School City of Hobart Mathematics The ISTEP+ assessment measures the academic performance of students in Mathematics. IN: Precalculus The Indiana Academic Standards for Mathematics include standards for students in Precalculus. |
Algebraic Concepts |
The Algebraic Concepts Unit includes Competencies/Objectives which focus on algebraic equations and operations. Students explore the symbolic nature of algebraic concepts by identifying and extending patterns in algebra, by following algebraic procedures, and by proving theorems with properties. |
Equations: Comprehend/Logic
The learner will be able to comprehend that the logic of finding the solutions to equations begins with the assumption that the variable is a number that satisfies the equation, and that the process used when solving equations generates new equations that usually have the same solution set as the original, and understand that similar logic applies to obtaining solutions to systems of equations simultaneously.
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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. |
Conic Sections: Write/Graphs
The learner will be able to write the equations of conic sections in standard form to determine the type of conic sections and to determine its geometric properties.
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Conic Sections: Study/Graph
The learner will be able to study and create graphs of circles, ellipses, parabolas, and hyperbolas.
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Complex Numbers: Define
The learner will be able to express a definition of complex numbers.
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Complex Numbers: DeMoivre's/Explain
The learner will be able to explain DeMoivre's theorem.
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Complex Numbers in Trigonometric Form
The learner will be able to show complex numbers in trigonometric form.
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Complex Numbers in Trigonometric Form
The learner will be able to perform the multiplication of complex numbers in trigonometric form.
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DeMoivre's Theorem: Apply
The learner will be able to use DeMoivre's Theorem.
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Complex Numbers: DeMoivre's/Prove
The learner will be able to prove DeMoivre's theorem.
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Limits: Limit Concept
The learner will be able to understand the concept of a limit.
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Problem Solving: Mathematical Induction
The learner will be able to apply the concept of Mathematical Induction as a means of mathematical proof.
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Data Interpretation |
The Data Interpretation Unit includes Competencies/Objectives which focus on the study and use of graphical forms. Students collect and classify data, organize and display data, use logical reasoning, and problem solving. |
Graphs: Create/Analyze
The learner will be able to create and analyze graphs.
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Functions |
The Functions Unit includes Competencies/Objectives which focus on exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions. |
Functions: Linear/Nonlinear
The learner will be able to use linear and nonlinear functions to model data.
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Exponential/Logarithmic Functions
The learner will be able to determine the domain, range, intercepts, and asymptotes of logarithmic and exponential functions.
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Logarithmic/Exponential Function: Define
The learner will be able to define, determine, and check the inverse functions of logarithmic and exponential functions.
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Graphing: Comprehend/Draw
The learner will be able to comprehend curves defined parametrically and create drawings of their graphs.
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Problem Solving: Model/Solve
The learner will be able to use functions and equations to model and obtain solutions to word problems.
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Functions: Determine/Domain/Range
The learner will be able to determine the domain, range, intercepts, zeros, poles, asymptotes, and points of discontinuity of functions, using paper and pencil techniques and graphing calculators.
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Functions: Determine/Illustrate
The learner will be able to determine a quadratic, exponential, logarithmic, power, or sinusoidal function to illustrate a set of data and describe the parameters of the model.
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Functions: Identify/Graph
The learner will be able to identify and create graphs of different types of functions including polynomial, rational, algebraic, and absolute value using paper and pencil techniques and graphing calculators.
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Functions: Apply/Write
The learner will be able to write functions applying polynomial, rational, and algebraic functions, and draw graphs to obtain solutions to word problems, to determine composite and inverse functions, and to study functions and graphs.
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Inverses: Define
The learner will be able to define the inverse of a function.
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Inverses: Finding
The learner will be able to find the inverse of a given function.
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Inverse Functions: Check
The learner will be able to check the inverse of a function.
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Exponential Functions: Word Problems
The learner will be able to obtain solutions to word problems involving exponential functions.
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Logarithmic Functions: Word Problems
The learner will be able to obtain solutions to word problems involving logarithmic functions.
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Exponential/Logarithmic Functions: Graph
The learner will be able to graph both exponential and logarithmic functions.
