Pennsylvania Math Standards - Pennsylvania Core Standards - Mathematics

400 standards, Kindergarten through AP.

PA Core Standards for Mathematics are grounded in Common Core but use a distinctive four strand organization: Numbers, Operations and Algebra, Geometry, and Measurement and Data. That structure applies consistently from K through high school.

CC

Print
CC.2 CC.2
CC.2.1 CC.2.1
CC.2.1.1 CC.2.1.1
CC.2.1.1.B Numbers & Operations in Base Ten
CC.2.1.1.B.1Extend the counting sequence to read and write numerals to represent objects.
CC.2.1.1.B.2Use place-value concepts to represent amounts of tens and ones and to compare two digit numbers.
CC.2.1.1.B.3Use place-value concepts and properties of operations to add and subtract within 100.
CC.2.1.2 CC.2.1.2
CC.2.1.2.B Numbers & Operations in Base Ten
CC.2.1.2.B.1Use place-value concepts to represent amounts of tens and ones and to compare three digit numbers.
CC.2.1.2.B.2Use place-value concepts to read, write, and skip count to 1000.
CC.2.1.2.B.3Use place-value understanding and properties of operations to add and subtract within 1000.
CC.2.1.3 CC.2.1.3
CC.2.1.3.B Numbers & Operations in Base Ten
CC.2.1.3.B.1Apply place-value understanding and properties of operations to perform multi-digit arithmetic.
CC.2.1.3.C Numbers & Operations — Fractions
CC.2.1.3.C.1Explore and develop an understanding of fractions as numbers.
CC.2.1.4 CC.2.1.4
CC.2.1.4.B Numbers & Operations in Base Ten
CC.2.1.4.B.1Apply place-value concepts to show an understanding of multi-digit whole numbers.
CC.2.1.4.B.2Use place-value understanding and properties of operations to perform multi-digit arithmetic.
CC.2.1.4.C Numbers & Operations — Fractions
CC.2.1.4.C.1Extend the understanding of fractions to show equivalence and ordering.
CC.2.1.4.C.2Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
CC.2.1.4.C.3Connect decimal notation to fractions, and compare decimal fractions (base 10 denominator, e.g., 19/100).
CC.2.1.5 CC.2.1.5
CC.2.1.5.B Numbers & Operations in Base Ten
CC.2.1.5.B.1Apply place-value concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals.
CC.2.1.5.B.2Extend an understanding of operations with whole numbers to perform operations including decimals.
CC.2.1.5.C Numbers & Operations — Fractions
CC.2.1.5.C.1Use the understanding of equivalency to add and subtract fractions.
CC.2.1.5.C.2Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
CC.2.1.6 CC.2.1.6
CC.2.1.6.D Ratios & Proportional Relationships
CC.2.1.6.D.1Understand ratio concepts and use ratio reasoning to solve problems.
CC.2.1.6.E The Number System
CC.2.1.6.E.1Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
CC.2.1.6.E.2Identify and choose appropriate processes to compute fluently with multi-digit numbers.
CC.2.1.6.E.3Develop and/or apply number theory concepts to find common factors and multiples.
CC.2.1.6.E.4Apply and extend previous understandings of numbers to the system of rational numbers.
CC.2.1.7 CC.2.1.7
CC.2.1.7.D Ratios & Proportional Relationships
CC.2.1.7.D.1Analyze proportional relationships and use them to model and solve real-world and mathematical problems.
CC.2.1.7.E The Number System
CC.2.1.7.E.1Apply and extend previous understandings of operations with fractions to operations with rational numbers.
CC.2.1.8 CC.2.1.8
CC.2.1.8.E The Number System
CC.2.1.8.E.1Distinguish between rational and irrational numbers using their properties.
CC.2.1.8.E.4Estimate irrational numbers by comparing them to rational numbers.
CC.2.1.HS CC.2.1.HS
CC.2.1.HS.F Number and Quantity
CC.2.1.HS.F.1Apply and extend the properties of exponents to solve problems with rational exponents.
CC.2.1.HS.F.2Apply properties of rational and irrational numbers to solve real world or mathematical problems.
