School City of Hobart
School City of Hobart Mathematics

Mathematics - IN: Calculus

Mathematics

The ISTEP+ assessment measures the academic performance of students in Mathematics.

The Indiana Academic Standards provide educators and administrators with a complete set of Indiana's K-12 academic standards for Mathematics. Schools should work to align curriculum instruction and classroom assessment with the new standards. While the standards set expectations for student learning they do not prescribe how the standards should be taught.

Teachers should use their skills, experience, talents, and resources to design classroom lessons to meet the individual needs of their students. With these new academic standards in place students in Indiana will be well equipped with the skills and knowledge to prepare them for the future.

IN: Calculus

The Indiana Academic Standards for Mathematics include standards for students in Calculus.


Calculus and Pre-Calculus
The Calculus/Pre-Calculus Unit includes Competencies/Objectives which focus on calculus concepts. Students study limits, matrix algebra, functions, vectors, conic sections, mathematical induction, and sequence and series using graphical calculators, computers, and models.

    Definite Integral: Fundamental Theorems
The learner will be able to apply the Fundamental Theorem of Calculus to evaluate definite and indefinite integrals and to illustrate a specific antiderivative, and complete analytical and graphical analysis of functions so defined.
Strand Bloom's Scope Source
Definite Integral Master IN: Academic Standards, 2000, Calculus, C.4.5
  
    Definite Integral: Rate of Change
The learner will be able to determine the definite integral of the rate of change of a quantity over an interval as the change of the quantity over the interval: the integral from a to b of f'(x)dx = f(b) - f(a).
Strand Bloom's Scope Source
Definite Integral Master IN: Academic Standards, 2000, Calculus, C.4.4
  
    Definite Integral: Riemann Sum
The learner will be able to comprehend and apply Riemann sums, the Trapezoidal Rule, and technology to estimate definite integrals of functions illustrated algebraically, geometrically, and by tables of values.
Strand Bloom's Scope Source
Definite Integral Master IN: Academic Standards, 2000, Calculus, C.4.8
  
    Definite Integral: Riemann Sums
The learner will be able to compute the values of Riemann Sums over equal subdivisions applying left, right, and midpoint evaluation points.
Strand Bloom's Scope Source
Definite Integral Master IN: Academic Standards, 2000, Calculus, C.4.2
  
    Differential Equations: Solve
The learner will be able to obtain solutions to separable differential equations and apply them as models.
Strand Bloom's Scope Source
Differential Equations Master IN: Academic Standards, 2000, Calculus, C.5.2
  
    Integration: Define/Apply
The learner will be able to make definitions of and/or use properties of the definite integral.
Strand Bloom's Scope Source
Integration Master IN: Academic Standards, 2000, Calculus, C.4.6
  
    Integration: Use/Model/Solve
The learner will be able to use integration to model and obtain solutions to problems in other areas outside of mathematics applying the integral as a rate of change to give accumulated change and applying the method of setting up and approximating Riemann Sum and illustrating its limit as a definite integral.
Strand Bloom's Scope Source
Integration Master IN: Academic Standards, 2000, Calculus, C.5.7
  
    Derivatives: Comprehend
The learner will be able to comprehend the idea of the derivative geometrically, numerically, and analytically.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Master IN: Academic Standards, 2000, Calculus, C.2.1
  
    Derivatives: Slope/Tangent
The learner will be able to use derivative concepts in solving for slopes, tangents, maximum and minimum points, and points of inflection.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Master IN: Academic Standards, 2000, Calculus, Standard 3
  
    Intermediate Value Theorem: Comprehend
The learner will be able to comprehend the Intermediate Value Theorem on a function over a closed interval.
Strand Bloom's Scope Source
Applying Calculus Concepts Comprehension Master IN: Academic Standards, 2000, Calculus, C.1.12
  
    Extreme Value Theorem: Comprehend
The learner will be able to comprehend the Extreme Value Theorem.
Strand Bloom's Scope Source
Applying Calculus Concepts Comprehension Master IN: Academic Standards, 2000, Calculus, C.1.13
  
    Intermediate Value Theorem: Apply
The learner will be able to use the Intermediate Value Theorem on a function over a closed interval.
Strand Bloom's Scope Source
Applying Calculus Concepts Application Master IN: Academic Standards, 2000, Calculus, C.1.12
  
