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COURSE OUTLINE

Course Title: Advanced Placement Calculus AB
Course Code: AP Calculus AB
Grade: 12
Course Type: Advanced Placement
Credit Value: 1.0
Prerequisite: Four years of secondary school mathematics
Curriculum Policy Document: Advanced Placement Course Audit Manual
Department: Mathematics
Course Developer: Ken Stewart
Development Date: Winter and Spring 2007
Course Revised by: -
Revision Date: -

Course Description:

This is a rigorous course designed to provide students with a learning experience equivalent to that of a college course in single variable calculus. The course develops students understanding of the concepts of calculus and provides experience with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically and verbally, with the connections among these representations highlighted.

Unit	Titles and Descriptions	Time and Sequence
Unit 1	Advanced Functions Several types of functions needed in this course will be reviewed along with their characteristics including: differences in polynomials, absolute value functions, polynomial in equalities and division, remainder theorem and factor theorem, and factoring polynomials.	12 hours
Unit 2	Concepts of Calculus A variety of mathematical operations with functions will be investigated including: rationalization, rates of change, the limit concept, indeterminate form, finding the slope of a curve, tangent slope function, derivatives and graphs.	12 hours
Unit 3	Derivatives In this unit students will see the power of the slope function and the applications of derivatives in a variety of style problems.	11 hours
Unit 4	Curve Sketching The key features of a properly sketched curve including x and y intercepts, vertical, horizontal and oblique asymptotes, maximum and minimum values, points of inflection, undefined tangent slope points will be examined separately before putting them all together into a full sketch of a curve.	11 hours
Unit 5	Derivative Applications A variety of types of problems will be presented in this unit and can generally be grouped into the following categories: Pythagorean problems, volume problems, trough problems, shadow problems, general rate problems. Each type will be examined separately.	11 hours
Unit 6	Exponents and Log Functions As a review of previous courses, the unit will begin with the rules associated with exponents. Then the exponential functions, applications and logarithms and log functions and applications will be covered.	11 hours
Unit 7	Derivatives of Exponents and Log Functions Exponential functions, logarithmic functions, curve sketching and logarithmic differentials are all topics of this unit.	11 hours
Unit 8	Trigonometry Differentials and Applications The unit begins with a review of the three basic trig functions (sine, cosine, tangent). Angles, the CAST rule, sums and differences for sine/cosine form the second major topic. Finally solving trigonometric equations are pursued with a focus on limits, derivatives and applications of trigometric functions.	11 hours
Unit 9	Antiderivatives and Applications The topics covered in this unit include the concept of antiderivatives, acceleration, velocity, differential equations, Riemann’s sums and areas, area function, definite integral and integration and area between curves.	12 hours
	Final Evaluation	8 hours
	Total	110 hours

Teaching / Learning Strategies:

Several teaching and learning strategies are employed in this course including guided exploration, visuals, independent study, model analysis, problem solving, direct instruction, graphing applications, independent reading and self-assessment.

Assessment and Evaluation Strategies of Student Performance:

Assessment is a systematic process of collecting information or evidence about a student’s progress towards meeting the learning expectations. Assessment is embedded in the instructional activities throughout a unit. The expectations for the assessment tasks are clearly articulated and the learning activity is planned to make that demonstration possible. This process of beginning with the end in mind helps to keep focus on the expectations of the course. The purpose of assessment is to gather the data or evidence and to provide meaningful feedback to the student about how to improve or sustain the performance in the course. Scaled criteria designed as rubrics are often used to help the student to recognize their level of achievement and to provide guidance on how to achieve the next level. Although assessment information can be gathered from a number of sources (the student himself, the student’s course mates, the teacher), evaluation is the responsibility of only the teacher. For evaluation is the process of making a judgment about the assessment information and determining the percentage grade or level.

The Final Grade:

The evaluation of the student’s achievement in this course is based on the student’s achievement of the curriculum expectations. The percentage grade represents the student’s overall achievement and reflects the corresponding level of achievement as described in the Achievement chart for this discipline. A credit will be granted if the final percentage awarded is 50% or more. The final grade will be determined as follows:

• 70% of the grade will be based upon assessment tasks completed throughout the course. This portion of the grade will reflect the student’s most consistent level of achievement throughout the course, although special consideration will be given to the most recent evidence of achievement.