CC.2.1.HS.F.3Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays.
CC.2.1.HS.F.4Use units as a way to understand problems and to guide the solution of multi-step problems.
CC.2.1.HS.F.5Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
CC.2.1.HS.F.6Extend the knowledge of arithmetic operations and apply to complex numbers.
CC.2.1.HS.F.7Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems.
CC.2.1.K CC.2.1.K
CC.2.1.K.A Counting & Cardinality
CC.2.1.K.A.1Know number names and write and recite the count sequence.
CC.2.1.K.A.2Apply one-to-one correspondence to count the number of objects.
CC.2.1.K.A.3Apply the concept of magnitude to compare numbers and quantities.
CC.2.1.K.B Numbers & Operations in Base Ten
CC.2.1.K.B.1Use place value to compose and decompose numbers within 19.
CC.2.2 CC.2.2
CC.2.2.1 CC.2.2.1
CC.2.2.1.A Operations and Algebraic Thinking
CC.2.2.1.A.1Represent and solve problems involving addition and subtraction within 20.
CC.2.2.1.A.2Understand and apply properties of operations and the relationship between addition and subtraction.
CC.2.2.2 CC.2.2.2
CC.2.2.2.A Operations and Algebraic Thinking
CC.2.2.2.A.1Represent and solve problems involving addition and subtraction within 100.
CC.2.2.2.A.2Use mental strategies to add and subtract within 20.
CC.2.2.2.A.3Work with equal groups of objects to gain foundations for multiplication.
CC.2.2.3 CC.2.2.3
CC.2.2.3.A Operations and Algebraic Thinking
CC.2.2.3.A.1Represent and solve problems involving multiplication and division.
CC.2.2.3.A.2Understand properties of multiplication and the relationship between multiplication and division.
CC.2.2.3.A.3Demonstrate multiplication and division fluency.
CC.2.2.3.A.4Solve problems involving the four operations, and identify and explain patterns in arithmetic.
CC.2.2.4 CC.2.2.4
CC.2.2.4.A Operations and Algebraic Thinking
CC.2.2.4.A.1Represent and solve problems involving the four operations.
CC.2.2.4.A.2Develop and/or apply number theory concepts to find factors and multiples.
CC.2.2.4.A.4Generate and analyze patterns using one rule.
CC.2.2.5 CC.2.2.5
CC.2.2.5.A Operations and Algebraic Thinking
CC.2.2.5.A.1Interpret and evaluate numerical expressions using order of operations.
CC.2.2.5.A.4Analyze patterns and relationships using two rules.
CC.2.2.6 CC.2.2.6
CC.2.2.6.B Expressions and Equations
CC.2.2.6.B.1Apply and extend previous understandings of arithmetic to algebraic expressions.
CC.2.2.6.B.2Understand the process of solving a one-variable equation or inequality and apply it to real-world and mathematical problems.
CC.2.2.6.B.3Represent and analyze quantitative relationships between dependent and independent variables.
CC.2.2.7 CC.2.2.7
CC.2.2.7.B Expressions and Equations
CC.2.2.7.B.1Apply properties of operations to generate equivalent expressions.
CC.2.2.7.B.3Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations.
CC.2.2.8 CC.2.2.8
CC.2.2.8.B Expressions and Equations
CC.2.2.8.B.1Apply concepts of radicals and integer exponents to generate equivalent expressions.
CC.2.2.8.B.2Understand the connections between proportional relationships, lines, and linear equations.
CC.2.2.8.B.3Analyze and solve linear equations and pairs of simultaneous linear equations.
CC.2.2.8.C Functions
CC.2.2.8.C.1Define, evaluate, and compare functions.
CC.2.2.8.C.2Use concepts of functions to model relationships between quantities.
CC.2.2.HS CC.2.2.HS
CC.2.2.HS.C Functions
CC.2.2.HS.C.1Use the concept and notation of functions to interpret and apply them in terms of their context.
CC.2.2.HS.C.2Graph and analyze functions and use their properties to make connections between the different representations.
CC.2.2.HS.C.3Write functions or sequences that model relationships between two quantities.
CC.2.2.HS.C.4Interpret the effects transformations have on functions and find the inverses of functions.