    Functions/Relations: Apply
The learner will be able to apply the relation between differentiability and continuity.
Strand Bloom's Scope Source
Applying Calculus Concepts Application Master IN: Academic Standards, 2000, Calculus, C.2.10
  
    Extreme Value Theorem: Application
The learner will be able to apply an understanding of the extreme value theorem.
Strand Bloom's Scope Source
Applying Calculus Concepts Application Master IN: Academic Standards, 2000, Calculus, C.1.13
  
    Curves: Analyze
The learner will be able to study curves, including of monotonicity and concavity.
Strand Bloom's Scope Source
Curve Sketching Analysis Master IN: Academic Standards, 2000, Calculus, C.3.5
  
    Definite Integral: Riemann Sums
The learner will be able to use Riemann Sums to give a definition of integrals.
Strand Bloom's Scope Source
Definite Integral Knowledge Master IN: Academic Standards, 2000, Calculus, Standard 4
  
    Definite Integral: Fundamental Theorems
The learner will be able to understand the fundamental theorems of integral calculus.
Strand Bloom's Scope Source
Definite Integral Comprehension Master IN: Academic Standards, 2000, Calculus, C.4.4
  
    Definite Integral: Properties
The learner will be able to understand the properties of the definite integral.
Strand Bloom's Scope Source
Definite Integral Comprehension Master IN: Academic Standards, 2000, Calculus, C.4.6
  
    Definite Integral: Area
The learner will be able to apply definite integrals to determine areas.
Strand Bloom's Scope Source
Definite Integral Application Master IN: Academic Standards, 2000, Calculus, Standard 5
  
    Definite Integral: Volume
The learner will be able to apply definite integrals to determine volumes.
Strand Bloom's Scope Source
Definite Integral Application Master IN: Academic Standards, 2000, Calculus, Standard 5
  
    Definite Integral: Area Under Curve
The learner will be able to use concepts of the definite integral to calculate the area between a curve and the x-axis.
Strand Bloom's Scope Source
Definite Integral Application Master IN: Academic Standards, 2000, Calculus, C.5.4
  
    Definite Integral: Average Value
The learner will be able to apply definite integrals to determine the average value of a function over a closed interval.
Strand Bloom's Scope Source
Definite Integral Application Master IN: Academic Standards, 2000, Calculus, C.5.5
  
    Definite Integral: Area Between Curves
The learner will be able to use concepts of the definite integral to calculate the area between two given curves.
Strand Bloom's Scope Source
Definite Integral Application Master IN: Academic Standards, 2000, Calculus, C.5.4
  
    Definite Integral: Volume/Known Areas
The learner will be able to use concepts of the definite integral to calculate the volume of a solid of revolution where the cross-sectional area is a known value.
Strand Bloom's Scope Source
Definite Integral Application Master IN: Academic Standards, 2000, Calculus, C.5.6
  
    Definite Integral: Riemann Sums
The learner will be able to interpret the definite integral as a limit of Riemann sums.
Strand Bloom's Scope Source
Definite Integral Analysis Master IN: Academic Standards, 2000, Calculus, C.4.3
  
    Differential Equations: Solve
The learner will be able to obtain solutions to separable differential equations.
Strand Bloom's Scope Source
Differential Equations Application Master IN: Academic Standards, 2000, Calculus, Standard 5
  
    Differential Equation: Solve
The learner will be able to obtain solutions to differential equations of the form y' = ky as applied to growth and decay problems.
Strand Bloom's Scope Source
Differential Equations Application Master IN: Academic Standards, 2000, Calculus, C.5.3
  
    Integration: Comprehend/Substitution
The learner will be able to comprehend integration by substitution to determine values of integrals.
Strand Bloom's Scope Source
Integration Comprehension Master IN: Academic Standards, 2000, Calculus, C.4.7
  
    Integration: Apply/Elementary Properties
The learner will be able to apply elementary properties of integrals.
Strand Bloom's Scope Source
Integration Application Master IN: Academic Standards, 2000, Calculus, Standard 4
  
    Integration: Substitution
The learner will be able to integrate using substitution.
Strand Bloom's Scope Source
Integration Application Master IN: Academic Standards, 2000, Calculus, Standard 4
  
    Integration: Approximation
The learner will be able to determine approximate integrals.
Strand Bloom's Scope Source
Integration Application Master IN: Academic Standards, 2000, Calculus, Standard 4
  
