Course Syllabus

Content (what students are expected to know)

To be delivered in the approximate order shown.  Certain components within a given topic may be moved to accommodate those students taking Pre-Calculus 12 concurrently.

I. Functions and Graphs (4%)
• parent functions from Pre-Calculus 12
• piecewise functions
• inverse trigonometric functions

II. Limits (15%)
• from table of values, graphically, and algebraically
• one-sided versus two-sided
• end behaviour
• intermediate value theorem
• left and right limits
• limits to infinity
• continuity

III. Differentiation (35%)

(III-A) Derivatives
• history
• definition of derivative
• notation
• rate of change
        o average versus instantaneous
        o slope of secant and tangent lines
• differentiation rules
        o power, product; quotient and chain
        o transcendental functions: logarithmic, exponential, trigonometric
• higher order, implicit

(III-B) Derivative Applications
• applications
        o relating graph of f(x) to f'(x) and f''(x)
        o increasing/decreasing, concavity
        o differentiability, mean value theorem
        o Newton’s method
        o problems in contextual situations, including related rates and optimization problems

IV. Integration (30%)

(IV-A) Integrals
• approximations
        o Riemann sum, rectangle approximation method, trapezoidal method
• fundamental theorem of calculus
• methods of integration
        o antiderivatives of functions
        o substitution
        o by parts

(IV-B) Applications of Integrals
• applications
        o area under a curve, volume of solids, average value of functions
        o differential equations
        o initial value problems
        o slope fields

Curricular Competencies (what students are expected to do)

Reasoning and modelling (4%)
• Develop thinking strategies to solve puzzles and play games
• Explore, analyze, and apply mathematical ideas using reason, technology, and other tools
• Estimate reasonably and demonstrate fluent, flexible, and strategic thinking about number
• Model with mathematics in situational contexts
• Think creatively and with curiosity and wonder when exploring problems

Understanding and solving (4%)
• Develop, demonstrate, and apply conceptual understanding of mathematical ideas through play, story, inquiry, and problem solving
• Visualize to explore and illustrate mathematical concepts and relationships
• Apply flexible and strategic approaches to solve problems
• Solve problems with persistence and a positive disposition
• Engage in problem-solving experiences connected with place, story, cultural practices, and perspectives relevant to local First Peoples communities, the local community, and other cultures

Communicating and representing (4%)
• Explain and justify mathematical ideas and decisions in many ways
• Represent mathematical ideas in concrete, pictorial, and symbolic forms
• Use mathematical vocabulary and language to contribute to discussions in the classroom
• Take risks when offering ideas in classroom discourse

Connecting and reflecting (4%)
• Reflect on mathematical thinking
• Connect mathematical concepts with each other, other areas, and personal interests
• Use mistakes as opportunities to advance learning
• Incorporate First Peoples world views, perspectives, knowledge, and practices to make connections with mathematical concepts

Assessment Breakdown

Course Content Emphasis

4%    Functions and Graphs [FG]

15%  Limits [L]

35%  Differentiation [D]

A. Derivatives and B. Derivative Applications

30%  Integration [I]

A. Integrals and B. Applications of Integrals

Curricular Competency Specific

4%     Reasoning and Modelling [RM]

4%     Understanding and Solving [US]

4%     Communicating and Representing [CRp]

4%     Connecting and Reflecting [CRf]

= 100% Total