Calculus 12

We will be using the BC Calculus 12 curriculum.

The Big Ideas are

  • The concept of a limit is foundational to calculus.

  • Differential calculus develops the concept of instantaneous rate of change.

  • Integral calculus develops the concept of determining a product involving a continuously changing quantity over an interval.

  • Derivatives and integrals are inversely related.

Textbook: Stewart, James et al., Calculus: A First Course, McGraw-Hill Ryerson, 1989.

Assessment will be based on unit tests, homework, quizzes, and a final exam.

Assignments 15%

Unit Tests and Quizzes 70%

Final Exam 15%

Assignments will be marked by the student and handed in. Answer keys will be provided.

Quizzes will fall throughout the course units.

Unit Tests will occur at the end of each unit.

The final exam will take place in the exam period.

Content

  • functions and graphs

    • parent functions from Pre-Calculus 12

    • piecewise functions

    • inverse trigonometric functions

  • limits

    • 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

  • differentiation

      • history

      • definition of derivative

      • notation

    • rate of change

      • average versus instantaneous

      • slope of secant and tangent lines

    • differentiation rules

    • power, product; quotient and chain

    • transcendental functions: logarithmic, exponential, trigonometric

  • higher order, implicit

  • applications

      • relating graph of f(x) to f'(x) and f''(x)

      • increasing/decreasing, concavity

      • differentiability, mean value theorem

      • Newton’s method

      • problems in contextual situations, including related rates and optimization problems

  • integration

    • definition of an integral

    • notation

    • definite and indefinite

    • approximations

      • Riemann sum, rectangle approximation method, trapezoidal method

    • fundamental theorem of calculus

    • methods of integration

      • antiderivatives of functions

      • substitution

      • by parts

    • applications

      • area under a curve, volume of solids, average value of functions

      • differential equations

      • initial value problems

      • slope fields