    Integration: Fundamental Theorem
The learner will be able to determine integrals using the Fundamental Theorem of Calculus.
Strand Bloom's Scope Source
Integration Application Master IN: Academic Standards, 2000, Calculus, Standard 4
  
    Integration: Estimate Definite Integrals
The learner will be able to estimate the value of a definite integral using rectangles or trapezoids.
Strand Bloom's Scope Source
Integration Application Master IN: Academic Standards, 2000, Calculus, C.4.1
  
    Integration: Apply/Substitution
The learner will be able to apply integration by substitution to determine values of integrals.
Strand Bloom's Scope Source
Integration Application Master IN: Academic Standards, 2000, Calculus, C.4.7
  
    Derivatives: Apply/Definition
The learner will be able to state the formal definition of a derivative.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Knowledge Master IN: Academic Standards, 2000, Calculus, C.2.2
  
    Derivatives: Mean Value Theorem
The learner will be able to comprehend the Mean Value Theorem.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Comprehension Master IN: Academic Standards, 2000, Calculus, C.2.11
  
    Derivatives: Comprehend
The learner will be able to comprehend the relationship of the concavity of functions and the sign of the second order derivative.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Comprehension Master IN: Academic Standards, 2000, Calculus, C.3.6
  
    Derivatives: Apply/Definition
The learner will be able to use the formal definition of a derivative.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Application Master IN: Academic Standards, 2000, Calculus, C.2.2
  
    Derivatives: Operations
The learner will be able to calculate derivatives of sums, products, and quotients.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Application Master IN: Academic Standards, 2000, Calculus, Standard 2, C.2.4
  
    Derivatives: Higher Order
The learner will be able to calculate higher order derivatives (second derivative, third derivative, etc.).
Strand Bloom's Scope Source
Derivatives/Antiderivatives Application Master IN: Academic Standards, 2000, Calculus, Standard 2, C.2.8
  
    Derivatives: Composite/Chain Rule
The learner will be able to calculate the derivative of composite functions using the chain rule.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Application Master IN: Academic Standards, 2000, Calculus, C.2.5
  
    Derivatives: Logarithmic Differentiation
The learner will be able to calculate derivatives using logarithmic differentiation.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Application Master IN: Academic Standards, 2000, Calculus, Standard 2, C.2.9
  
    Derivative: Slope of a Curve/Point
The learner will be able to determine the slope of a curve at a point, including points at which there are vertical tangents and no tangents.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Application Master IN: Academic Standards, 2000, Calculus, C.3.1
  
    Derivatives: Determine/Tangent
The learner will be able to determine tangent lines to a curve at a point and a local linear approximation.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Application Master IN: Academic Standards, 2000, Calculus, C.3.2
  
    Derivatives: Mean Value Theorem
The learner will be able to use the Mean Value Theorem.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Application Master IN: Academic Standards, 2000, Calculus, Standard 2, C.2.11
  
    Derivatives: Rates of Change
The learner will be able to use derivatives in solving for both instantaneous and average rates of change.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Application Master IN: Academic Standards, 2000, Calculus, C.3.10
  
    Derivatives: Initial Conditions
The learner will be able to apply initial conditions to determine a specific antiderivative.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Application Master IN: Academic Standards, 2000, Calculus, C.5.1
  
    Derivatives: Determine
The learner will be able to determine the derivatives of functions.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Application Master IN: Academic Standards, 2000, Calculus, C.2.3
  
    Derivative: Determine/Composite
The learner will be able to determine the derivatives of composites.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Application Master IN: Academic Standards, 2000, Calculus, Standard 2
  
    Derivatives: Apply/Graphs
The learner will be able to apply first and second derivatives to aid in sketching graphs.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Application Master IN: Academic Standards, 2000, Calculus, C.3.7
  
    Derivatives: Function/Implicitly Defined
The learner will be able to calculate the derivative of implicitly defined functions.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Application Master IN: Academic Standards, 2000, Calculus, C.2.6
  
    Derivatives: Determine
The learner will be able to apply implicit differentiation to determine derivatives of inverse functions.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Application Master IN: Academic Standards, 2000, Calculus, C.3.8
  
    Derivatives: Velocity/Acceleration
The learner will be able to determine both the velocity and acceleration of an object which is traveling in a straight line.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Application Master IN: Academic Standards, 2000, Calculus, C.3.11
  
    Antiderivatives: Distance/Velocity
The learner will be able to use antiderivatives in determining distance and velocity when acceleration and initial conditions are given.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Application Master IN: Academic Standards, 2000, Calculus, C.5.1
  
