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Introduction
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© 2004 by Bloomsburg Area School District and Scantron Corporation.
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Bloomsburg Area School District
Math 9-12 10/22/04
Mathematics - Pre-Calculus Honors

Algebraic Concepts
Operations: Apply
The learner will be able to apply operations such as opposite, reciprocal, absolute value, raising to a power, finding roots, and finding logarithms.
Strand Scope Source
Operations Master PA: Academic Standards, January 16, 1999, Grade 11, p.2,2.1.11.A
  
Algebraic Concepts: Problem Scenarios
The learner will be able to create expressions, equations, inequalities, systems of equations and inequalities, and matrices to represent routine and non-routine problem scenarios.
Strand Scope Source
Algebraic Concepts Master PA: Academic Standards, January 16, 1999, Grade 11, p.13,2.8.11.D
  
Algebraic Concepts: Relationship
The learner will be able to show the relationship between algebraic equations and inequalities and the geometry of relations in the coordinate plane.
Strand Scope Source
Algebraic Concepts Master PA: Academic Standards, January 16, 1999, Grade 11, p.14,2.8.11.J
  
Patterns: Analyze
The learner will be able to study a given set of data for the existence of a pattern and illustrate the pattern algebraically and graphically.
Strand Scope Source
Equality/Inequality Master PA: Academic Standards, January 16, 1999, Grade 11, p.13,2.8.11.A
  
Computation: Develop/Apply
The learner will be able to develop and apply computation ideas, operations and procedures with real numbers in problem solving situations.
Strand Scope Source
Computation Master PA: Academic Standards, January 16, 1999, Grade 11, p.4,2.2.11.A
  
Linear System of Equations: Solve
The learner will be able to calculate solutions to systems of linear equations.
Strand Scope Source
Linear Systems of Equations Reinforce PA: System of School Assessment, 1997, Grade 11, p.12,#5 week tested: 32.
  
Linear Equations: Solve
The learner will be able to obtain solutions to linear equations.
Strand Scope Source
Linear Equations Master PA: Academic Standards, January 16, 1999, Grade 11, p.14,2.8.11.N
  
Linear Equations: Graph/Two-Variables
The learner will be able to graph a linear equation in two variables.
Strand Scope Source
Linear Equations Reinforce PA: Academic Standards, January 16, 1999, Grade 11, p.14,2.8.11.N
  
Inequalities: System
The learner will be able to solve a system of inequalities.
Strand Scope Source
Inequalities Reinforce PA: System of School Assessment, 1997, Grade 11, p.12,#5 week tested: 32.
  
Quadratic Equations: Solving
The learner will be able to solve quadratic equations using the appropriate method.
Strand Scope Source
Quadratic Equations/Formula Master PA: Academic Standards, January 16, 1999, Grade 11, p.14,2.8.11.N
  
Exponents: Solve/Equations
The learner will be able to solve equations involving exponents symbolically and graphically.
Strand Scope Source
Exponents Reinforce PA: Academic Standards, January 16, 1999, Grade 11, p.14,2.8.11.N
  
Rates: Graph/Growth/Decay
The learner will be able to graph rates of growth and decay.
Strand Scope Source
Rates Master PA: Academic Standards, January 16, 1999, Grade 11, p.19,2.11.11.C
  
Rates: Interpret/Growth/Decay
The learner will be able to interpret rates of growth and decay.
Strand Scope Source
Rates Master PA: Academic Standards, January 16, 1999, Grade 11, p.19,2.11.11.C
  
Computation: Error/Estimations
The learner will be able to explain the amount of error that is possible when using estimation in computation.
Strand Scope Source
Computation Master PA: Academic Standards, January 16, 1999, Grade 11, p.4,2.2.11.D
  
Nonlinear Equations: Represent/Curves
The learner will be able to represent curves using equations.
Strand Scope Source
Nonlinear Equations Master PA: Academic Standards, January 16, 1999, Grade 11, p.13,2.8.11.E
  
Binomial Theorem
The learner will be able to apply the binomial theorem.
Strand Scope Source
Binomial Expansion Master Bloomsburg Area School District
  
