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# Course at a Glance AP Calculus

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```Course at
a Glance
UNIT
Limits and
Continuity
1
AP EXAM
WEIGHTING
CLASS PERIODS
Plan
CHA
1.1
2
LIM
~22–23 AB ~13–14 BC
CLASS PERIODS
Introducing Calculus:
Can Change Occur at
an Instant?
1.3
Estimating Limit
Values from Graphs
4
1.4
Estimating Limit
1.5
Determining Limits
Properties of Limits
1.6
1.7
Selecting Procedures
for Determining Limits
1.8
Determining Limits
Using the Squeeze
Theorem
1
LIM
Teach
3
MATHEMATICAL PRACTICES
LIM
Mathematical practices spiral throughout
1.9
2
1
2
Implementing
Mathematical
Processes
3
4
LIM
Communication
and Notation
Connecting
Representations
LIM
LIM
Discontinuities
Change
LIM
Limits
FUN
Analysis of
Functions
LIM
BC ONLY
LIM
3
and Continuity:
Determining When
Derivatives Do and
2.5
Applying the Power
Rule
FUN
2.6
Derivative Rules:
Constant, Sum,
1
Constant Multiple
FUN
2.7
Derivatives of cos x,
sin x, ex, and ln x
2.8
The Product Rule
2.9
The Quotient Rule
LIM
FUN
over an Interval
FUN
1.13
Removing
Discontinuities
1.14
1
2.10
Finding the Derivatives
of Tangent, Cotangent,
Secant, and/or
Cosecant Functions
Limits and Vertical
Asymptotes
1.15
2
FUN
Connecting
1
1.12
3
Assess
2.4
1
FUN
1
LIM
Estimating Derivatives
of a Function at a Point
1
1.11
1
2.3
1
3
BIG IDEAS
CHA
Connecting Multiple
Representations
1.10
3
of a Function and
Using Derivative
Notation
3
FUN
~9–10 BC
2.2
Determining Limits
Manipulation
~13–14 AB
4–7% BC
Instantaneous Rates of
Change at a Point
1
FUN
1
LIM
CHA
10–12% AB
2.1
2
1
1
LIM
CHA
CHA
2
LIM
Basic Derivative
Rules
AP EXAM
WEIGHTING
Using Limit Notation
2
LIM
2
4–7% BC
1.2
2
LIM
10–12% AB
UNIT
Connecting Limits at
Asymptotes
1.16
Working with the
Intermediate Value
Theorem (IVT)
Personal Progress Check 1
Personal Progress Check 2
Multiple-choice: ~45 questions
Multiple-choice: ~30 questions
Free-response: 3 questions (partial)
Free-response: 3 questions (partial)
NOTE:
Composite,
Implicit, and
Inverse Functions
UNIT
3
AP EXAM
WEIGHTING
CLASS PERIODS
FUN
3.1
9–13% AB
~10–11 AB
4
4–7% BC
~8–9 BC
The Chain Rule
1
FUN
UNIT
AP EXAM
WEIGHTING
CLASS PERIODS
CHA
4.1
1
CHA
3.2
4.2
1
1
FUN
3.3
Functions
3
FUN
Inverse Trigonometric
Functions
FUN
3.5
1
Selecting Procedures
for Calculating
Derivatives
~10–11 AB
6–9% BC
~6–7 BC
Interpreting the
Meaning of the
Straight-Line
Motion: Connecting
Position, Velocity, and
Acceleration
Rates of Change in
1
3.6
Order Derivatives
AP EXAM
WEIGHTING
15–18% AB 8–11% BC
CLASS PERIODS
~15–16 AB ~10–11 BC
FUN
FUN
4.4
1
CHA
4.5
Introduction to Related
Rates
Solving Related Rates
CHA
3
5.3
Determining Intervals
on Which a Function Is
Increasing or Decreasing
5.4
Using the First
Derivative Test to
Determine Relative
5.5
Using the Candidates
Test to Determine
5.6
Determining Concavity
of Functions over Their
Domains
5.7
Using the Second
Derivative Test to
5.8
Sketching Graphs of
Functions and Their
Derivatives
5.9
Connecting a Function,
Its First Derivative, and
Its Second Derivative
3
1
4.6
of a Function Using
Local Linearity and
Linearization
1
LIM
Points
2
FUN
Using the Mean Value
Theorem
5.2
3
FUN
CHA
5.1
3
Than Motion
3
FUN
5
FUN
4.3
2
3.4
1
CHA
10–15% AB
Analytical
Applications of
UNIT
Applications of
4.7
FUN
2
FUN
for Determining Limits
of Indeterminate Forms
3
FUN
2
FUN
2
FUN
5.10
Introduction to
5.11
Solving Optimization
2
FUN
3
FUN
1
5.12
Implicit Relations
3
Personal Progress Check 3
Personal Progress Check 4
Personal Progress Check 5
Multiple-choice: ~15 questions
Free-response: 3 questions
(partial/full)
Multiple-choice: ~15 questions
Free-response: 3 questions
Multiple-choice: ~35 questions
Free-response: 3 questions
Integration and
Accumulation
UNIT
AP EXAM
WEIGHTING
17–20 % AB 17–20 % BC
AP EXAM
WEIGHTING