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Exponential/Logarithmic: Graph/Analyze
The learner will be able to analyze the graphs of both exponential and logarithmic functions.
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Trigonometric Functions: Define
The learner will be able to define the six trigonometric functions.
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Trig. Function: Unit Circle
The learner will be able to define the trigonometric functions applying the unit circle.
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Trig. Functions: Inverse/Define
The learner will be able to define the inverse of a trigonometric function.
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Trigonometric Functions: Problem Solving
The learner will be able to obtain solutions to word problems by applying trigonometric functions.
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Trigonometric Functions: Inverse/Value
The learner will be able to find the values of inverse trigonometric functions.
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Trigonometric Functions: Graph/Inverse
The learner will be able to graph the inverse of trigonometric functions.
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Trigonometric Functions: Graphing
The learner will be able to graph trigonometric functions.
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Trig. Functions: Translation/Graph
The learner will be able to graph the translation of a given trigonometric function.
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Trigonometric Functions: Attributes
The learner will be able to determine the following attributes for trigonometric functions: domain, range, period, amplitude, intercepts, and asymptotes.
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Trigonometric Functions: Value
The learner will be able to determine the values of trigonometric functions.
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Trig. Functions: Study/Translation
The learner will be able to study the graphs of the translations of trigonometric functions.
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Graphing: Symmetry/Describe
The learner will be able to describe how the graphs of functions are symmetrical.
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Functions: Odd-Even/Identify
The learner will be able to identify odd and even functions.
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Functions: Apply/Transformations
The learner will be able to apply transformations to functions.
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Functions: Compare
The learner will be able to make a comparison of the relative magnitudes of functions and their rates of change.
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Geometry |
The Geometry Unit includes Competencies/Objectives which focus on exploring geometric concepts from multiple perspectives. Students study properties and construction of figures, proofs and theorems, history of geometry, transformations, logic, and problem solving. |
Inductive Reasoning: Define
The learner will be able to define what is meant by mathematical induction.
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Mathematics Processes |
The Mathematics Processes Unit includes Competencies/Objectives which focus on mathematical connections. Students communicate and model concepts and procedures. |
Reasoning: True/False
The learner will be able to determine if a given algebraic statement is true always, never, or occasionally.
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Math as Reasoning: Create/Evaluate
The learner will be able to create and evaluate mathematical arguments and proofs.
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Modeling: Determine/Linear
The learner will be able to determine linear models applying the median fit and least squares regression methods, and determine which model gives a better fit.
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Numeration |
The Numeration Unit includes Competencies/Objectives which focus on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships. |
Sequences: Comprehend/Apply
The learner will be able to comprehend and apply the concept of limit of a sequence or function as the independent variable approaches infinity or a number.
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Sequences: Define/Recursively
The learner will be able to recursively define sequences.
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Sequences: Convergent/Divergent
The learner will be able to determine whether a given sequence converges or diverges.
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Series: Sum/Infinite Geometric
The learner will be able to determine the sum of an infinite geometric series.
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Series: Prove/Finite/Infinite
The learner will be able to prove the sum formulas for arithmetic series, as well as for finite and infinite geometric series.
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Sequence/Series: Define
The learner will be able to give definitions of both arithmetic and geometric sequences and series.
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Sequence/Series: Apply
The learner will be able to apply both arithmetic and geometric sequences and series.
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Sequence/Series: Problem Solving
The learner will be able to apply sequences and series to obtain solutions to word problems.
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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.). |
Correlation: Coefficient
The learner will be able to evaluate the "best-fit" line using the correlation coefficient and residuals.
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Summation Notation: Comprehend
The learner will be able to comprehend summation notation.
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Summation Notation: Apply
The learner will be able to apply summation notation.
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Correlation: Coefficient/Compute
The learner will be able to compute the correlation coefficient for collected data.
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Correlation: Coefficient/Interpret
The learner will be able to interpret the correlation coefficient for collected data.
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Problem Solving |
The Problem Solving Unit includes Competencies/Objectives which focus on analyzing problems, evaluating solutions, exploring problems, and developing strategies for solving problems. |
Solutions: Evaluate Reasonableness
The learner will be able to evaluate the reasonableness of a given solution within the context of the original problem.