Binomial Expansion: Finding Terms
The learner will be able to find an nth term within a binomial expansion.
Strand Scope Source
Binomial Expansion Master Bloomsburg Area School District
  
Logarithms: Simplifying
The learner will be able to use logarithmic properties to simplify expressions.
Strand Scope Source
Logarithms Master Bloomsburg Area School District
  
Logarithmic Equations
The learner will be able to solve equations involving logarithms.
Strand Scope Source
Logarithms Master Bloomsburg Area School District
  
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Calculus and Pre-Calculus
Connecting: Exponential/Logarithmic
The learner will be able to analyze the relationship between exponential and logarithmic functions, and how each is used to deal with real world situations.
Strand Scope Source
Connecting Master Bloomsburg Area School District
  
Vectors: Perpendicular/Parallel
The learner will be able to recognize both perpendicular and parallel vectors.
Strand Scope Source
Vectors Master Bloomsburg Area School District
  
Vectors: Components
The learner will be able to resolve a given vector into its component vectors.
Strand Scope Source
Vectors Master Bloomsburg Area School District
  
Vectors: Magnitude/Direction
The learner will be able to find the magnitude and direction of a given vector.
Strand Scope Source
Vectors Master Bloomsburg Area School District
  
Vectors: Dot Product
The learner will be able to determine the dot product of two vectors.
Strand Scope Source
Vectors Master Bloomsburg Area School District
  
Vectors: Standard Position
The learner will be able to determine the equivalent vector in standard position to a given vector.
Strand Scope Source
Vectors Master Bloomsburg Area School District
  
Vectors: Real World Problems
The learner will be able to solve real world problems using vectors.
Strand Scope Source
Vectors Master Bloomsburg Area School District
  
Matrices: Operations with Matrices
The learner will be able to perform addition, subtraction, multiplication, and scalar multiplication with matrices and find inverse matrices.
Strand Scope Source
Matrices Reinforce PA: Academic Standards, January 16, 1999, Grade 11, p.14,2.8.11.I
  
Matrices: Organize Data
The learner will be able to use matrices to organize real world data.
Strand Scope Source
Matrices Master PA: Academic Standards, January 16, 1999, Grade 11, p.14,2.8.11.I
  
Applying: Limits
The learner will be able to analyze and apply the concept of limits.
Strand Scope Source
Applying Calculus Concepts Master Bloomsburg Area School District
  
Applying: Derivative
The learner will be able to gain a working knowledge of the concept of the derivative.
Strand Scope Source
Applying Calculus Concepts Master Bloomsburg Area School District
  
Applying: Equation/Tangent Lines
The learner will be able to determine the equation of tangent lines to a curve at a point and apply it to estimate function values.
Strand Scope Source
Applying Calculus Concepts Master Bloomsburg Area School District
  
Derivative: Apply/Formulas
The learner will be able to apply formulas to determine derivatives.
Strand Scope Source
Differentiation Master Bloomsburg Area School District
  
Derivatives: Apply/Definition
The learner will be able to use the formal definition of a derivative.
Strand Scope Source
Derivatives/Antiderivatives Master Bloomsburg Area School District
  
Derivatives: Chain Rule
The learner will be able to apply the chain rule in finding derivatives.
Strand Scope Source
Derivatives/Antiderivatives Master Bloomsburg Area School District
  
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Functions
Logarithmic Functions: Base 10 and e
The learner will be able to evaluate a logarithmic function with base 10 and e and represent it on a graph.
Strand Scope Source
Logarithmic Functions Master Bloomsburg Area School District
  
Circular Functions: Display
The learner will be able to display periodic and circular functions using graphing calculators.
Strand Scope Source
Circular Functions Master PA: Academic Standards, January 16, 1999, Grade 11, p.18,2.10.11.A
  
Trigonometric Functions: Graph/Analyze
The learner will be able to analyze the graphs of trigonometric functions.
Strand Scope Source
Trigonometric Functions Master PA: Academic Standards, January 16, 1999, Grade 11, p.18,2.10.11.A
  
Representations: Problem Situations
The learner will be able to use functions to represent problem situations.
Strand Scope Source
Representations of Functions Master PA: Academic Standards, January 16, 1999, Grade 11, p.15,2.8.11.R
  
