Grade: 12th Grade
Course: Calculus
Discipline: Math
Additional Course Information:
Course Description
1 credit. Elective. Weighted
Objectives:
Unit
A1
Local Objective
C-A1 Use and solve equivalent forms of equations and inequalities.
Unit
A2
Local Objective
C-A2 Perform simple transformations and their compositions on linear and quadratic functions.
Unit
A3
Local Objective
C-A3 Understand and compare the properties of exponential, polynomial, and rational functions.
Unit
A4
Local Objective
C-A4 Construct visual models to represent and solve problems.
Unit
A5
Local Objective
C-A5 Use trigonometric relationships to determine angle measures, graphs, and information in triangles.
Unit
B1
Local Objective
C-B1 Determine the limit of variable expressions using algebraic simplification processes or graphs.
Unit
B2
Local Objective
C-B2 Use a chart or table to determine the limit of an expression.
Unit
B3
Local Objective
C-B3 Interpret symbolic notation referring to limits.
Unit
B4
Local Objective
C-B4 Determine where problems may exist when trying to find a limit.
Unit
B5
Local Objective
C-B5 Given variable expressions, determine where vertical asymptotes are located on a graph. Technology Standard III.1. Use
content-specific technological tools and resources to manage data and produce a product or system.
Unit
C1
Local Objective
C-C1 Demonstrate and use concepts about derivatives and differentiability.
Unit
C2
Local Objective
C-C2 Calculate derivatives using the limit formula.
Unit
C3
Local Objective
C-C3 Graph functions and determine differentiability.
Unit
C4
Local Objective
C-C4 Calculate the derivative and find the equation of the tangent line at a specific point.
Unit
D1
Local Objective
C-D1 Demonstrate and use concepts regarding differentiation rules and rules for trigonometric functions.
Unit
D2
Local Objective
C-D2 Determine the derivative using the power rule, the product rule, or the chain rule.
Unit
D3
Local Objective
C-D3 Determine the derivative, the slope of the function at the given point, and the equation of the tangent line at the same point.
Unit
E1
Local Objective
C-E1 Differentiate implicitly.
Unit
E2
Local Objective
C-E2 Compare and contrast implicit and explicit differentiation by finding the derivative of a problem each way.
Unit
E3
Local Objective
C-E3 Determine the first and second derivative of an equation.
Unit
E4
Local Objective
C-E4 Find dy/dx by using implicit differentiation. Then find the slope of the derivative, the equation of the tangent line, and the
equation of the normal line.
Unit
E5
Local Objective
C-E5 Solve using related rates.
Unit
F1
Local Objective
C-F1 Demonstrate and use concepts using terminology relating to mathematical theorems.
Unit
F2
Local Objective
C-F2 Evaluate the derivative of a function and find the critical numbers.
Unit
F3
Local Objective
C-F3 Evaluate the derivative of a function, find the critical numbers, and determine the extrema on an interval.
Unit
F4
Local Objective
C-F4 Use Rolle’s Theorem to determine critical numbers in an interval.
Unit
F5
Local Objective
C-F5 Use the Mean Value Theorem to determine critical numbers in an interval.
Unit
G1
Local Objective
C-G1 Demonstrate and use knowledge about the first and second derivative of a function.
Unit
G2
Local Objective
C-G2 Determine the critical numbers of a function and determine if and when a function is increasing or decreasing on an open
interval. Technology Standard III.1. Use content-specific technological tools and resources to manage data and produce a product or
system.
Unit
G3
Local Objective
C-G3 Evaluate the derivative and find all relative extrema of a function on an open interval. Technology Standard III.1. Use contentspecific technological tools and resources to manage data and produce a product or system.
Unit
H1
Local Objective
C-H1 Demonstrate knowledge and use information relating to integration.
Unit
H2
Local Objective
C-H2 Evaluate trigonometric integrals and polynomial integrals at a specific location.
Unit
H3
Local Objective
C-H3 Use sigma notation properties to simplify problems.
Unit
H4
Local Objective
C-H4 Use properties of sigma notation to approximate the area under a curve in a set interval. Technology Standard III.1. Use contentspecific technological tools and resources to manage data and produce a product or system.
Unit
I1
Local Objective
C-I1 Apply properties to evaluate definite integrals.
Unit
I2
Local Objective
C-I2 Integrate and evaluate definite integrals.
Unit
J1
Local Objective
C-J1 Integrate indefinite integrals and integrate and evaluate definite integrals.
Unit
K1
Local Objective
C-K1 Apply the properties of u-substitution to find derivatives of logarithms.
Unit
K2
Local Objective
C-K2 Apply the properties of u-substitution to integrate and evaluate logarithms.