Calculus Course Outline
Objectives:
Lesson Topic 
Overall Objectives 
Specific Objectives 
A. PreCalculus Review 

Lesson Topic 
Overall Objectives 
Specific Objectives 
A1. Properties of Functions 
1. Review characteristics of
functions (R) 2. Review/Extend
application of linear models (R/E) 3. Introduce new function
concepts pertinent to Calculus (N) 
1s. Fcn
char like domain, range, max, min, 2s. Calculus concepts like intervals
of increase, decrease, concavity, end behaviour,
rate of change 
A2. Linear Functions 
1. Review linear fcns from an algebraic, graphic, numeric perspective (R) 2. Review/Extend
application of linear models (R/E) 3. Incorporate new calculus
concepts to linear fcns (N) 
1s. Calculate slope 1s. Determine linear
equations from given info (i. pointslope, ii. 2
points) 1s. Recognize and utilize
slope relationships in parallel and perpendicular lines 1s. Solve linear equations 2s. model with linear
relations 3s. Determine rates of
change of functions using slope calcs. 
A3. Quadratic Functions 
1. Review Quadratics from
an algebraic, graphic, numeric perspective (R) 2. Review/Extend
application of quadratic models (R/E) 3. Incorporate new calculus
concepts to quadratic fcns (N) 
1s. Factor quadratic
expressions 1s. Solve quadratic
equations 1s. Find max/min on
quadratic fcns 1s. sketch and graph
quadratic fcns 2s. quadratic models in
physics (motion), business (profit, cost), etc for finding roots, max/min,
points 3s. Using technology,
determine where a quadratic function in/decreases and its concavity 
A4. Polynomial Functions 
1. Review cubics and quartics from an
algebraic, graphic, numeric perspective (R) 2. Review/Extend
application of polynomial models (R/E) 3. Incorporate new calculus
concepts to polynomial fcns (N) 
1s. Factor polynomial
expressions 1s. Solve polynomial
equations 1s. Find max/min on
polynomial fcns 1s. Sketch and graph
polynomial fcns 2s. polynomial models in
biology (populations), business (profit, cost, revenue) etc for finding
roots, max/min, points 3s. Using technology,
determine where a polynomial function in/decreases and its concavity 
A5. Rational Functions 
1. Review Rational Fcns from an algebraic, graphic, numeric perspective (R) 2. Review/Extend
application of rational fcn models (R/E) 3. Incorporate new calculus
concepts to rational fcns (N) 
1s. Simplify rational
expressions 1s. Solve rational
expressions 1s. Find asymptotes on
rational fcns 1s. Sketch and graph
rational fcns 2s. rational fcn models in science, economics 3s. Using technology,
determine where a quadratic function in/decreases and its concavity 
A6. Inequalities (chap R5) 
1. Review inequalities from
an algebraic, graphic, numeric perspective (R) 
1s. Solve linear equalities
algebraically and graphically 1s. Solve quadratic
equalities algebraically and graphically 1s. Solve polynomial
equalities algebraically and graphically 
A7. Exponential Functions 
1. Review exponential fcns from an algebraic, graphic, numeric perspective (R) 2. Review/Extend
application of exponential models (R/E) 3. Incorporate new calculus
concepts to linear fcns (N) 
1s. Simplify exponential expressions 1s. Solve exponential
equations 1s. Find max/min on
exponential fcns 1s. Sketch and graph
exponential fcns 2s. Exponential models in
biology (populations), business (profit, cost, revenue) 3s. Using technology,
determine where an exponential function in/decreases and its concavity 
A8. Logarithmic Functions 
1. Review Quadratics from
an algebraic, graphic, numeric perspective (R) 2. Review/Extend
application of logarthmic models (R/E) 3. Incorporate new calculus
concepts to logarithmic fcns (N) 
1s. Simplify logarithmic
expressions 1s. Solve logarithmic
equations 1s. Find max/min on
logarithmic fcns 1s. Sketch and graph
logarithmic fcns 2s. Logarithmic models in
science,
economics. 3s. Using technology, determine
where a logarithmic function in/decreases and its concavity 
B.
Differentiation 