Functions: Maximum/Minimum
The learner will be able to identify the maximum and minimum values of a function over a specified interval.
Strand Scope Source
Functions Master PA: Academic Standards, January 16, 1999, Grade 11, p.19,2.11.11.A
  
Functions: Interpret
The learner will be able to interpret functions.
Strand Scope Source
Functions Master PA: Academic Standards, January 16, 1999, Grade 11, p.15,2.8.11.R
  
Functions: Analyze
The learner will be able to analyze the general properties and behavior of functions.
Strand Scope Source
Functions Master PA: Academic Standards, January 16, 1999, Grade 11, p.15,2.8.11.S
  
Problem Solving: Functions/Inverses
The learner will be able to use the inverse of a trigonometric or circular function to solve a problem.
Strand Scope Source
Problem Solving Master Bloomsburg Area School District
  
Polynomial Functions: Roots
The learner will be able to find both real and complex roots of polynomial functions.
Strand Scope Source
Polynomial Functions Master Bloomsburg Area School District
  
Exponential Functions: Real World
The learner will be able to solve real world problems involving exponential functions.
Strand Scope Source
Exponential Functions Master Bloomsburg Area School District
  
Limits: Using Theorems
The learner will be able to determine the limits of functions using limit theorems.
Strand Scope Source
Limits Master Bloomsburg Area School District
  
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Geometry
Circles: Properties/Problem Solving
The learner will be able to identify and apply circle properties in order to solve problems.
Strand Scope Source
Circles Master PA: System of School Assessment, 1997, Grade 11, p.11,#3 week tested: 32.
  
Geometric Concepts
The learner will be able to understand and/or apply the concepts of solid, coordinate, and/or transformational geometry.
Strand Scope Source
Geometric Concepts Master PA: System of School Assessment, 1997, Grade 11, p.11,#3 week tested: 32.
  
Problem Solving: Analytic Geometry
The learner will be able to solve both real world and mathematical problems using concepts of analytic geometry.
Strand Scope Source
Problem Solving Master PA: Academic Standards, January 16, 1999, Grade 11, p.16,2.9.11.G
  
Lines/Angles: Properties
The learner will be able to understand and/or apply properties of lines and/or angles.
Strand Scope Source
Lines/Angles/Polygons Reinforce PA: System of School Assessment, 1997, Grade 11, p.11,#3 week tested: 32.
  
Circles: Problem Solving
The learner will be able to obtain solutions to problems involving circles using the properties of angles, arcs, chords, tangents, and secants.
Strand Scope Source
Circles Master PA: Academic Standards, January 16, 1999, Grade 11, p.16,2.9.11.F
  
Problem Solving: Geometric Models
The learner will be able to obtain solutions to problem situations with geometric models.
Strand Scope Source
Problem Solving Master PA: Academic Standards, January 16, 1999, Grade 11, p.17,2.9.11.I
  
Problem Solving: Geometric Models
The learner will be able to geometrically model situations to formulate problems.
Strand Scope Source
Problem Solving Master PA: Academic Standards, January 16, 1999, Grade 11, p.17,2.9.11.I
  
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Mathematics Processes
Mathematical Concepts: Communication
The learner will be able to apply symbols, mathematical terminology, standard notation, rules, graphing and other mathematical illustrations to communicate observations, predictions, ideas procedures, generalizations, and results.
Strand Scope Source
Communication Master PA: Academic Standards, January 16, 1999, Grade 11, p.8,2.5.11.B
  
Communication: Clearly
The learner will be able to communicate mathematical procedures and results clearly, systematically, succinctly and accurately.
Strand Scope Source
Communication Master PA: Academic Standards, January 16, 1999, Grade 11, p.8,2.5.11.C
  
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Area/Perimeter: Problem Solving
The learner will be able to develop an understanding of area and perimeter by applying various problem solving techniques.
Strand Scope Source
Perimeter/Area/Volume Master PA: System of School Assessment, 1997, Grade 11, p.11,#2 week tested: 32.
  
