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ENDURING UNDERSTANDING
CHA-3 Derivatives allow us to solve real-world problems involving rates of change.
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Topic Name |
Essential Knowledge |
9.1 Defining and Differentiation Parametric Equations BC ONLY
LEARNING OBJECTIVE CHA-3.G Calculate derivatives of parametric functions. BC ONLY |
CHA-3.G.1 Methods for calculating derivatives of real-valued functions can be extended to parametric functions. BC ONLY |
CHA-3.G.2 For a curve defined parametrically, the value of at a point on the curve is the slope of the line tangent to the curve at that point. the slope of the line tangent to a curve defined using parametric equations, can be determined by dividing by , provided does not equal zero. BC ONLY |
Blog Posts
Implicit Differentiation of Parametric Equations
A Vector’s Derivatives What they mean and how to find them. BC topic.
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9.2 Second Derivatives of Parametric Equations BC ONLY
LEARNING OBJECTIVE CHA-3.G Calculate derivatives of parametric functions. BC ONLY |
CHA-3.G.3 can be calculated by dividing by . BC ONLY |
Blog Posts
Implicit Differentiation of Parametric Equations
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ENDURING UNDERSTANDING
CHA-6 Definite integrals allow us to solve problems involving the accumulation of change in length over an interval.
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9.3 Finding Arc Lengths of Curves Given by Parametric Equations BC ONLY
LEARNING OBJECTIVE CHA-6.B Determine the length of a curve in the plane defined by parametric functions, using a definite integral. BC ONLY |
CHA-6.B.1 The length of a parametrically defined curve can be calculated using a definite integral. BC ONLY |
Blog Posts
none
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ENDURING UNDERSTANDING
CHA-3 Derivatives allow us to solve real-world problems involving rates of change.
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9.4 Defining and Differentiating Vector-Valued Functions BC ONLY
LEARNING OBJECTIVE CHA-3.H Calculate derivatives of vector-valued functions. BC ONLY |
CHA-3.H.1 Methods for calculating derivatives of real-valued functions can be extended to vector-valued functions. BC ONLY |
Blog Posts
Implicit Differentiation of Parametric Equations
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ENDURING UNDERSTANDING
FUN-8 Solving an initial value problem allows us to determine an expression for the position of a particle moving in the plane.
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9.5 Integrating Vector Valued Functions BC ONLY
LEARNING OBJECTIVE FUN-8.A Determine a particular solution given a rate vector and initial conditions. BC ONLY |
FUN-8.A.1 Methods for calculating integrals of real-valued functions can be extended to parametric or vector-valued functions. BC ONLY |
Blog Posts
None
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9.6 Solving Motion Problems Using Parametric and Vector Valued Functions BC ONLY
LEARNING OBJECTIVE FUN-8.B Determine values for positions and rates of change in problems involving planar motion. BC ONLY |
FUN-8.B.1 Derivatives can be used to determine velocity, speed, and acceleration for a particle moving along a curve in the plane defined using parametric or vector-valued functions. BC ONLY |
FUN-8.B.2 For a particle in planar motion over an interval of time, the definite integral of the velocity vector represents the particle’s displacement (net change in position) over the interval of time, from which we might determine its position. The definite integral of speed represents the particle’s total distance traveled over the interval of time. BC ONLY |
Blog Posts
None
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ENDURING UNDERSTANDING
FUN-3 Recognizing opportunities to apply derivative rules can simplify differentiation.
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9.7 Defining Polar Coordinates and Differentiating in Polar Form BC ONLY
LEARNING OBJECTIVE FUN-3.G Calculate derivatives of functions written in polar coordinates. BC ONLY |
FUN-3.G.1 Methods for calculating derivatives of real-valued functions can be extended to functions in polar coordinates. BC ONLY |
FUN-3.G.2 For a curve given by a polar equation , derivatives of r, x, and y with respect to , and first and second derivatives of y with respect to x can provide information about the curve. BC ONLY |
Blog Posts
None
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ENDURING UNDERSTANDING
CHA-5 Definite integrals allow us to solve problems involving the accumulation of change in area or volume over an interval.
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9.8 Finding Area of a Polar Region or the Area Bounded by a Single Polar Curve BC ONLY
LEARNING OBJECTIVE CHA-5.D Calculate areas of regions defined by polar curves using definite integrals. BC ONLY |
CHA-5.D.1 The concept of calculating areas in rectangular coordinates can be extended to polar coordinates. BC ONLY |
Blog Posts
None
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9.9 Finding the Area of the Region Bounded by Two Polar Curves BC ONLY
LEARNING OBJECTIVE CHA-5.D Calculate areas of regions defined by polar curves using definite integrals. BC ONLY |
CHA-5.D.2 Areas of regions bounded by polar curves can be calculated with definite integrals. BC ONLY |
Blog Posts
None
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Review Posts
Type 8: Parametric and Vector Equations (3-30-2018) Review Notes
Type 9: Polar Equation Questions (4-3-2018) Review Notes
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