CC.2.2.HS.C.5Construct and compare linear, quadratic, and exponential models to solve problems.
CC.2.2.HS.C.6Interpret functions in terms of the situations they model.
CC.2.2.HS.C.7Apply radian measure of an angle and the unit circle to analyze the trigonometric functions.
CC.2.2.HS.C.8Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs.
CC.2.2.HS.C.9Prove the Pythagorean identity and use it to calculate trigonometric ratios.
CC.2.2.HS.D Algebra
CC.2.2.HS.D.1Interpret the structure of expressions to represent a quantity in terms of its context.
CC.2.2.HS.D.10Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.
CC.2.2.HS.D.2Write expressions in equivalent forms to solve problems.
CC.2.2.HS.D.3Extend the knowledge of arithmetic operations and apply to polynomials.
CC.2.2.HS.D.4Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs.
CC.2.2.HS.D.5Use polynomial identities to solve problems.
CC.2.2.HS.D.6Extend the knowledge of rational functions to rewrite in equivalent forms.
CC.2.2.HS.D.7Create and graph equations or inequalities to describe numbers or relationships.
CC.2.2.HS.D.8Apply inverse operations to solve equations or formulas for a given variable.
CC.2.2.HS.D.9Use reasoning to solve equations and justify the solution method.
CC.2.2.K CC.2.2.K
CC.2.2.K.A Operations and Algebraic Thinking
CC.2.2.K.A.1Extend the concepts of putting together and taking apart to add and subtract within 10.
CC.2.3 CC.2.3
CC.2.3.1 CC.2.3.1
CC.2.3.1.A Geometry
CC.2.3.1.A.1Compose and distinguish between two- and three-dimensional shapes based on their attributes.
CC.2.3.1.A.2Use the understanding of fractions to partition shapes into halves and quarters.
CC.2.3.2 CC.2.3.2
CC.2.3.2.A Geometry
CC.2.3.2.A.1Analyze and draw two- and three-dimensional shapes having specified attributes.
CC.2.3.2.A.2Use the understanding of fractions to partition shapes into halves, quarters, and thirds.
CC.2.3.3 CC.2.3.3
CC.2.3.3.A Geometry
CC.2.3.3.A.1Identify, compare, and classify shapes and their attributes.
CC.2.3.3.A.2Use the understanding of fractions to partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole.
CC.2.3.4 CC.2.3.4
CC.2.3.4.A Geometry
CC.2.3.4.A.1Draw lines and angles and identify these in two-dimensional figures.
CC.2.3.4.A.2Classify two-dimensional figures by properties of their lines and angles.
CC.2.3.4.A.3Recognize symmetric shapes and draw lines of symmetry.
CC.2.3.5 CC.2.3.5
CC.2.3.5.A Geometry
CC.2.3.5.A.1Graph points in the first quadrant on the coordinate plane and interpret these points when solving real world and mathematical problems.
CC.2.3.5.A.2Classify two-dimensional figures into categories based on an understanding of their properties.
CC.2.3.6 CC.2.3.6
CC.2.3.6.A Geometry
CC.2.3.6.A.1Apply appropriate tools to solve real-world and mathematical problems involving area, surface area, and volume.
CC.2.3.7 CC.2.3.7
CC.2.3.7.A Geometry
CC.2.3.7.A.1Solve real-world and mathematical problems involving angle measure, area, surface area, circumference, and volume.
CC.2.3.7.A.2Visualize and represent geometric figures and describe the relationships between them.
CC.2.3.8 CC.2.3.8
CC.2.3.8.A Geometry
CC.2.3.8.A.1Apply the concepts of volume of cylinders, cones, and spheres to solve real-world and mathematical problems.
CC.2.3.8.A.2Understand and apply congruence, similarity, and geometric transformations using various tools.
CC.2.3.8.A.3Understand and apply the Pythagorean Theorem to solve problems.
CC.2.3.HS CC.2.3.HS
CC.2.3.HS.A Geometry
CC.2.3.HS.A.1Use geometric figures and their properties to represent transformations in the plane.
CC.2.3.HS.A.10Translate between the geometric description and the equation for a conic section.
