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