Contact Information: lilim@sd38.bc.ca
Prerequisites:
Students need to have a strong foundation in reasoning with algebraic symbols and working with algebraic structures. Their strong understanding of functions should include linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise-defined functions. In particular, before studying calculus, students must be familiar with the properties of functions, the composition of functions, the algebra of functions, and the graphs of functions. Students must also understand the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and descriptors such as increasing and decreasing). Students should also know how the sine and cosine functions are defined from the unit circle and know the values of the trigonometric functions at the numbers and their multiples.
Course Description:
College Board’s Advanced Placement® Program (AP®) enables willing and academically prepared students to pursue college-level studies—with the opportunity to earn college credit, advanced placement, or both—while still in high school. AP Calculus AB is a college-level calculus course designed to meet the Advanced Placement curricular requirements for Calculus AB (equivalent to a one-semester college course). Through the use of big ideas of calculus (e.g., modeling change, approximation and limits, and analysis of functions), we cover major topics of limits, derivatives, integrals, and the Fundamental Theorem of Calculus. We will investigate and analyze course topics using equations, graphs, tables, and words, with a particular emphasis on a conceptual understanding of calculus. Applications, in particular to solid geometry and physics, will be studied where appropriate.
For more detailed information on the curriculum and exam description for the course, please access the website created by the College Board’s Advanced Placement® Program: https://apcentral.collegeboard.org/courses/ap-calculus-ab?course=ap-calculus-ab
Unit 1 – Limits and Continuity
[CR1a] — The course is structured around the enduring understandings within Big Idea 1: Limits.
- 1.5 Mathematical models; Linear models
- 1.2 Properties of functions
- 1.4 New functions from old
- 2.1 Estimating limit values
- 2.2 Determining limits using algebraic properties of limits and algebraic manipulation
- 2.4 Defining continuity and exploring types of discontinuities; Working with the Intermediate Value Theorem
- 2.5 Limits & Continuity of Trigonometric Functions
Unit 2 – Differentiation: Definition and Fundamental Properties; Composite, Implicit, and Inverse Functions
[CR1b] — The course is structured around the enduring understandings within Big Idea 2: Derivatives.
- 3.1 Tangent lines and rates of change
- 3.2 The derivative of a function; Differentiability
- 3.3 Techniques and rules of differentiation; Higher order derivatives
- 3.5 The Chain Rule
- 4.3 Implicit differentiation
Unit 3 – Differentiation: Composite, Implicit, and Inverse Functions
[CR1b] — The course is structured around the enduring understandings within Big Idea 2: Derivatives.
- 3.4 Derivatives of Trigonometric Functions
- 4.4 Derivatives of Logarithmic and Exponential Functions
- 4.5 Derivatives of Inverse Trigonometric Functions
- 4.7 Hôpital’s Rule; Indeterminate Forms
Unit 4 – Contextual Applications of Differentiation
[CR1b] — The course is structured around the enduring understandings within Big Idea 2: Derivatives.
- 4.6 Related rates
- 6.3 Rectilinear motion
- 3.6 Local linear approximation
- 6.4 Newton’s Method to approximate a solution
Unit 5 – Analytical Applications of Differentiation
[CR1b] — The course is structured around the enduring understandings within Big Idea 2: Derivatives.
- 5.1 Analysis of functions I – Increase, decrease and concavity
- 5.2 Analysis of functions II – Relative extrema; First and second derivatives tests
- 5.3 Analysis of functions III – Graphing functions
- 6.1 Absolute maxima and minima
- 6.2 Applied maximum and minimum (optimization) problems
- 6.5 Rolle’s Theorem & Mean Value Theorem
Unit 6 – Integration and Accumulation of Change
[CR1c] — The course is structured around the enduring understandings within Big Idea 3: Integrals and the Fundamental Theorem of Calculus.
- 7.2 The indefinite integral; Integral curves and direction fields
- 7.3 Integration by substitution
- 9.4 Integration by long division and completing the square
- 7.5 The definite integral
- 7.6 The Fundamental Theorem of Calculus
- 7.8 Evaluating definite integrals by substitution
- 7.7 Rectilinear motion revisited
Unit 7 – Applications of Definite Integral
[CR1c] — The course is structured around the enduring understandings within Big Idea 3: Integrals and the Fundamental Theorem of Calculus.