CC.2.3.HS.A.11Apply coordinate geometry to prove simple geometric theorems algebraically.
CC.2.3.HS.A.12Explain volume formulas and use them to solve problems.
CC.2.3.HS.A.13Analyze relationships between two-dimensional and three-dimensional objects.
CC.2.3.HS.A.14Apply geometric concepts to model and solve real world problems.
CC.2.3.HS.A.2Apply rigid transformations to determine and explain congruence.
CC.2.3.HS.A.3Verify and apply geometric theorems as they relate to geometric figures.
CC.2.3.HS.A.4Apply the concept of congruence to create geometric constructions.
CC.2.3.HS.A.5Create justifications based on transformations to establish similarity of plane figures.
CC.2.3.HS.A.6Verify and apply theorems involving similarity as they relate to plane figures.
CC.2.3.HS.A.7Apply trigonometric ratios to solve problems involving right triangles.
CC.2.3.HS.A.8Apply geometric theorems to verify properties of circles.
CC.2.3.HS.A.9Extend the concept of similarity to determine arc lengths and areas of sectors of circles.
CC.2.3.K CC.2.3.K
CC.2.3.K.A Geometry
CC.2.3.K.A.1Identify and describe two- and three-dimensional shapes.
CC.2.3.K.A.2Analyze, compare, create, and compose two- and three-dimensional shapes.
CC.2.4 CC.2.4
CC.2.4.1 CC.2.4.1
CC.2.4.1.A Measurement and Data
CC.2.4.1.A.1Order lengths and measure them both indirectly and by repeating length units.
CC.2.4.1.A.2Tell and write time to the nearest half hour using both analog and digital clocks.
CC.2.4.1.A.4Represent and interpret data using tables/charts.
CC.2.4.2 CC.2.4.2
CC.2.4.2.A Measurement and Data
CC.2.4.2.A.1Measure and estimate lengths in standard units using appropriate tools.
CC.2.4.2.A.2Tell and write time to the nearest five minutes using both analog and digital clocks.
CC.2.4.2.A.3Solve problems and make change using coins and paper currency with appropriate symbols.
CC.2.4.2.A.4Represent and interpret data using line plots, picture graphs, and bar graphs.
CC.2.4.2.A.6Extend the concepts of addition and subtraction to problems involving length.
CC.2.4.3 CC.2.4.3
CC.2.4.3.A Measurement and Data
CC.2.4.3.A.1Solve problems involving measurement and estimation of temperature, liquid volume, mass, and length.
CC.2.4.3.A.2Tell and write time to the nearest minute and solve problems by calculating time intervals.
CC.2.4.3.A.3Solve problems and make change involving money using a combination of coins and bills.
CC.2.4.3.A.4Represent and interpret data using tally charts, tables, pictographs, line plots, and bar graphs.
CC.2.4.3.A.5Determine the area of a rectangle and apply the concept to multiplication and to addition.
CC.2.4.3.A.6Solve problems involving perimeters of polygons and distinguish between linear and area measures.
CC.2.4.4 CC.2.4.4
CC.2.4.4.A Measurement and Data
CC.2.4.4.A.1Solve problems involving measurement and conversions from a larger unit to a smaller unit.
CC.2.4.4.A.2Translate information from one type of data display to another.
CC.2.4.4.A.4Represent and interpret data involving fractions using information provided in a line plot.
CC.2.4.4.A.6Measure angles and use properties of adjacent angles to solve problems.
CC.2.4.5 CC.2.4.5
CC.2.4.5.A Measurement and Data
CC.2.4.5.A.1Solve problems using conversions within a given measurement system.
CC.2.4.5.A.2Represent and interpret data using appropriate scale.
CC.2.4.5.A.4Solve problems involving computation of fractions using information provided in a line plot.
CC.2.4.5.A.5Apply concepts of volume to solve problems and relate volume to multiplication and to addition.
CC.2.4.6 CC.2.4.6
CC.2.4.6.B Statistics and Probability
CC.2.4.6.B.1Demonstrate an understanding of statistical variability by displaying, analyzing, and summarizing distributions.
