Chetek-Weyerhaeuser High School
AP Calculus Units and Learning Targets
AP Calculus A
Unit 1 Prerequisites for Calculus (11 days + 1 summative test day)
Essential Question:
Without a complete understanding of algebra and advanced math
(trigonometry and pre-calculus) is it possible to understand calculus?
Learning Targets
1. Students will apply the point-slope, slope-intercept, and general equations of lines to graph
and write equations for linear functions
2. Students will be able to define functions as even or odd based on their equation or graph.
3. Students will understand the exponent rules to graph, write equations for, and solve
exponential equations.
4. Students will find the inverse of a function, determine whether it is one-to-one and apply
inverse properties and logarithms.
5. Students will predict graphs of trigonometric functions, and correctly state the value of sine,
cosine and tangent of the common angles in both radians and degrees.
Unit 2 Limits and Continuity (13 days + 1 summative test day)
Essential Question:
What is the limit of a function and how can a limit be used to determine
the continuity of a function?
Learning Targets
1. Students will compare the average rate of change of a function over an interval to the
instantaneous rate of change of the function at any point.
2. Students will find limits (general, left-hand, and right-hand) graphically, algebraically, and by
substitution at specific values and as functions approach infinity.
3. Students will locate horizontal and vertical asymptotes of functions by applying the zero
product property and limits for end behavior.
4. Students will classify functions as continuous, as having removable discontinuities, or nonremovable discontinuities.
5. Students will use the four-step process to find the slope of a tangent line through a particular
point on a curve, then using the point-slope formula, write the equation of the line tangent to
the curve at that point.
Unit 3 Simple Derivatives (14 days + 1 summative test day)
Essential Question: What is a derivative and how do they work?
Learning Targets
1.
Mr. Munch
Students will apply the definition of derivative to find the derivative of a function, use the
correct notation to write the derivative, and relate the graphs of derivatives and functions.
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2. Students will compute numerical derivatives on a calculator, recognize when a derivative will
fail to exist, and apply the intermediate value theorem.
3. Students will find derivatives by applying the various rules for derivatives. (constant, power,
constant multiple, sum and difference, product and quotient), and find higher order
derivatives.
4. Students will correlate instantaneous rates of change to velocity and correlate that velocity to
the speed of an object.
5. Students will apply derivatives to economics by finding marginal costs and marginal
revenues of functions.
Unit 4 Advanced Derivatives (15 days + 1 summative test day)
Essential Question:
How can the derivatives of more complex functions (trigonometric,
implicit, powers, exponential and logarithmic) be found?
Learning Targets
1. Students will analyze various trigonometric functions to find the slope of tangent lines at
various points both analytically and numerically.
2. Students will recognize when to use the chain rule or general power rule to find the derivative
of complex algebraic and trigonometric functions.
3. Students will classify functions as explicit or implicit and apply implicit differentiation to
functions needing it.
4. Students will calculate the derivative of exponential and logarithmic functions both
analytically and numerically.
AP Calculus B
Unit 5 Applications of Derivatives (11 days)
Essential Question: How can the derivative be applied to learn more about functions?
Learning Targets
1. The students will locate absolute and local extrema and critical points and apply the extreme
value theorem to find maximum and minimum values of a function over any interval.
2. The students will find critical points of a function.
3. The students will utilize the mean value theorem over any interval in a continuously
differentiable function.
4. The students will analyze the increasing or decreasing nature of a function by examining its
derivative at any point and locate any critical points of the function.
5. The students will use the second derivative test to locate points of inflection and discuss the
concavity of a function.
6. The students will create interval tables using the first and second derivatives to connect the
first and second derivatives to the graph of a function.
Unit 6 Modeling and Rates of Change (14 days)
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Essential Question:
How can calculus find the perfect solution to optimization and related
rates?
Learning Targets
1. The students will predict the minimum and maximum values of functions by finding
horizontal tangent lines and evaluating the shape of the curve at that point.
2. The students will discuss the local linearity of a function and produce a linear model for the
function at that point.
3. The students will generate the rate of change of a function by using differentials.
4. The students will compare the rates of change of two variables in a function with respect to
time.
Unit 7 Areas Under Curves (20 days)
Essential Question:
What is the antiderivative and how can it be used to find the area under
a curve?
Learning Targets
1. The students will use various right, left and mid-point rectangular approximation methods to
estimate the area between the x-axis and a curve.
2. The students will use Simpson’s and Trapezoidal rules both analytically and using computer
technology to find the area between the x-axis and a curve.
3. The students will find the distance traveled by an object by analyzing the area under a
velocity-time graph.
4. The students will use definite integrals and antidifferentiation to find the area between the xaxis and a curve analytically.
5. The students will utilize computer technology to find the area under curves using various
methods.
6. The students will find the average (mean) value of a function over any interval and use the
mean value theorem to locate where the function is at its mean.
7. The students will apply the Fundamental Theorem of calculus.
Unit 8 Differential Equations and Mathematical Models ( 16 days)
Essential Question:
If we know the rate of change of something, how can we find the original
function?
Learning Targets
1. The students will construct a slope field for a given differential equation both by hand and by
using a grapher, then sketch an approximate graph of a function through a given point.
2. The students will use Euler’s Method and local linearity to approximate the value of a
function at a point given its derivative and nearby point.
3. The students will solve initial value and general solution differential equations.
4. The students will evaluate integrals where substitution is necessary.
5. The students will solve a differential equation by separating the variables.
6. The students will use the law of exponential change to solve growth and decay problems.
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