula sheet, extra time, or quiet space. How can I find out?

Students who are entitled to such accommodations typically have consulted with a psycho-educational for specialized testing. An Individualized Educational Plan (IEP) has been prepared by teachers from the Learning Centre and has been implemented throughout the year. It is highly unlikely that accommodations would be offered to students right before the final exam without expert diagnosis and long-term approach.

I have questions about the exam that

are not addressed by this outline. What should I do?

Speak or email your teacher right away.

I don’t even know how to plan to study.

What should I do?

The Learning Centre has teachers that specialize in helping students with organization. Make an appointment to speak to the these teachers right away.

MCV4U CALCULUS & VECTORS WINTER-SRING 2013