CC.2.4.7 CC.2.4.7
CC.2.4.7.B Statistics and Probability
CC.2.4.7.B.1Draw inferences about populations based on random sampling concepts.
CC.2.4.7.B.2Draw informal comparative inferences about two populations.
CC.2.4.7.B.3Investigate chance processes and develop, use, and evaluate probability models.
CC.2.4.8 CC.2.4.8
CC.2.4.8.B Statistics and Probability
CC.2.4.8.B.1Analyze and/or interpret bivariate data displayed in multiple representations.
CC.2.4.8.B.2Understand that patterns of association can be seen in bivariate data utilizing frequencies.
CC.2.4.HS CC.2.4.HS
CC.2.4.HS.B Statistics and Probability
CC.2.4.HS.B.1Summarize, represent, and interpret data on a single count or measurement variable.
CC.2.4.HS.B.2Summarize, represent, and interpret data on two categorical and quantitative variables.
CC.2.4.HS.B.3Analyze linear models to make interpretations based on the data.
CC.2.4.HS.B.4Recognize and evaluate random processes underlying statistical experiments.
CC.2.4.HS.B.5Make inferences and justify conclusions based on sample surveys, experiments, and observational studies.
CC.2.4.HS.B.6Use the concepts of independence and conditional probability to interpret data.
CC.2.4.HS.B.7Apply the rules of probability to compute probabilities of compound events in a uniform probability model.
CC.2.4.K CC.2.4.K
CC.2.4.K.A Measurement and Data
CC.2.4.K.A.1Describe and compare attributes of length, area, weight, and capacity of everyday objects.
CC.2.4.K.A.4Classify objects and count the number of objects in each category.

AP Calculus Learning Objectives

Print
CB.Calc.LIM Limits
CB.Calc.LIM-1 Reasoning with definitions, theorems, and properties can be used to justify claims about limits.
CB.Calc.LIM-1.ARepresent limits analytically using correct notation.
CB.Calc.LIM-1.BInterpret limits expressed in analytic notation.
CB.Calc.LIM-1.CEstimate limits of functions.
CB.Calc.LIM-1.DDetermine the limits of functions using limit theorems.
CB.Calc.LIM-1.EDetermine the limits of functions using equivalent expressions for the function or the squeeze theorem.
CB.Calc.LIM-2 Reasoning with definitions, theorems, and properties can be used to justify claims about continuity.
CB.Calc.LIM-2.AJustify conclusions about continuity at a point using the definition.
CB.Calc.LIM-2.BDetermine intervals over which a function is continuous.
CB.Calc.LIM-2.CDetermine values of x or solve for parameters that make discontinuous functions continuous, if possible.
CB.Calc.LIM-2.DInterpret the behavior of functions using limits involving infinity.
CB.Calc.LIM-3 The derivative of a function is defined as the limit of a difference quotient.
CB.Calc.LIM-3.AInterpret a limit as a definition of a derivative.
CB.Calc.LIM-4 L'Hospital's Rule allows us to determine the limits of some indeterminate forms.
CB.Calc.LIM-4.ADetermine limits of functions that result in indeterminate forms.
CB.Calc.LIM-5 Definite integrals can be approximated using geometric and numerical methods.
CB.Calc.LIM-5.AApproximate a definite integral using geometric and numerical methods.
CB.Calc.LIM-5.BInterpret the limiting case of the Riemann sum as a definite integral.
CB.Calc.LIM-5.CRepresent the limiting case of the Riemann sum as a definite integral.
CB.Calc.LIM-6 Improper integrals can be determined using limits of definite integrals.
CB.Calc.LIM-6.AEvaluate an improper integral or determine that the integral diverges.
CB.Calc.LIM-7 The behavior of a convergent or divergent series can be determined or estimated.
CB.Calc.LIM-7.ADetermine whether a series converges or diverges.
CB.Calc.LIM-7.BApproximate the sum of a series.
CB.Calc.LIM-8 Power series and Taylor series can represent functions.
CB.Calc.LIM-8.ARepresent a function at a point as a Taylor polynomial.
CB.Calc.LIM-8.BApproximate function values using a Taylor polynomial.