    Antiderivatives: Determine
The learner will be able to determine specific antiderivatives applying initial conditions including applications to motion along a line.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Application Master IN: Academic Standards, 2000, Calculus, C.5.1
  
    Antiderivatives: Position/Velocity
The learner will be able to use antiderivatives in determining position functions from velocity functions.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Application Master IN: Academic Standards, 2000, Calculus, C.5.1
  
    Derivatives: Compare
The learner will be able to make comparisons of the corresponding attributes of the graphs of f, f', and f".
Strand Bloom's Scope Source
Derivatives/Antiderivatives Analysis Master IN: Academic Standards, 2000, Calculus, C.3.7
  
    Derivatives: Interpret
The learner will be able to interpret the derivative as a rate of change.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Analysis Master IN: Academic Standards, 2000, Calculus, C.2.1
  
    Derivative: Interpret/Rate of Change
The learner will be able to interpret the derivative as a rate of change in different applied contexts including velocity, speed, and acceleration.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Analysis Master IN: Academic Standards, 2000, Calculus, C.3.10
  
    Limits: Limit Concept
The learner will be able to understand the concept of a limit.
Strand Bloom's Scope Source
Limits Comprehension Master IN: Academic Standards, 2000, Calculus, Standard 1, C.1.1
  
    Limits: Infinity
The learner will be able to explain asymptotic behavior in terms of limits involving infinity.
Strand Bloom's Scope Source
Limits Comprehension Master IN: Academic Standards, 2000, Calculus, C.1.7
  
    Limits: Comprehend/Rate of Change
The learner will be able to comprehend instantaneous rate of change as the limit of average rate of change.
Strand Bloom's Scope Source
Limits Comprehension Master IN: Academic Standards, 2000, Calculus, C.3.10
  
    Limits: Substitution
The learner will be able to determine limits using substitution.
Strand Bloom's Scope Source
Limits Application Master IN: Academic Standards, 2000, Calculus, C.1.2
  
    Limits: At Infinity
The learner will be able to determine limits which are set at infinity.
Strand Bloom's Scope Source
Limits Application Master IN: Academic Standards, 2000, Calculus, C.1.6
  
    Limits: Infinite
The learner will be able to determine when the limit of a given expression is infinite.
Strand Bloom's Scope Source
Limits Application Master IN: Academic Standards, 2000, Calculus, C.1.7
  
    Limits: One-Sided
The learner will be able to determine limits which are one-sided.
Strand Bloom's Scope Source
Limits Application Master IN: Academic Standards, 2000, Calculus, C.1.5
  
    Limits: Approximate/Graphs/Tables
The learner will be able to approximate limits from graphs or tables of data.
Strand Bloom's Scope Source
Limits Application Master IN: Academic Standards, 2000, Calculus, C.1.1
  
    Limits: Determine
The learner will be able to determine limits of sums, differences, products, and quotients.
Strand Bloom's Scope Source
Limits Application Master IN: Academic Standards, 2000, Calculus, C.1.3
  
    Differentiation: Comprehend
The learner will be able to comprehend the relationship between differentiability and continuity.
Strand Bloom's Scope Source
Differentiation Comprehension Master IN: Academic Standards, 2000, Calculus, C.2.10
  

Functions
The Functions Unit includes Competencies/Objectives which focus on exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions.

    Inverses: Derivatives
The learner will be able to find the derivative of the inverse of a function.
Strand Bloom's Scope Source
Inverses Application Master IN: Academic Standards, 2000, Calculus, Standard 2, C.2.7
  
    Limits: Identify/Special Limits
The learner will be able to identify the limit of special functions.
Strand Bloom's Scope Source
Limits Knowledge Master IN: Academic Standards, 2000, Calculus, C.1.8
  
    Limits: Continuity
The learner will be able to illustrate a comprehension of continuity in terms of limits.
Strand Bloom's Scope Source
Limits Comprehension Master IN: Academic Standards, 2000, Calculus, C.1.9
  
    Limits: Determine/Functions
The learner will be able to determine limits of functions at points and at infinity.
Strand Bloom's Scope Source
Limits Application Master IN: Academic Standards, 2000, Calculus, Standard 1
  
    Limits: Rational Function/Indeterminant
The learner will be able to determine the limit of a rational function which is in indeterminant form.
Strand Bloom's Scope Source
Limits Application Master IN: Academic Standards, 2000, Calculus, C.1.4
  