• 30% of the grade will be based on a final assessment task that occurs at or near the end of the course. In the case of this course, this final assessment task will take the form of a final examination which will be completed online under the supervision of a pre-approved proctor. The final exam is prepared by the Advanced Placement Board and is the same exam written on the same day for all AB Calculus students from around the world.

The report card will focus on two distinct but related aspects of student achievement; the achievement of curriculum expectations and the development of learning skills. The report card will contain separate sections for the reporting of these two aspects.

A Summary Description of Achievement in Each Percentage Grade Range and Corresponding Level of Achievement
Percentage Grade Range	Achievement Level	Summary Description
80-100%	Level 4	A very high to outstanding level of achievement. Achievement is above the provincial standard.
70-79%	Level 3	A high level of achievement. Achievement is at the provincial standard.
60-69%	Level 2	A moderate level of achievement. Achievement is below, but approaching, the provincial standard.
50-59%	Level 1	A passable level of achievement. Achievement is below the provincial standard.
below 50%	Level R	Insufficient achievement of curriculum expectations. A credit will not be granted.

Achievement Chart: Mathematics, Grades 9-12

Categories	50-59% (Level 1)	60-69% (Level 2)	70-79% (Level 3)	80-100% (Level 4)
Knowledge and Understanding - Subject-specific content acquired in each course (knowledge), and the comprehension of its meaning and significance (understanding)
	The student:
Knowledge of content (e.g., facts, terms, procedural skills, use of tools)	demonstrates limited knowledge of content	demonstrates some knowledge of content	demonstrates considerable knowledge of content	demonstrates thorough knowledge of content
Understanding of matematical concepts	demonstrates limited understanding of content	demonstrates some understanding of content	demonstrates considerable understanding of content	demonstrates thorough and insightful understanding of content
Thinking - The use of critical and creative thinking skills and/or processes
	The student:
Use of planning skills -understanding the problem (e.g., formulating and interpreting the problem, making conjectures) -making a plan for problem solving	uses planning skills with limited effectiveness	uses planning skills with moderate effectiveness	uses planning skills with considerable effectiveness	uses planning skills with a high degree of effectiveness
Use of processing skills -carrying out a plan (e.g., collecting data, questioning, testing, revising, modelling, solving, inferring, forming conclusions) -looking back at the solution (e.g., evaluating reasonableness, making convincing arguments, reasoning, justifying, proving, reflecting)	uses processing skills with limited effectiveness	uses processing skills with some effectiveness	uses processing skills with considerable effectiveness	uses processing skills with a high degree of effectiveness
Use of critical/creative thinking processess (e.g., problem solving, inquiry)	uses critical / creative thinking processes with limited effectiveness	uses critical / creative thinking processes with some effectiveness	uses critical / creative thinking processes with considerable effectiveness	uses critical / creative thinking processes with a high degree of effectiveness
Communication - The conveying of meaning through various forms
	The student:
Expression and organization of ideas and mathematical thinking (e.g., clarity of expression, logical organization), using oral, visual, and written forms (e.g., pictorial, graphic, dynamic, numeric, algebraic forms; concrete materials)	expresses and organizes mathematical thinking with limited effectiveness	expresses and organizes mathematical thinking with some effectiveness	expresses and organizes mathematical thinking with considerable effectiveness	expresses and organizes mathematical thinking with a high degree of effectiveness
Communication for different audiences (e.g., peers and teachers) and purposes (e.g., to present data, justify a solution, express a mathematical argument) in oral, visual, and written forms	communicates for different audiences and purposes with limited effectiveness	communicates for different audiences and purposes with some effectiveness	communicates for different audiences and purposes with considerable effectiveness	communicates for different audiences and purposes with a high degree of effectiveness
Use of conventions, vocabulary, and terminology of the discipline (e.g., terms, symbols) in oral, visual, and written forms	uses conventions, vocabulary, and terminology of the discipline with limited effectiveness	uses conventions, vocabulary, and terminology of the discipline with some effectiveness	uses conventions, vocabulary, and terminology of the discipline with considerable effectiveness	uses conventions, vocabulary, and terminology of the discipline with a high degree of effectiveness
Application - The use of knowledge and skills to make connections within and between various contexts
	The student:
Application of knowledge and skills in familiar contexts	applies knowledge and skills in familiar contexts with limited effectiveness	applies knowledge and skills in familiar contexts with some effectiveness	applies knowledge and skills in familiar contexts with considerable effectiveness	applies knowledge and skills in familiar contexts with a high degree of effectiveness
Transfer of knowledge and skills to new contexts	transfers knowledge and skills to new contexts with limited effectiveness	transfers knowledge and skills to new contexts with some effectiveness	transfers knowledge and skills to new contexts with considerable effectiveness	transfers knowledge and skills to new contexts with a high degree of effectiveness
Making connections within and between various contexts (e.g., connections between concepts, representations, and forms within mathematics; connections involving use of prior knowledge and experience; connections between mathematics, other disciplines, and the real world))	makes connections within and between various contexts with limited effectiveness	makes connections within and between various contexts with some effectiveness	makes connections within and between various contexts with considerable effectiveness	makes connections within and between various contexts with a high degree of effectiveness