CB.Calc.LIM-8.CDetermine the error bound associated with a Taylor polynomial approximation.
CB.Calc.LIM-8.DDetermine the radius of convergence and interval of convergence for a power series.
CB.Calc.LIM-8.ERepresent a function as a Taylor series or a Maclaurin series.
CB.Calc.LIM-8.FInterpret Taylor series and Maclaurin series.
CB.Calc.LIM-8.GRepresent a given function as a power series.
CB.Calc.CHA Change
CB.Calc.CHA-1 The derivative of a function is the instantaneous rate of change of the function.
CB.Calc.CHA-1.AInterpret the rate of change at an instant in terms of average rates of change over intervals containing that instant.
CB.Calc.CHA-2 Derivatives can be computed using definitions and rules.
CB.Calc.CHA-2.ADetermine average rates of change using difference quotients.
CB.Calc.CHA-2.BRepresent the derivative of a function as the limit of a difference quotient.
CB.Calc.CHA-2.CDetermine the equation of a line tangent to a curve at a given point.
CB.Calc.CHA-2.DEstimate derivatives.
CB.Calc.CHA-3 Derivatives can be used to model rates of change in applied contexts.
CB.Calc.CHA-3.AInterpret the meaning of a derivative in context.
CB.Calc.CHA-3.BCalculate rates of change in applied contexts.
CB.Calc.CHA-3.CInterpret rates of change in applied contexts.
CB.Calc.CHA-3.DCalculate related rates in applied contexts.
CB.Calc.CHA-3.EInterpret related rates in applied contexts.
CB.Calc.CHA-3.FApproximate a value on a curve using the equation of a tangent line.
CB.Calc.CHA-3.GCalculate derivatives of parametric functions.
CB.Calc.CHA-3.HCalculate derivatives of vector-valued functions.
CB.Calc.CHA-4 Integrals can be used to model accumulation and net change in applied contexts.
CB.Calc.CHA-4.AInterpret the meaning of areas associated with the graph of a rate of change in context.
CB.Calc.CHA-4.BDetermine the average value of a function using definite integrals.
CB.Calc.CHA-4.CDetermine values for positions and rates of change using definite integrals in problems involving rectilinear motion.
CB.Calc.CHA-4.DInterpret the meaning of a definite integral in accumulation problems.
CB.Calc.CHA-4.EDetermine net change using definite integrals in applied contexts.
CB.Calc.CHA-5 Definite integrals can be used to calculate areas, volumes, and lengths.
CB.Calc.CHA-5.ACalculate areas in the plane using the definite integral.
CB.Calc.CHA-5.BCalculate volumes of solids with known cross sections using definite integrals.
CB.Calc.CHA-5.CCalculate volumes of solids of revolution using definite integrals.
CB.Calc.CHA-5.DCalculate areas of regions defined by polar curves using definite integrals.
CB.Calc.CHA-6 Arc length can be calculated using definite integrals.
CB.Calc.CHA-6.ADetermine the length of a curve in the plane defined by a function, using a definite integral.
CB.Calc.CHA-6.BDetermine the length of a curve in the plane defined by parametric functions, using a definite integral.
CB.Calc.FUN Analysis of Functions
CB.Calc.FUN-1 Existence theorems can be used to draw conclusions about the behavior of functions.
CB.Calc.FUN-1.AExplain the behavior of a function on an interval using the Intermediate Value Theorem.
CB.Calc.FUN-1.BJustify conclusions about functions by applying the Mean Value Theorem over an interval.
CB.Calc.FUN-1.CJustify conclusions about functions by applying the Extreme Value Theorem.
CB.Calc.FUN-2 A function's derivative, when it exists, can be used to determine whether the function is increasing or decreasing.
CB.Calc.FUN-2.AExplain the relationship between differentiability and continuity.
CB.Calc.FUN-3 Derivatives can be calculated for various types of functions.
CB.Calc.FUN-3.ACalculate derivatives of familiar functions.
CB.Calc.FUN-3.BCalculate derivatives of products and quotients of differentiable functions.
CB.Calc.FUN-3.CCalculate derivatives of compositions of differentiable functions.