    Functions: Derivative/Definition
The learner will be able to demonstrate an understanding of the definitions of the derivative of a function.
Strand Bloom's Scope Source
Calculus with Functions Comprehension Master IN: Academic Standards, 2000, Calculus, C.2.2
  
    Functions: Comprehend
The learner will be able to comprehend the relationship between the increasing and decreasing behavior of functions and the sign of the first order derivative.
Strand Bloom's Scope Source
Calculus with Functions Comprehension Master IN: Academic Standards, 2000, Calculus, C.3.3
  
    Functions: Comprehend/Point/Inflection
The learner will be able to comprehend that points of inflection are places where concavity changes.
Strand Bloom's Scope Source
Calculus with Functions Comprehension Master IN: Academic Standards, 2000, Calculus, C.3.6
  
    Functions: Derivative/Types
The learner will be able to find derivatives of the following types of functions: logarithmic, exponential, trigonometric, and algebraic.
Strand Bloom's Scope Source
Calculus with Functions Application Master IN: Academic Standards, 2000, Calculus, Standard 2, C.2.3
  
    Functions: Determine/Maxima/Minima
The learner will be able to determine local and absolute maximum and minimum points.
Strand Bloom's Scope Source
Calculus with Functions Application Master IN: Academic Standards, 2000, Calculus, C.3.4
  
    Functions: Determine/Position
The learner will be able to determine position functions from their derivatives.
Strand Bloom's Scope Source
Calculus with Functions Application Master IN: Academic Standards, 2000, Calculus, Standard 5
  
    Functions: Determine/Velocity
The learner will be able to determine velocity functions from their derivatives.
Strand Bloom's Scope Source
Calculus with Functions Application Master IN: Academic Standards, 2000, Calculus, Standard 5
  
    Functions: Apply/Continuity
The learner will be able to apply continuity theorems.
Strand Bloom's Scope Source
Calculus with Functions Application Master IN: Academic Standards, 2000, Calculus, Standard 1
  
    Functions: Continuous
The learner will be able to identify whether a given function is continuous.
Strand Bloom's Scope Source
Functions Knowledge Master IN: Academic Standards, 2000, Calculus, Standard 1
  
    Functions: Increasing/Decreasing
The learner will be able to identify where a function is increasing and where it is decreasing.
Strand Bloom's Scope Source
Functions Knowledge Master IN: Academic Standards, 2000, Calculus, C.3.3
  
    Functions: Continuous at a Point
The learner will be able to find whether a given function is continuous at a point.
Strand Bloom's Scope Source
Functions Application Master IN: Academic Standards, 2000, Calculus, C.1.10
  
    Functions: Points of Inflection
The learner will be able to determine the points of inflection of functions.
Strand Bloom's Scope Source
Functions Application Master IN: Academic Standards, 2000, Calculus, C.3.6
  
    Functions: Discontinuity Types/Classify
The learner will be able to classify types of discontinuities of functions.
Strand Bloom's Scope Source
Functions Analysis Master IN: Academic Standards, 2000, Calculus, C.1.11
  

Mathematics Processes
The Mathematics Processes Unit includes Competencies/Objectives which focus on mathematical connections. Students communicate and model concepts and procedures.

    Modeling: Rate of Change
The learner will be able to create models of rates of change, including associated rates problems.
Strand Bloom's Scope Source
Mathematical Modeling Master IN: Academic Standards, 2000, Calculus, C.3.12
  

Measurement
The Measurement Unit includes Competencies/Objectives which focus on measurement concepts, applications, and analysis. Students study length, area, circumference, perimeter, volume, weight, formulas, distance, calendar, money, tools, accuracy, units, constructions, patterns, and problem solving.

    Measurement Concepts: Rate of Change
The learner will be able to use the concept of rate of change.
Strand Bloom's Scope Source
Measurement Concepts Application Master IN: Academic Standards, 2000, Calculus, Standard 3
  

Probability/Statistics
The Probability/Statistics Unit includes Competencies/Objectives which focus on data analysis and probability concepts. Students collect, analyze, and make sense of real world data (including overlapping data, inconclusive data, etc.).

    Optimization Problems
The learner will be able to solve optimization problems.
Strand Bloom's Scope Source
Correlation/Deviation/Variance Application Master IN: Academic Standards, 2000, Calculus, Standard 3, C.3.9
  

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