Overall Objectives 
Specific Objectives 
B.3.1  Limits 
1. Define a limit 2. Determine if a limit
exists 3. Determine the value of a
limit, if it exists 
1. Use algebraic, graphic
and numeric (AGN) methods to determine if a limit exists 2. Use algebraic, graphic
and numeric methods to determine the value of a limit, if it exists 3. Use algebraic, graphic
and numeric methods to determine the value of a limit at infinity, if it
exists 4. Be able to state and
then work with the various properties of limits 5. Apply continuity to
application/real world problems 
B.3.2  Continuity 
1. Define continuity 2. Understand one sided
limits 3. Understand the
conditions under which a function is NOT continuous on both open and closed
intervals 
1. Use AGN methods to
determine continuity or points of discontinuity 2. Sketch graphs having
various limit and continuity conditions 3. Apply continuity to
application/real world problems 
B.3.3  Rates of Change 
1. Understand the
geometrical interpretation of a derivative (slope of a tangent) 2. Use difference quotients
and limits to find an instantaneous rate of change of a function at a point 
1. Calculate an average
rate of change 2. Calculate the value of a
derivative at a point 3. Calculate instantaneous
rates of change in real world problems 
B.3.4  Definition of a
Derivative 
1. Find the equation of a derivative
function from the limit definition of a derivative 
1. Calculate the derivative
of simple polynomial and rational functions from first principles 2. Determine the conditions
for existence of a derivative 3. Calculate derivatives
and apply to real world scenarios 
B.3.5  Graphical
Differentiation 
1. Given the equation of a
function, graph it and then make conjectures about the relationship between
the derivative function and the original function 2. From a function, sketch
its derivative and from a derivative, graph an original function 
1. Relate Òincreasing
functionÓ to a positive derivative and vice versa 2. Relate Òdecreasing
functionÓ to a negative derivative and vice versa 3. Relate Òmax/minÓ to a
zero derivative 4. Relate Òconcave upÓ to
an increasing derivative and vice versa 5. Relate Òconcave downÓ to
a decreasing derivative and vice versa 6. Relate function features
of graphs of functions and derivatives modeling real world applications 


B.4.1  Techniques for finding
the derivative 
1. Derive the power rule 2. Derive the constant rule 3. Extend the power rule to
the sum or difference rules 4. Determine the antiderivatives of power functions 
1. Use first principles to
develop the power rule 2. Use graphic differentiation
to verify the power rule 3. Use graphic evidence to
verify antiderivative functions 4. Apply the power rule to
real world problems 
B.4.2  Derivatives of
Products 
1. Derive the product rule 2. Differentiate equations using
the product rule 
1. Use first principles to
develop the product rule 2. Use graphic
differentiation to verify the product rule 3. Apply the product rule
to real world problems 
B.4.3  Derivatives of
Rational Functions Ð The Quotient Rule 
1. Derive the quotient rule 2. Differentiate equations
using the quotient rule 
1. Use first principles to
develop the quotient rule 2. Use graphic
differentiation to verify the quotient rule 3. Apply the quotient rule
to real world problems 
B.4.4 Ð Derivatives of
Composite Functions Ð The Chain Rule 
1. Derive the chain rule 2. Differentiate equations
using the chain rule 3. Apply the chain rule to
real world problems 

B.4.5  Derivatives of
Exponential Functions 
1. Derive the derivatives
of exponential functions algebraically and graphically 2. Differentiate equations
involving exponential functions 3. Apply exponential
functions and their derivatives to real world problems 

B.4.6  Derivatives of
Logarithmic functions 
1. Derive the derivatives
of logarithmic functions algebraically and graphically 2. Differentiate equations
involving logarithmic functions 3. Apply logarithmic
functions and their derivatives to real world problems 

B.4.7  Derivatives of
Trigonometric functions 
1. Derive the derivatives
of trigonometric functions algebraically and graphically 2. Differentiate equations
involving trigonometric functions 3. Apply sinusoidal
functions and their derivatives to real world problems 



B.5.1  Increasing and
Decreasing Functions 
1. Apply knowledge of the
first derivative to functions in a mathematical context and in the context of
a real world problem 
1. Define the terms
increasing and decreasing 2. Use calculus methods to
determine the intervals in which a function increases or decreases 3. Use calculus methods to
determine critical numbers of a function 4. Apply the concepts of
increase, decrease and critical numbers to a real world problem 
B.5.2  Relative Extrema 
1. Calculate all extrema of a function in a mathematical context and in
the context of a real world problem 
1. Define the term relative
(or local) extrema of a function 2. Apply definitions of extrema to functions on open and on closed intervals 3. Apply the first
derivative test to classifying extremas 4. Predict the appearance
of graphs based upon intervals of increase/decrease and extremas 5. Apply concepts of
increase, decrease and critical numbers to a real world problem 
B.5.3  Higher Derivatives,
Concavity 
1. Calculate higher order
derivatives of functions 2. Determine the intervals
of concavity of a function in a mathematical context and in the context of a
real world problem 
1. Calculate second and
third derivatives of functions 2. Define concavity and
inflection point 3. Test for concavity in a
function using the second derivative 4. Perform the second
derivative test to determine the nature of relative extrema 5. Apply concepts of concavity,
second derivatives, inflection points to a real world problem 
B.5.4  Curve Sketching 
1. Apply the concepts of
test for concavity, test for increasing and decreasing functions and the
concepts of limits at infinity to help us sketch graphs and describe the behaviour of functions 