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Strategies: Use
The learner will be able to use a variety of strategies to solve problems.
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Real Numbers and the Coordinate Plane |
The Real Numbers and the Coordinate Plane Unit includes Competencies/Objectives which focus on graphing concepts. Students graph equations and make connections between algebraic concepts and their geometric correspondences. |
Properties: Apply
The learner will be able to apply the properties of number systems as well as the order of operations to justify the process of simplifying functions and obtaining solutions to equations.
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Trigonometry |
The Trigonometry Unit includes Competencies/Objectives which focus on trigonometric concepts. Students study triangles, trigonometric ratios, and triangle measurements; apply triangle properties; and solve right triangle problems. |
Trigonometric Ratios: Sine/Cosine
The learner will be able to know the exact sine, cosine and tangent values for 0, pi/6, pi/4, pi/3, and pi/2 and multiples of pi, and apply those values to determine other trigonometric values.
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Connecting: Functions/Polar/Complex
The learner will be able to define polar coordinates and complex numbers and comprehend the relationship with trigonometric functions.
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Connecting: Triangle/Trig./Circular
The learner will be able to make connections between concepts of ratios within right triangles, the trigonometric functions, and circular functions.
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Trigonometric Identities
The learner will be able to comprehend and apply formulas for double angles and half angles for sines, cosines, and tangents.
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Trig. Ratios: Sine/Cosine/Tangent
The learner will be able to comprehend the addition formulas for sines, cosines, and tangents.
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Trig. Ratios: Apply/Addition/Formulas
The learner will be able to apply the addition formulas for sines, cosines, and tangents.
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Trigonometric Ratios: Apply
The learner will be able to apply the laws of sines and cosines.
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Trig. Ratios: Law of Sines/Cosines
The learner will be able to use the Law of Sines and Cosines to solve problems.
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Triangles: Determine/Area
The learner will be able to determine the area of a triangle knowing the two sides and the included angle.
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Triangles: Word Problems
The learner will be able to obtain solutions to word problems involving triangle trigonometry.
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Triangles: Oblique/Problem Solve
The learner will be able to obtain solutions to word problems using oblique triangles.
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Trigonometric Identities: Knowledge
The learner will be able to know the following trig identity: cosine squared + sine squared = 1.
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Trig. Identities: Apply
The learner will be able to apply basic trigonometric identities to simplify expressions.
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Trig. Identities: Apply
The learner will be able to apply basic trigonometric identities to verify other identities.
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Trig. Identities: Verifying
The learner will be able to verify the trigonometric identities.
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Trigonometric Identities: Proving
The learner will be able to prove that the identity cos(x) squared + sine(x) squared = 1 is equivalent to the Pythagorean Theorem.
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Trig. Equations: Solving
The learner will be able to calculate solutions for trigonometric equations.
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Trigonometric Equations: Problem Solving
The learner will be able to apply trigonometric equations and/or inequalities in obtaining word problem solutions.
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Angles: Degrees/Radians
The learner will be able to apply degrees and radians.
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Angle Measures: Degree/Radian
The learner will be able to convert angle measures between degrees and radians.
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Polar Coordinates: Define
The learner will be able to give a definition of polar coordinates.
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Polar Equations: Graph
The learner will be able to create graphs of equations in the polar coordinate plane.
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Polar Forms/Equations: Represent
The learner will be able to display equations given in rectangular coordinates in the context of polar coordinates.
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Polar Form: Relate/Cartesian
The learner will be able to make the connection between polar coordinates and Cartesian coordinates.
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Trigonometric Concepts: Tangent/Slope
The learner will be able to understand that the tangent of the angle by a line intersecting the x-axis is the same as the slope of that line.
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Right Triangles: Trigonometric Functions
The learner will be able to use right triangles to define trigonometric functions.
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Right Triangles: Solve/Word Problems
The learner will be able to obtain solutions to word problems using right triangles.
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Unit Circle: Apply/Concept
The learner will be able to apply the concept of unit circle to define sine and cosine.
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