Principles of Math 12 Honours / Calculus AB Course Syllabus
IMPORTANT DATES!!!
AP Exam:
(to be filled in by students)
Euclid Contest:
Sun Life COMC:
This course is intended to prepare students for the Advanced Placement exam for Calculus
AB. The course meets daily for the entire year (36 weeks) and will also teach the outcomes for
Principles of Math 12 to ensure that any foundation skills have been taught before beginning
Calculus. In addition, students will also prepare for the Waterloo Euclid math contest as well as the
Calculus Challenge exam for our provincial Universities.
Textbooks:
Calculus of a Single Variable: Early Transcendental Functions Third Edition
Larson, Hostetler, Edwards ISBN 0-618-22308-8
McGraw-Hill Ryerson: Pre-Calculus 12
McAskill, Watt, Balzarini, Johnson, Kennedy, Melnyk, Zarski ISBN 0-07-073872-6
Student Resources:
Barron’s How to Prepare for the AP Advanced Placement Exam Calculus 8th Edition
Hockett, Bock ISBN-13: 978-0-7641-2382-5
Course website will be maintained at (notes, assignments, review materials and other resources):
mrjoyce.wordpress.com
Weekly Overview
Week 1-2 Math 12
Week 3
Math 12
Week 4-5 Math 12
Week 6-7 Math 12
Week 8-9 Math 12
Week 10-11 Math 12
Week 12-13 Math 12
Week 14
Math 12
Week 15
Calculus
Week 16-18 Calculus
Week 19-21 Calculus
Week 22-24 Calculus
Week 25
Calculus
Week 26-27 Calculus
Week 28-30 Calculus
Week 31-32 Math 12
Week 32-33 Math 12
Week 34-35 Math 12
Week 35-36 Math 12
Transformations
Pre-Calculus 12: CH1
Radical Functions
Pre-Calculus 12: CH2
Trigonometry and the Unit Circle
Pre-Calculus 12: CH4
Trigonometric Functions
Pre-Calculus 12: CH5
Trigonometric Equations and Identities
Pre-Calculus 12: CH6
Exponential Functions
Pre-Calculus 12: CH7
Logarithmic Functions
Pre-Calculus 12: CH8
Function Operations
Pre-Calculus 12: CH10
Limits and Their Properties
Calculus of a single variable: CH1
Differentiation
Calculus of a single variable: CH2
Applications of Differentiation
Calculus of a single variable: CH3
Integration
Calculus of a single variable: CH4
Differential Equations
Calculus of a single variable: CH5
Applications of Integration
Calculus of a single variable: CH6
Review for AP exam
Supplement: Barron’s & handouts
Polynomial Functions
Pre-Calculus 12: CH3
Rational Functions
Pre-Calculus 12: CH9
Combinatorics
Pre-Calculus 12: CH11
Final Exam Review
Handouts/practice exams
***Schedule is subject to change based on needs of class***
Grading – Pre-Calculus 12:
Transformations and
Functions
Trigonometry and the
Unit Circle
Exponential Functions
Function Operations
9%
Radical Functions
6%
Polynomial Functions
6%
5%
Trigonometric Functions
and Graphs
Logarithmic Functions
Permutations,
Combinations and the
Binomial Theorem
8%
Trigonometric Identities
8%
8%
9%
Rational Functions
5%
Applications of
Differentiation
15%
6%
5%
*Final Exam is worth 25% of overall mark
Grading – AP Calculus:
Limits
5%
Differentiation
20%
Integration
20%
Differential Equations
and Applications of
Integration
15%
*Final Exam is worth 25% of overall mark
*AP Exam score will not be incorporated with your Calculus mark ☺
This course is very rigorous and will require you to think at higher levels and in new ways
about Mathematics. To support your learning you must provide clear concise solutions to your
work. Any work submitted without work shown will not be marked. Communicating the ideas
with your peers is also necessary in demonstrating your understanding of the topics. You will be
asked to work in cooperative learning situations often and should be prepared to discuss your
solutions with classmates. It is not enough to memorize algorithms and complete your
assignments. To be successful there will be an emphasis on communicating the concepts of our
course.
It is mandatory that you have a graphing calculator for this course. Technology will play an
important role in developing the ideas of Calculus and Principles of Math 12. There will be
questions/projects/assignments which will not be possible without the use of a graphing calculator
as an aid. I will keep a few extras in our class room for the odd time when you forget to bring
yours but you must have access to one for everyday of the course. Basic instruction will be
provided during our lessons on usage of the graphing calculator. We are also fortunate to have use
of an LCD projector, a tablet and screen capture software. These tools along with the graphing
calculator will be a regular supplement to our daily lessons.