B.6.1  Absolute Extrema 
1. Determine the absolute extrema of a given function in a mathematical context and
in the context of a real world problem 
1. Use Calculus methods to determine
the absolute extrema of a function 2. State the absolute value
theorem 3. Apply concepts of
increase, decrease and critical numbers and absolute extrema
to a real world problem 
B.6.2  Applications of Extrema 
1. Solve optimization
problems using a variety of calculus and noncalculus based strategies 2. Solve optimization
problems with and without the use of the TI 89 GDC 3. Work with problems set
in mathematical contexts or in the context of a real world problem 

B.6.3 Ð Further Business
Applications 
1. Solve problems related
to marginal costs, revenues and profits and average costs 2. Solve problems related
to economic lot size, economic order quantity, and elasticity of demand 

B.6.4  Implicit
Differentiation 
1. Use the implicit
differentiation method to find the derivatives of implicitly defined
equations 
1. Define the terms
explicit and implicit equations 2. Implicitly differentiate
implicitly defined equations 3. Determine the equation
of tangents and normals of implicitly defined
equations 4. Apply implicit
differentiation to real world problems 
B.6.5  Related Rates 
1. Given a situation in
which several quantities vary, predict the rate at which one of them is
changing when you know the other related rates 

B.6.6  Differentials:
Linear Approximations 
1. Given the equation of a
function and a fixed point on its graph, find an equation for a linear
function that best fits the given function 2. Use the linear equation
to find approximate values for f(x) and values for the differentials dx and dy 
1. Define differentials 2. Use differentials to
find approximate values of Dy 3. Write equations of
linear functions that best fit a function for values of x close to a given
point x = c 
C.
Integration 


Overall Objective 
Specific Objective 
C.7.1  Antiderivatives 
1. Determine the antiderivative of basic functions 2. Understand the
connection between antiderivatives as indefinite
integrals 
1. Define an antiderivative 2. Recognize the role of
and determine the value of a constant of integration 3. Understand the notation
of ˜
f(x)dx 4. Antidifferentiate
or integrate basic functions like power, exponential, simple trigonometric
functions 5. Apply concepts of antiderivatives and indefinite integrals to a real world
problems 
C.7.2 Ð Integration by
Substitution 
1. Use the method of
substitution to integrate simple
power, exponential, and trigonometric functions both in a mathematical
context and in a real world problem context 

C.7.3  Area & the
Definite Integral 
1. Determine methods for
approximating the area under a given function 2. Summarize the process of
estimating the area under a curve by the use of the definite integral 
1. Use a varying number of
rectangles constructed at various ÒendpointsÓ (i.e. left endpoint, right
endpoint, midpoints) to approximate total area under a curve 2. Use a varying number of
trapezoids to approximate total area under a curve 3. Understand that the definite
integral is simply the sum of an infinite number of rectangles 4. Understand that a
definite integral can represent (i) area under a
curve, (ii) total change in the function 5. Apply definite integrals
to a real world problems 
C.7.4  The Fundamental
Theorem of Calculus 
1. Understand that the
connection between antiderivatives and definite
integrals is summarized by the Fundamental Theorem of Calculus 
1. Calculate simple
definite integrals using the FTC 2. Calculate definite
integrals using the properties of definite integrals 3. Determine total areas
under curves using the FTC 4. Differentiate integral
functions with variable (i) upper limits of
integration and (ii) lower limits of integration 5. Apply definite integrals
to a real world problems 
C.7.5  The Area Between
Two Curves 
1. Given two functions,
determine the area between the two functions using definite integrals 2. Apply definite integrals
and area between curves to a real world problems 

C.7.6  Numerical
Integration 
1. Use numerical methods
like the trapezoidal rule and SimpsonÕs rule to estimate integrals 2. Understand when
numerical methods of integration are more useful than algebraic methods 3. Apply definite integrals
to a real world problems 



C.8.1  Integration by
parts 
1. Use the method of
integration by parts to integrate simple power, exponential, and
trigonometric functions both in a mathematical context and in a real world
problem context 

C.8.2  Volume 
1. Determine the volume of revolution
of an object rotated about the xaxis 2. Determine by slicing (disk and washer method) or cylindrical shells
to calculate volumes of solids 3. Determine
the average value of a function 4. Apply volumes and
average values to a real world problems 

C.8.4  Improper Integrals 
1. Calculate and interpret
the values of improper integrals 2. Apply improper integrals
to a real world problems 



C.9.1  Differential
Equations 
1. Solve differential equations
with and without initial conditions in a variety of real world applications 

C.9.2 Ð Slope Fields 
1. Sketch a slope field for
a given differential equation and use the given boundary conditions to identify
a specific solution curve on their slope field. 2. Provide a geometric
interpretation of differential equations using slope fields. 3. Explain the relationship
between slope fields and solution curves for differential equations. 

C.9.3  Exponential Growth
and Decay 
1. Solve problems involving
exponential decay in a variety of application (Radioactivity, Air resistance
is proportional to velocity, Continuously compounding interest, Population
growth) 

C.9.4  Populations 
1. Solve problems involving
population growth using exponential modeling and the logistic equation 