CB.Calc.FUN-3.DCalculate derivatives of implicitly defined functions.
CB.Calc.FUN-3.ECalculate derivatives of inverse and inverse trigonometric functions.
CB.Calc.FUN-3.FDetermine higher order derivatives of a function.
CB.Calc.FUN-3.GCalculate derivatives of functions written in polar coordinates.
CB.Calc.FUN-4 A function's derivative can be used to understand function behavior.
CB.Calc.FUN-4.AJustify conclusions about the behavior of a function based on the behavior of its derivatives.
CB.Calc.FUN-4.BCalculate minimum and maximum values in applied contexts or analysis of functions.
CB.Calc.FUN-4.CInterpret minimum and maximum values calculated in applied contexts.
CB.Calc.FUN-4.DDetermine critical points of implicit relations.
CB.Calc.FUN-4.EJustify conclusions about the behavior of an implicitly defined function based on evidence from its derivatives.
CB.Calc.FUN-5 The Fundamental Theorem of Calculus connects differentiation and integration.
CB.Calc.FUN-5.ARepresent accumulation functions using definite integrals.
CB.Calc.FUN-6 Recognizing and applying techniques for antidifferentiation.
CB.Calc.FUN-6.ACalculate a definite integral using areas and properties of definite integrals.
CB.Calc.FUN-6.BEvaluate definite integrals analytically using the Fundamental Theorem of Calculus.
CB.Calc.FUN-6.CDetermine antiderivatives of functions and indefinite integrals, using knowledge of derivatives.
CB.Calc.FUN-6.DUse substitution and rearrangements into equivalent forms, such as long division and completing the square, for integrands requiring these techniques.
CB.Calc.FUN-6.EUse integration by parts for integrands requiring this technique.
CB.Calc.FUN-6.FUse integration by linear partial fractions for integrands requiring this technique.
CB.Calc.FUN-7 Solving differential equations allows us to model rates of change.
CB.Calc.FUN-7.AInterpret verbal statements of problems as differential equations involving a derivative expression.
CB.Calc.FUN-7.BVerify solutions to differential equations.
CB.Calc.FUN-7.CEstimate solutions to differential equations.
CB.Calc.FUN-7.DDetermine general solutions to differential equations.
CB.Calc.FUN-7.EDetermine particular solutions to differential equations.
CB.Calc.FUN-7.FInterpret the meaning of a differential equation and its variables in context.
CB.Calc.FUN-7.GDetermine general and particular solutions for problems involving differential equations in context.
CB.Calc.FUN-7.HInterpret the meaning of the logistic growth model in context.
CB.Calc.FUN-8 Solutions to differential equations can model motion in the plane.
CB.Calc.FUN-8.ADetermine a particular solution given a rate vector and initial conditions.
CB.Calc.FUN-8.BDetermine values for positions and rates of change in problems involving planar motion.

AP Statistics Learning Objectives

Print
CB.Stats.VAR Variation and Distribution
CB.Stats.VAR-1 Exploring data through asking and answering statistical questions.
CB.Stats.VAR-1.AIdentify questions to be answered, based on variation in one-variable data.
CB.Stats.VAR-1.BIdentify variables in a set of data.
CB.Stats.VAR-1.CClassify types of variables.
CB.Stats.VAR-1.DIdentify questions to be answered about possible relationships in data.
CB.Stats.VAR-1.EIdentify questions to be answered about data collection methods.
CB.Stats.VAR-1.FIdentify questions suggested by patterns in data.
CB.Stats.VAR-1.GIdentify questions suggested by variation in statistics for samples collected from the same population.
CB.Stats.VAR-1.HIdentify questions suggested by variation in the shapes of distributions of samples taken from the same population.
CB.Stats.VAR-1.IIdentify questions suggested by probabilities of errors in statistical inference.
CB.Stats.VAR-1.JIdentify questions suggested by variation between observed and expected counts in categorical data.
CB.Stats.VAR-1.KIdentify questions suggested by variation in scatter plots.
CB.Stats.VAR-2 Normal distributions and comparing data.
CB.Stats.VAR-2.ACompare a data distribution to the normal distribution model.