Accuracy
The learner will be able to realize the degree of accuracy necessary in calculations is dependent upon how the results are going to be used and the tools used to find the measurements.
Strand Scope Source
Accuracy Master PA: Academic Standards, January 16, 1999, Grade 11, p.4,2.2.11.E
  
Accuracy: Choose/Apply Tools
The learner will be able to choose and use suitable tools and units to measure to the degree of accuracy required in a particular scenario.
Strand Scope Source
Accuracy Master PA: Academic Standards, January 16, 1999, Grade 11, p.6,2.3.11.A
  
Circumference: Application
The learner will be able to solve real world application problems involving circumference measurements.
Strand Scope Source
Circumference Master PA: System of School Assessment, 1997, Grade 11, p.11,#2 week tested: 32.
  
Measurement: Accuracy
The learner will be able to measure an object to a given degree of accuracy.
Strand Scope Source
Measurement: Application Master PA: Academic Standards, January 16, 1999, Grade 11, p.6,2.3.11.D
  
Angle Measure: Degrees
The learner will be able to measure angles in degrees.
Strand Scope Source
Angle Measurement Master PA: Academic Standards, January 16, 1999, Grade 11, p.6,2.3.11.B
  
Angle Measure: Radians
The learner will be able to measure angles in radians.
Strand Scope Source
Angle Measurement Master PA: Academic Standards, January 16, 1999, Grade 11, p.6,2.3.11.B
  
Angle Measure: Compare
The learner will be able to compare angles in degrees and radians.
Strand Scope Source
Angle Measurement Master PA: Academic Standards, January 16, 1999, Grade 11, p.6,2.3.11.B
  
Area of a Triangle: Oblique
The learner will be able to compute the area of an oblique triangle.
Strand Scope Source
Area of a Triangle Master Bloomsburg Area School District
  
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Number Systems: Applying Properties
The learner will be able to understand and apply number systems and properties to model and solve problems including dealing with special number properties (i.e., 1, and 0).
Strand Scope Source
Number Systems Master PA: System of School Assessment, 1997, Grade 11, p.11,#1 week tested: 32.
  
Number Sense: Display/Knowledge
The learner will be able to display a knowledge of number sense.
Strand Scope Source
Number Sense Master PA: System of School Assessment, 1997, Grade 11, p.11,#1 week tested: 32.
  
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Numeration
Estimate/Problems: No Exact Results
The learner will be able to make estimations and/or round-off to obtain problem solutions where exact results are not necessary.
Strand Scope Source
Estimate/Problems Master PA: Academic Standards, January 16, 1999, Grade 11, p.4,2.2.11.B
  
Sequences: Reproduce/Extend/Create
The learner will be able to reproduce, extend, and create sequences.
Strand Scope Source
Sequences Master PA: System of School Assessment, 1997, Grade 11, p.12,#5 week tested: 32.
  
Patterns: Problem Solving/Recognize
The learner will be able to use pattern recognition to solve problems.
Strand Scope Source
Patterns: Problem Solving Master PA: Academic Standards, January 16, 1999, Grade 11, p.13,2.8.11.C
  
Sequences: Sum of Finite
The learner will be able to determine sums of finite sequences of numbers.
Strand Scope Source
Sequences Master PA: Academic Standards, January 16, 1999, Grade 11, p.19,2.11.11.D
  
Series: Sum/Infinite Geometric
The learner will be able to determine the sum of an infinite geometric series.
Strand Scope Source
Series Master PA: Academic Standards, January 16, 1999, Grade 11, p.19,2.11.11.D
  
Patterns: Give Examples/Other Areas
The learner will be able to give examples of patterns that exist in data from other content areas.
Strand Scope Source
Patterns Master PA: Academic Standards, January 16, 1999, Grade 11, p.13,2.8.11.B
  
Sequence/Series: Problem Solving
The learner will be able to apply sequences and series to obtain solutions to word problems.
Strand Scope Source
Sequences/Series Master PA: Academic Standards, January 16, 1999, Grade 11, p.13,2.8.11.C
  
Sequences: Expression/Rule
The learner will be able to find any term in a sequence given an expression or rule for the nth term.
Strand Scope Source
Sequences Master Bloomsburg Area School District
  
Sequences: Determine/Formula
The learner will be able to determine a formula for the nth term given any sequence.
Strand Scope Source
Sequences Master Bloomsburg Area School District
  
Series: Sigma Notation
The learner will be able to show a series in correct sigma notation.
Strand Scope Source
Series Master Bloomsburg Area School District
  
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Number Sense: Applying
The learner will be able to show an intuitive sense of what a percent is, and how percents are used in real world scenarios by completing sentences involving percentages with appropriate and reasonable choices.
Strand Scope Source
Number Sense Master PA: System of School Assessment, 1997, Grade 11, p.11,#1 week tested: 32.
  
