Important Terms and Concepts
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Learning OutcomesIn this chapter, students will...
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Chapter 1 Sections
1-1 The Concept of Instantaneous Rate
Objective: Given the equation for a function relating two variables, estimate the instantaneous rate of change of the dependent variable with respect to the independent variable at a given point.
Aligned Instructional Resources: Newton, Leibniz, and Usain Bolt Video
Homework: Problems 1, 2
Objective: Given the equation for a function relating two variables, estimate the instantaneous rate of change of the dependent variable with respect to the independent variable at a given point.
Aligned Instructional Resources: Newton, Leibniz, and Usain Bolt Video
Homework: Problems 1, 2
1-2 Rate of Change by Equation, Graph, or Table
Objective: Given a function y = ƒ(x) specified by a graph, by a table of values, or by an equation, describe whether the y-value is increasing or decreasing as x increases through a particular value, and estimate the instantaneous rate of change of y at that value of x.
Aligned Instructional Resources: Interactive Flash "Practice Sketching Derivatives" Demonstration
Homework: Q Problems 1-10, Problems 1-9 odd, 13, 16 (not part d), 18, 20-28 even
Objective: Given a function y = ƒ(x) specified by a graph, by a table of values, or by an equation, describe whether the y-value is increasing or decreasing as x increases through a particular value, and estimate the instantaneous rate of change of y at that value of x.
Aligned Instructional Resources: Interactive Flash "Practice Sketching Derivatives" Demonstration
Homework: Q Problems 1-10, Problems 1-9 odd, 13, 16 (not part d), 18, 20-28 even
1-3 One Type of Integral of a Function
Objective: Given the equation or the graph of a function, estimate on a graph, the definite integral of the function between x = a and x = b by counting squares.
Aligned Instructional Resources: Interactive Flash "The Definite Integral in Terms of Areas" Demonstration
Homework: Q Problems 1-10, Problems 5, 6, 7, 8, 11
Objective: Given the equation or the graph of a function, estimate on a graph, the definite integral of the function between x = a and x = b by counting squares.
Aligned Instructional Resources: Interactive Flash "The Definite Integral in Terms of Areas" Demonstration
Homework: Q Problems 1-10, Problems 5, 6, 7, 8, 11
1-4 Definite Integrals by Trapezoids, from Equations, and Data
Objective: Estimate the value of a definite integral by dividing the region under a graph into trapezoids.
Aligned Instructional Resources: Area of a trapezoid Video
Homework Day 1: Q Problems 1-10, Problems 1, 2, 10
Homework Day 2: Problems 3, 4, 7-13
Objective: Estimate the value of a definite integral by dividing the region under a graph into trapezoids.
Aligned Instructional Resources: Area of a trapezoid Video
Homework Day 1: Q Problems 1-10, Problems 1, 2, 10
Homework Day 2: Problems 3, 4, 7-13