- 10.1 First-order differential equations and applications
- 10.2 Direction fields
- 10.3 Modeling with differential equations; Exponential Growth and Decay
Unit 8– Applications of Definite Integral
[CR1c] — The course is structured around the enduring understandings within Big Idea 3: Integrals and the Fundamental Theorem of Calculus.
- Using Accumulation Functions and Definite Integrals in Applied Contexts
- 8.1 Areas in the plane
- 8.2 Volumes
Course Evaluation:
| Percentage of Final Mark | |
| Check-Your-Understanding Assignments, Project & Presentation | At most 15% |
| Unit Tests | At least 70% |
| Final Exam | At most 15% |
Textbook:
- Anton, Howard, et al. Calculus: A New Horizon (6th edition).
Additional Resources:
- Barron’s. AP Calculus (2019 or newer). – Copies are available for in-class use. If you prefer your own copy, you may purchase it through Amazon.
Calculator:
A graphing calculator is required for all students. TI-84 by Texas Instruments is recommended. If you decide to purchase a different calculator, please check that it is on the list of approved graphing calculators (https://apcentral.collegeboard.org/ap-coordinators/on-exam-day/calculator-policy). Students can either purchase one of their own or borrow one from the department. If you decide to borrow one, a security deposit cheque of $160 payable to McMath Secondary, post-dated to 1 June 2024, will be required.
Use of the graphing calculator by students to solve problems includes, but is not limited to, plotting and analyzing the graphs of functions within an arbitrary viewing window, finding the zeros of functions, finding the limit of a function at a specific value, and analytically and numerically calculating both the derivative of a function and the value of a definite integral.
AP Calculus AB Exams (13 May 2024, 8:00 am, Monday):
Please note that the format of the exams may change as we navigate through the year. In the past, the exams are 3 hours and 15 minutes long and include 45 multiple-choice questions and 6 free-response questions. Raw scores are converted into a composite AP score on a 1 – 5 score.
While colleges and universities are responsible for setting their own credit and placement policies, most private colleges and universities award credit and/or advanced placement for AP scores of 3 or higher. To confirm a specific college’s AP credit/placement policy, a search engine is available at: https://apstudents.collegeboard.org/getting-credit-placement/search-policies
For example, both UBC and SFU require a minimum AP score of 4, giving 3 credits with the equivalent course, Math 100 (UBC) / Math 151 (SFU).
The AP exams assess each of the units of the course with the following exam weighting on the multiple-choice section:
| UNITS | EXAM WEIGHTING |
| 1: Limits and Continuity | 10-12% |
| 2: Differentiation: Definition and Basic Derivative Rules | 10-12% |
| 3: Differentiation: Composite, Implicit, and Inverse Functions | 9-13% |
| 4: Contextual Applications of Differentiation | 10-15% |
| 5: Applying Derivatives to Analyze Functions | 15-18% |
| 6: Integration and Accumulation of Change | 17-20% |
| 7: Differential Equations | 6-12% |
| 8: Applications of Integration | 10-15% |
Classroom Rules and Expectations:
All school rules must be followed and the following P.R.I.D.E. classroom behaviours are expected of every member in the classroom.
- Positive Attitude – We will be actively involved in our learning by using class time productively, following instructions, and maintaining appropriate focus.
- Respect – We treat others the way we wish to be treated, kindly, politely and with empathy. We strive to keep our classroom and learning materials in good condition. Food and beverage are permitted provided they do not distract from the learning environment and garbage is disposed in appropriate waste containers.
- Integrity – We take ownership for our actions and the associated consequences. Cheating and plagiarizing in any form will result in a mark of zero, parental contact and administration involvement.
- Diversity – We celebrate individual differences. We demonstrate co-operation, courtesy and inclusiveness in our school by treating people with dignity and respect.
- Effort – We arrive for class on time and with all necessary materials. When absent, we take responsibility for missed work and for our learning. We work to the best of our ability and ask for help when needed.
Extra Help & Contact Information:
Parents and students need to be aware that learning and achievement in this course is CUMULATIVE. Success in this course is directly related to your completion of homework and assignments consistently.
Students should make optimal use of class time for extra help. You will mark much of your own homework. You will note your challenges and seek help when you need it. If you require additional assistance outside of class time, you can utilize the weekly Personal Learning Time (Tuesdays and Thursdays) or make appointments with me in person or via email for after-school help at lilim@sd38.bc.ca.
Here is my homework blog (https://limmath.edublogs.org/) where you can track your homework, test and exam dates, and links to other Math resources.
If you have pertinent information to share with me, please email me at lilim@sd38.bc.ca.