CLASS PERIODS
~18–20 AB ~15–16 BC
CLASS PERIODS
UNIT
6
CHA
Accumulations of
Change
4
LIM
with Riemann Sums
LIM
6.3
FUN
6.4
FUN
Notation
FUN
1
FUN
6.5
2
FUN
The Fundamental
Theorem of Calculus
and Accumulation
Functions
Interpreting
the Behavior of
Accumulation Functions
Involving Area
6.6
Applying Properties of
6.7
The Fundamental
Theorem of Calculus
7.1
FUN
6.8
~9–10 BC
CLASS PERIODS
Modeling Situations
Verifying Solutions for
7.3
Sketching Slope Fields
CHA
7.4
4
7.6
FUN
Finding General
Solutions Using
Integrals: Basic Rules
and Notation
3
6.9
Integrating Using
Finding Particular
Solutions Using
Initial Conditions and
6.11
1
FUN
Equations
7.9
Logistic Models with
BC ONLY
6.12
CHA
Integrals in Applied
8.4
8.5
6.14
Selecting Techniques
Finding the Area
Between Curves
8.6
Finding the Area
Between Curves That
Intersect at More Than
Two Points
8.7
Volumes with Cross
Sections: Squares and
Rectangles
8.8
Volumes with Cross
Sections: Triangles and
Semicircles
8.9
Volume with Disc
Method: Revolving
Around the x- or y
3
3
CHA
8.10
Volume with Disc
Method: Revolving
8.11
Volume with Washer
Method: Revolving
Around the x- or y
8.12
Volume with Washer
Method: Revolving
8.13
The Arc Length of a
Smooth, Planar Curve
and Distance Traveled
2
CHA
4
CHA
Using Linear Partial
Fractions BC ONLY
Evaluating Improper
Integrals BC ONLY
Finding the Area
Between Curves
Functions of x
2
CHA
Integrating Using
6.13
1
FUN
Integrating Functions
Using Long Division
and Completing the
Square
BC ONLY
1
LIM
Using Accumulation
3
6.10
1
FUN
8.3
1
CHA
7.8
1
FUN
Connecting
Position, Velocity,
and Acceleration
of Functions Using
Integrals
Functions of y
7.7
3
FUN
8.2
4
CHA
~19–20 AB ~13–14 BC
Finding the Average
Value of a Function on
an Interval
3
CHA
Solutions Using Euler’s
Method BC ONLY
1
FUN
Reasoning Using Slope
Fields
7.5
1
FUN
CHA
10–15% AB 6–9% BC
8.1
1
1
2
FUN
CHA
CHA
4
FUN
Finding Antiderivatives
AP EXAM
WEIGHTING
7.2
1
3
~8–9 AB
6–9% BC
Equations
3
FUN
6–12% AB
3
Riemann Sums,
Summation Notation,
2
8
Equations
2
FUN
6.2
1
7
FUN
6.1
Applications
of Integration
UNIT
2
CHA
3
1
BC ONLY
Personal Progress Check 6
Personal Progress Check 7
Personal Progress Check 8
Multiple-choice:
Multiple-choice:
Multiple-choice: ~30 questions
Free-response: 3 questions
Free-response: 3 questions
Free-response: 3 questions
Parametric
Equations, Polar
Coordinates, and
Vector-Valued
Functions BC ONLY
UNIT
9
AP EXAM
WEIGHTING
N/A AB
CLASS PERIODS
N/A AB
CHA
CHA
1
CHA
~10–11 BC
Second Derivatives
of Parametric
Equations
Finding Arc Lengths
of Curves Given
1
9.4
1
FUN
9.5
Integrating VectorValued Functions
9.6
Solving Motion
1
FUN
N/A AB
LIM
Parametric and VectorValued Functions
9.7
Coordinates and
2
10.2
Working with
Geometric Series
10.3
The th Term Test for
Divergence
10.4
Integral Test for
Convergence
3
3
10.5
-Series
3
10.6
Comparison Tests for
Convergence
10.7
Alternating Series Test
for Convergence
10.8
Ratio Test for
Convergence
3
LIM
3
LIM
3
LIM
10.9
or Conditional
Convergence
3
Polar Form
CHA
9.8
Find the Area of a Polar
Region or the Area
3
Polar Curve
CHA
3
9.9
Finding the Area of the
Two Polar Curves
LIM
~17–18 BC
Series
3
LIM
17–18% BC
10.1
3
LIM
Valued Functions
1
FUN
CLASS PERIODS
LIM
Equations
CHA
N/A AB
LIM
9.3
Sequences and
Series BC ONLY
AP EXAM
WEIGHTING
LIM
Parametric Equations
9.2
10
11–12% BC
9.1
2
UNIT
10.10
Alternating Series
Error Bound
10.11
3
Finding Taylor
Polynomial
2
of Functions
1
LIM
LIM
10.12
Lagrange Error Bound
10.13
Radius and Interval
of Convergence of
Power Series
10.14
Finding Taylor or
Maclaurin Series for
a Function
10.15
Representing
Functions as
Power Series
1
LIM
2
LIM
2
LIM
3
Personal Progress Check 9
Personal Progress Check 10
Multiple-choice: ~25 questions
Free-response: 3 questions
Multiple-choice: ~45 questions
Free-response: 3 questions
```