# Pennsylvania State Standards for Mathematics: Grade 11

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PA.2.1.11. Numbers, Number Systems and Number Relationships: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.1.11.A. Model and compare values of irrational and complex numbers.

PA.2.2.11. Computation and Estimation: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.2.11.A. Intentionally Blank

2.2.11.B. Intentionally Blank

2.2.11.C. Evaluate numerical expressions that include the four basic operations and operations of powers and roots, reciprocals, opposites, and absolute values.

2.2.11.D. Intentionally Blank

2.2.11.E. Recognize that the degree of precision needed in calculating a number depends on how the results will be used and the instruments used to generate the measure.

2.2.11.F. Demonstrate skills for using computer spreadsheets and scientific and graphing calculators.

PA.2.3.11. Measurement and Estimation: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.3.11.A. Intentionally Blank

2.3.11.B. Intentionally Blank

2.3.11.C. Use properties of geometric figures and measurement formulas to solve for a missing quantity (e.g., the measure of a specific angle created by parallel lines and a transversal).

PA.2.4.11. Mathematical Reasoning and Connections: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.4.11.A. Write formal proofs (direct proofs, indirect proofs/proofs by contradiction, use of counter-examples, truth tables, etc.) to validate conjectures or arguments.

2.4.11.B. Use statements, converses, inverses and contrapositives to construct valid arguments or to validate arguments.

2.4.11.C. Determine the validity of an argument.

2.4.11.D. Use truth tables to reveal the logic of mathematical statements.

2.4.11.E. Demonstrate mathematical solutions to problems (e.g., in the physical sciences).

PA.2.5.11. Mathematical Problem Solving and Communication: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.5.11.A. Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts.

2.5.11.B. Use symbols, mathematical terminology, standard notation, mathematical rules, graphing and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas, and results.

2.5.11.C. Present mathematical procedures and results clearly, systematically, succinctly and correctly.

2.5.11.D. Conclude a solution process with a summary of results and evaluate the degree to which the results obtained represent an acceptable response to the initial problem and why the reasoning is valid.

PA.2.6.11. Statistics and Data Analysis: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.6.11.A. Design and conduct an experiment using random sampling.

2.6.11.B. Intentionally Blank

2.6.11.C. Select or calculate the appropriate measure of central tendency, calculate and apply the inter quartile range for one-variable data, and construct a line of best fit and calculate its equation for two-variable data.

2.6.11.D. Intentionally Blank

2.6.11.E. Make predictions based on lines of best fit or draw conclusions on the value of a variable in a population based on the results of a sample.

2.6.11.F. Determine the degree of dependence of two quantities specified by a two-way table.

2.6.11.G. Describe questions of experimental design, control groups, treatment groups, cluster sampling and reliability.

2.6.11.H. Use sampling techniques to draw inferences about large populations.

2.6.11.I. Describe the normal curve and use its properties to answer questions about sets of data that are assumed to be normally distributed.

PA.2.7.11. Probability and Predictions: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.7.11.A. Use probability to predict the likelihood of an outcome in an experiment.

2.7.11.B. Intentionally Blank

2.7.11.C. Compare odds and probability.

2.7.11.D. Intentionally Blank

2.7.11.E. Use probability to make judgments about the likelihood of various outcomes.

PA.2.8.11. Algebra and Functions: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.8.11.A. Intentionally Blank

2.8.11.B. Evaluate and simplify algebraic expressions and solve and graph linear, quadratic, exponential, and logarithmic equations and inequalities, and solve and graph systems of equations and inequalities.

2.8.11.C. Recognize, describe and generalize patterns using sequences and series to predict long-term outcomes.

2.8.11.D. Demonstrate an understanding and apply properties of functions (domain, range, inverses) and characteristics of families of functions (linear, polynomial, rational, trigonometric, exponential, logarithmic).

2.8.11.E. Use combinations of symbols and numbers to create expressions, equations, and inequalities in two or more variables, systems of equations and inequalities, and functional relationships that model problem situations.

2.8.11.F. Interpret the results of solving equations, inequalities, systems of equations, and inequalities in the context of the situation that motivated the model.

2.8.11.G. Analyze and explain systems of equations, systems of inequalities and matrices.

2.8.11.H. Select and use an appropriate strategy to solve systems of equations and inequalities using graphing calculators, symbol manipulators, spreadsheets and other software.

2.8.11.I. Use matrices to organize and manipulate data, including matrix addition, subtraction, multiplication and scalar multiplication.

2.8.11.J. Demonstrate the connection between algebraic equations and inequalities and the geometry of relations in the coordinate plane.

2.8.11.K. Select, justify and apply an appropriate technique to graph a linear function in two variables, including slope-intercept, x- and y-intercepts, graphing by transformations and the use of a graphing calculator.

2.8.11.L. Write the equation of a line when given the graph of the line, two points on the line, or the slope of the line and a point on the line.

2.8.11.M. Given a set of data points, write an equation for a line of best fit.

2.8.11.N. Solve linear, quadratic and exponential equations both symbolically and graphically.

2.8.11.O. Determine the domain and range of a relation, given a graph or set of ordered pairs.

2.8.11.P. Analyze a relation to determine whether a direct or inverse variation exists and represent it algebraically and graphically.

2.8.11.Q. Represent functional relationships in tables, charts and graphs.

2.8.11.R. Create and interpret functional models.

2.8.11.S. Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic).

2.8.11.T. Analyze and categorize functions by their characteristics.

PA.2.9.11. Geometry: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.9.11.A. Create justifications for arguments related to geometric relations.

2.9.11.B. Use arguments based on transformations to establish congruence or similarity of 2- dimensional shapes.

2.9.11.C. Use techniques from coordinate geometry to establish properties of lines, shapes, and solids.

2.9.11.D. Identify corresponding parts in congruent triangles to solve problems.

2.9.11.E. Solve problems involving inscribed and circumscribed polygons.

2.9.11.F. Use the properties of angles, arcs, chords, tangents and secants to solve problems involving circles.

2.9.11.G. Solve problems using analytic geometry.

2.9.11.H. Construct a geometric figure and its image using various transformations.

2.9.11.I. Model situations geometrically to formulate and solve problems.

2.9.11.J. Analyze figures in terms of the kinds of symmetries they have.

PA.2.10.11. Trigonometry: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.10.11.A. Identify, create, and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean Theorem.

2.10.11.B. Graph periodic and circular functions; describe properties of the graphs.

PA.2.11.11. Concepts of Calculus: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.11.11.A. Determine and interpret maximum and minimum values of a function over a specified interval.

2.11.11.B. Analyze and interpret rates of growth/decay.

2.11.11.C. Estimate areas under curves using sums of areas.

2.11.11.D. Determine sums of finite sequences of numbers and infinite geometric series.

2.11.11.E. Estimate areas under curves using sequences of areas.

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