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Probability/Statistics
Data: Statistical Measures
The learner will be able to explain data as an example of distribution applying statistical measures of center and spread.
Strand Scope Source
Data Master PA: Academic Standards, January 16, 1999, Grade 11, p.9,2.6.11.A
  
Probability Distribution: Normal Curve
The learner will be able to explain (in non-specific terms) the normal curve and use its attributes in answering questions about data that is assumed to be normally distributed.
Strand Scope Source
Probability Distribution Master PA: Academic Standards, January 16, 1999, Grade 11, p.10,2.6.11.I
  
Binomial Expansion: Pascal's Triangle
The learner will be able to explore patterns that occur in the expansion of a binomial of degree "n" using Pascal's Triangle, show how to make such an expansion.
Strand Scope Source
Binomial Probabilities Master Bloomsburg Area School District
  
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Problem Solving
Solutions: Summarize/Evaluate
The learner will be able to finish a solution procedure with a summary of results and evaluate the degree to which the results are acceptable and validate reasoning.
Strand Scope Source
Solution Master PA: Academic Standards, January 16, 1999, Grade 11, p.8,2.5.11.D
  
Strategies: Choose/Apply
The learner will be able to choose and apply appropriate mathematical concepts and strategies from various areas of mathematics and use them to solve non-routine and multi-step problems.
Strand Scope Source
Strategies Master PA: Academic Standards, January 16, 1999, Grade 11, p.8,2.5.11.A
  
Solution: Illustrate
The learner will be able to illustrate mathematical solutions to problems.
Strand Scope Source
Solution Master PA: Academic Standards, January 16, 1999, Grade 11, p.7,2.4.11.E
  
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Computers: Show Ability
The learner will be able to show the ability to use scientific and graphing calculators.
Strand Scope Source
Computers Master PA: Academic Standards, January 16, 1999, Grade 11, p.4,2.2.11.F
  
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Connecting: Trigonometric/Circular
The learner will be able to make connections between circular and trigonometric expressions, their functions, and how each translates to graphical form.
Strand Scope Source
Circles Master Bloomsburg Area School District
  
Trig. Identities
The learner will be able to identify and use the trigonometric identities.
Strand Scope Source
Trigonometric Identities Master Bloomsburg Area School District
  
Trig. Identities: Verifying
The learner will be able to verify identities.
Strand Scope Source
Trigonometric Identities Master Bloomsburg Area School District
  
Problem Solving: Right Triangles
The learner will be able to recognize, create, and solve practical right triangle problems by applying trigonometric functions and the Pythagorean Theorem.
Strand Scope Source
Problem Solving Master PA: Academic Standards, January 16, 1999, Grade 11, p.18,2.10.11.B
  
Trig. Ratios: Law of Sines/Cosines
The learner will be able to use the Law of Sines and Cosines to solve problems.
Strand Scope Source
Trigonometric Ratios Master Bloomsburg Area School District
  
Triangles: SSA Case
The learner will be able to discern whether 0,1, or 2 triangles exist, and what they are in an SSA (side, side, angle) case.
Strand Scope Source
Triangles Master Bloomsburg Area School District
  
Trig. Equations: Solutions
The learner will be able to determine possible solutions for trigonometric equations.
Strand Scope Source
Trigonometric Equations Master Bloomsburg Area School District
  
Trigonometric/Circular Functions: Graph
The learner will be able to graph and analyze the 6 circular and trigonometric functions.
Strand Scope Source
Circles Master Bloomsburg Area School District
  
Trigonometric/Circular Functions: Change
The learner will be able to perform changes to amplitude, period, and phase shift of circular and trigonometric functions.
Strand Scope Source
Trigonometric Equations Master Bloomsburg Area School District
  
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