Units 5 - Differential Calculus
Statement of Inquiry
Calculus describes rates of change between two variables. Understanding these rates of change allows us to model, interpret, and analyze real-world problems and situations. Calculus helps us understand the behavior of functions and allows us to interpret the features of graphs.
Concepts
Change,
Relationships
Change: a variation in size, amount or behavior. READ MORE >
Relationships: the connections and associations between properties, objects, people, and ideas -- including the human community's connections with the world in which we live. READ MORE >
Learning Topics
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Limit of a function at a point
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Derivative function as the gradient
of a curve, and as a rate of change -
The power rule for differentiating
polynomial functions -
Tangents and normals to curves
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Differentiation rules: chain, product, quotient
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Maxima, minima, and points of inflexion
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Kinematics problems
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Optimization
Prior Learning Support
Prior Learning 1 - Finding Gradients of Lines
Prior Learning 2 - Graphing Functions
Prior Learning 3 - Sequences
Course Syllabus Topics
Conceptual Understandings
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The derivative may be represented physically as a rate of change and geometrically as the gradient or slope function
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Examining rates of change close to turning points helps you identify intervals where the function increases/decreases, and identify concavity of the function
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Mathematical modeling can provide effective solutions to real-life problems in optimization by maximising or minimising a quantity, such as cost or profit
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Derivatives and integrals describe real-world kinematics problems in two and three dimensional space by examining displacement, velocity, and acceleration
Unit Discussion
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Further Conceptual Understandings
Lesson 1:
Limits
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Lesson 2:
Basic Derivative
Rules
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Lesson 3:
Tangent and
Normal Lines
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Lesson 4:
The Chain Rule
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Lesson 5:
Product and
Quotient Rules
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Lesson 6:
First Derivative
Test
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Lesson 7:
Graphing
Derivatives
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Lesson 8:
Second Derivative Test & Concavity
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Lesson 9:
Optimization
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Lesson 10:
Kinematics
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Lesson 11:
Unit Review
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Learn
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