Potential Resources:

• AP Calculus AB online course of study
• visuals
• graphing calculator 
• The key resources used in creating this course have been identified in each online unit. No further resources are needed on the part of the student.

Program Planning Considerations for Mathematics:

Teachers who are planning a program in Mathematics must take into account considerations in a number of important areas. Essential information that pertains to all disciplines is provided in the companion piece to this document, The Ontario Curriculum, Grades 9 to 12: Program Planning and Assessment, 2000. The areas of concern to all teachers that are outlined there include the following:

• types of secondary school courses
• education for exceptional students
• the role of technology in the curriculum
• English as a second language (ESL) and English literacy development (ELD)
• career education
• cooperative education and other workplace experiences
• health and safety

Considerations relating to the areas listed above that have particular relevance for program planning in Mathematics are noted here.

Education for Exceptional Students. In planning courses in Mathematics, teachers should take into account the needs of exceptional students as set out in their Individual Education Plan. All Mathematics courses reflect the real world very closely, which offers a vast array of opportunities for exceptional students. Students who use alternative techniques for communication may find a venue for their talents as they go about researching the nature of their world.

The Role of Technology in the Curriculum. Information technology is considered a learning tool that must be accessed by Mathematics students when the situation is appropriate. As a result, students will develop transferable skills through their experience with word processing, internet research, presentation software, and equation editors as would be expected in any environment. 

English As a Second Language and English Literacy Development (ESL/ELD). This Mathematics course can provide a wide range of options to address the needs of ESL/ELD students. Assessment and evaluation exercises will help ESL students in mastering the English language and all of its idiosyncrasies. In addition, since all occupations require employees with a wide range of English skills and abilities, many students will learn how the operation of their own physical world can contribute to their success in their social world.

Career Education. Mathematics definitely helps prepare students for employment in a huge number of diverse areas - Engineering, Science, Business, etc. The skills, knowledge and creativity that students acquire through this course are essential for a wide range of careers. Being able to express oneself in a clear concise manner without ambiguity, solve problems, make connections between this Mathematics course and the larger world, etc., would be an overall intention of this Mathematics course, as it helps students prepare for success in their working lives.

Cooperative Education and Other Workplace Experiences. By applying the skills they have developed, students will readily connect their classroom learning to real-life activities in the world in which they live. Cooperative education and other workplace experiences will broaden their knowledge of employment opportunities in a wide range of fields. In addition, students will increase their understanding of workplace practices and the nature of the employer-employee relationship. Teachers of Mathematics should maintain links with community-based workers to ensure that students have access to hands-on experiences that will reinforce the knowledge they have gained in school.

Health and Safety. The Mathematics program provides the reading and analytical skills for the student to be able to explore the variety of concepts relating to health and safety in the workplace. Teachers who provide support for students in workplace learning placements need to assess placements for safety and ensure that students can read and understand the importance of issues relating to health and safety in the workplace.