Topic Outline (Approx. one topic per day)
Math 12: Transformations
1.1 Horizontal and Vertical Translations of Functions
1.2 Reflections and Stretches of Functions
1.3 Combining Transformations
1.4 Inverse of a Relation
Review
Unit Test
Math 12: Radical Functions
2.1 Radical Functions and Transformations
2.2 Square Root of a Functions
2.3 Solving Radical Equations Graphically
Review
Unit Test
Math 12: Trigonometry and the Unit Circle
4.1 Angles and Angle Measure
4.2 The Unit Circle
4.3 Trigonometric Ratios
4.4 Introduction to Trigonometric Equations
Review
Unit Test
Math 12: Trigonometric Functions and Graphs
5.1 Graphing Sine and Cosine Functions
5.2 Transformations of Sinusoidal Functions
5.3 The Tangent Function
5.4 Equations and Graphs of Trigonometric Functions
Review
Unit Test
Math 12: Trigonometric Identities
6.1 Reciprocal, Quotient, and Pythagorean Identities
6.2 Sum, Difference, and Double Angle Identities
6.3 Proving Identities
6.4 Solving Trigonometric Equations Using Identities
Review
Unit Test
Math 12: Exponential Functions
7.1 Characteristics of Exponential Functions
7.2 Transformations of Exponential Functions
7.3 Solving Exponential Equations
Review
Unit Test
Math 12: Logarithmic Functions
8.1 Characteristics of Exponential Functions
8.2 Transformations of Logarithmic Functions
8.3 Laws of Logarithms
8.4 Logarithmic and Exponential Equations
Review
Unit Test
Math 12: Function Operations
10.1 Sums and Products of Functions
10.2 Products and Quotients of Functions
10.3 Composite Functions
Review
Unit Test
Calculus 12: Limits
1.2 Finding Limits Graphically and Numerically
1.3 Evaluating Limits Analytically
1.4 Continuity and One-Sided Limits
1.5 Infinite Limits
3.5 Limits at Infinity
Review
Unit Test
Calculus 12: Differentiation
2.1 The Derivative and the Tangent Line Problem
2.2 Basic Differentiation Rules and Rates of Change
2.3 The Product and Quotient Rules and Higher-Order Derivatives
2.4 The Chain Rule
2.5 Implicit Differentiation
2.6 Derivatives of Inverse Functions
2.7 Related Rates
2.8 Newton’s Method
Review
Unit Test
Calculus 12: Applications of Differentiation
3.1 Extrema on an Interval
3.2 Rolle’s Theorem and the Mean-Value Theorem
3.3 Increasing and Decreasing Functions and The First Derivative Test
3.4 Concavity and the Second Derivative Test
3.6 Curve Sketching
3.7 Optimization Problems
3.8 Differentials
7.7 L’Hopital’s Rule
Review
Unit Test
Calculus 12: Integration
4.1 Antiderivatives and Indefinite Integration
4.2 Area
4.3 Riemann Sums and Definite Integrals
4.4 The Fundamental Theorem of Calculus
4.5 Integration by Substitution
4.6 Numerical Integration
4.7 The Natural Logarithmic Function: Integration
4.8 Inverse Trigonometric Functions: Integration
Review
Unit Test
Calculus 12: Differential Equations
5.1 Differential Equations: Growth and Decay
5.2 Differential Equations: Separation of Variables
5.2 Slope Fields
Review
Unit Test
Calculus 12: Applications of Integration
6.1 Area of a Region Between Two Curves
6.2 Volume: the Disk Method
6.2 Volume of Known Cross Sections
6.3 Volume: the Shell Method
Review
Unit Test
AP Exam Review
2 weeks will be spent reviewing the materials in the Barron’s Study guide
1+ week on supplemental materials posted on the course website
Previous exams: http://www.collegeboard.com/student/testing/ap/calculus_ab/samp.html
Math 12: Polynomial Functions
3.1 Characteristics of Polynomial Functions
3.2 The Remainder Theorem
3.3 The Factor Theorem
3.4 Equations and Graphs of Polynomial Functions
Review
Unit Test
Math 12: Rational Functions
9.1 Exploring Rational Functions and Using Transformations
9.2 Analysing Rational Functions
9.3 Connecting Graphs and Rational Equations
Review
Unit Test
Math 12: Combinatorics
11.1 Permutations
11.2 Combinations
11.3 The Binomial Theorem
Review
Unit Test
Final Exam Review
The remainder of our course (~3 weeks) will be dedicated to reviewing for the class exam.
The materials for review have been posted on the course website, however some will be handed
out during class. Some resources are available from the Ministry of Education:
http://www.bced.gov.bc.ca/exams/search/