| OUTCOME/
ESSENTIAL
QUESTION |
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| What
is a limit and why is it important to me? |
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1.
Existance
2. Properties of
3. Evaluating
4. Continuity and One Sided
5. Infinite |
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1.
Visual (1-2-A, 2-3-K, 2-3-A, 3-1-K, 3-1-A)
2. Algebraic and trig knowledge
3. Cancellation and rationalization techniques
4. Open and closed intervals, properties of
continuity
5. Vertical asymptotes |
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Homework
Quizzes
Tests
Board Evaluations |
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| How
is the derivative used in calculus? |
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1.
Tangent Lines
2. Basic Differentiation Rules
3. Rates of Change
4. Product and Quotient Rules-Higher Order
Derivative
5. Chain Rule
6. Implicit Differentiation
7. Related Rates |
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1.
Use def. of tangent line (2-2-K, 2-2-A, 3-2-K,
3-2-A, 3-4-K, 3-4-A)
2. Constant, powers, constant multiple, sum and
difference
3. Recognition of product and quotient and applying
the formula
4. Simplification of derivatives and trig
identifications
5. Problem solving with related rates |
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Homework
Quizzes
Tests
Board Evaluations |
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| What
are the techniques for graphing used in calculus? |
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1.
Identifying Extrema
2. Rolle's Theorem
3. Mean Value Theorem
4. Increasing functions
5. Decreasing functions
6. 1st Derivative Test |
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1.
Relative extrema, critical numbers, finding extrema
on closed intervals (2-3-K, 2-3-A, 2-4-K, 2-4-A)
2. Evaluating formulas
3. Finding the where a function will increase and
decrease
4. Graphing function |
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Homework
Quizzes
Tests
Board Evaluations |
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| What
does the graph of functions tell us? |
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1.
Concavity
2. Limits at infinity
3. Summary of graphs |
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1.
2nd derivative test, finding points of inflection
(2-3-K, 2-3-A, 2-4-K, 2-4-A)
2. Horizontal asymptotes
3. Summarizing all of the graphing techniques
learned since November |
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Homework
Quizzes
Tests
Board Evaluations |
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| How
are the problem solving techniques used in calculus? |
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1.
Optimization Problems
2. Newtons Method
3. Differentials
4. Business and Economic Applications |
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1.
Applying derivatives to real life problems 1-3-K,
1-3-A, 2-1-K, 2-1-A)
2. Algebraic solutions of polynomial equations
3. Linear approximations and error propagation
4. Problem solving |
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Homework
Quizzes
Tests
Board Evaluations |
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| What
is the purpose of integral calculus? |
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1.
Anti Derivatives and Indefinite Integration
2. Area of Regions
3. Rermann Sums and Definite Integrals |
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1.
Notation, basic integration rules, initial
conditions (1-4-K, 1-4-A)
2. Sigma notation, upper and lower limits
3. Evaluating integrals |
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Homework
Quizzes
Tests
Board Evaluations |
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| How
is integration and differentiation related? |
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1.
Fundamental Theorem of Calculus
2. Integration by Substitution
3. Numerical Integration |
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1.
Evaluating mean value theorem-average value of a
function, 2nd fundamental theorem of calculus
(3-2-K, 3-2-A)
2. Pattern recognition, change of variables, general
power rule, even and odd functions
3. Trapezoidal rule, Simpsons rule, error |
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Homework
Quizzes
Tests
Board Evaluations |
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| Why
are logarithmic and exponential functions used? |
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1.
Natural Logarithmic, Function and Differentiation,
Integration
2. Inverse Functions
3. Exponential Functions
4. Inverse Trig and Bases Other E |
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1.
Differentiating and integrating ln, e, log functions
(1-4-K, 1-4-A 2-1-A)
2. Existance and derivative of inverse functions
3. Differentiating and integrating exponential
function, bases other than e
4. Derivative other than e and inverse trig |
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Homework
Quizzes
Tests
Board Evaluations |
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| How
can volume and area of similar objects be
calculated? |
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1.
Area of Region Between 2 Curves
2. Volume Disc Method
3. Volume Washer Method |
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1.
Graph lines/use area formulas and integration
(1-4-K, 1-4-A, 2-4-K, 2-4-A, 3-3-K, 3-3-A)
2. Disk and washer method and integration
3. Problem solving methods
4. Application of deff. integrals |
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Homework
Quizzes
Tests
Board Evaluations |
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