CB.Stats.VAR-2.BDetermine proportions and percentiles from a normal distribution.
CB.Stats.VAR-2.CCompare measures of relative position in data sets.
CB.Stats.VAR-3 Designing and analyzing experiments.
CB.Stats.VAR-3.AIdentify the components of an experiment.
CB.Stats.VAR-3.BDescribe elements of a well-designed experiment.
CB.Stats.VAR-3.CCompare experimental designs and methods.
CB.Stats.VAR-3.DExplain why a particular experimental design is appropriate.
CB.Stats.VAR-3.EInterpret the results of a well-designed experiment.
CB.Stats.VAR-4 Probability rules and calculations.
CB.Stats.VAR-4.ACalculate probabilities for events and their complements.
CB.Stats.VAR-4.BInterpret probabilities for events.
CB.Stats.VAR-4.CExplain why two events are (or are not) mutually exclusive.
CB.Stats.VAR-4.DCalculate conditional probabilities.
CB.Stats.VAR-4.ECalculate probabilities for independent events and for the union of two events.
CB.Stats.VAR-5 Discrete random variables and probability distributions.
CB.Stats.VAR-5.ARepresent the probability distribution for a discrete random variable.
CB.Stats.VAR-5.BInterpret a probability distribution.
CB.Stats.VAR-5.CCalculate parameters for a discrete random variable.
CB.Stats.VAR-5.DInterpret parameters for a discrete random variable.
CB.Stats.VAR-5.ECalculate parameters for linear combinations of random variables.
CB.Stats.VAR-5.FDescribe the effects of linear transformations of parameters of random variables.
CB.Stats.VAR-6 Normal distributions and hypothesis testing for proportions.
CB.Stats.VAR-6.ACalculate the probability that a particular value lies in a given interval of a normal distribution.
CB.Stats.VAR-6.BDetermine the interval associated with a given area in a normal distribution.
CB.Stats.VAR-6.CDetermine the appropriateness of using the normal distribution to approximate probabilities for unknown distributions.
CB.Stats.VAR-6.DIdentify the null and alternative hypotheses for a population proportion.
CB.Stats.VAR-6.EIdentify an appropriate testing method for a population proportion.
CB.Stats.VAR-6.FVerify the conditions for making statistical inferences when testing a population proportion.
CB.Stats.VAR-6.GCalculate an appropriate test statistic and p-value for a population proportion.
CB.Stats.VAR-6.HIdentify the null and alternative hypotheses for a difference of two population proportions.
CB.Stats.VAR-6.IIdentify an appropriate testing method for the difference of two population proportions.
CB.Stats.VAR-6.JVerify the conditions for making statistical inferences when testing a difference of two population proportions.
CB.Stats.VAR-6.KCalculate an appropriate test statistic for the difference of two population proportions.
CB.Stats.VAR-7 t-distributions and hypothesis testing for means and regression.
CB.Stats.VAR-7.ADescribe t-distributions.
CB.Stats.VAR-7.BIdentify an appropriate testing method for a population mean with unknown sigma, including the mean difference between values in matched pairs.
CB.Stats.VAR-7.CIdentify the null and alternative hypotheses for a population mean with unknown sigma, including the mean difference between values in matched pairs.
CB.Stats.VAR-7.DVerify the conditions for the test for a population mean, including the mean difference between values in matched pairs.
CB.Stats.VAR-7.ECalculate an appropriate test statistic for a population mean, including the mean difference between values in matched pairs.
CB.Stats.VAR-7.FIdentify an appropriate selection of a testing method for a difference of two population means.
CB.Stats.VAR-7.GIdentify the null and alternative hypotheses for a difference of two population means.
CB.Stats.VAR-7.HVerify the conditions for the significance test for the difference of two population means.
CB.Stats.VAR-7.ICalculate an appropriate test statistic for a difference of two means.
CB.Stats.VAR-7.JIdentify the appropriate selection of a testing method for a slope of a regression model.
CB.Stats.VAR-7.KIdentify appropriate null and alternative hypotheses for a slope of a regression model.
CB.Stats.VAR-7.LVerify the conditions for the significance test for the slope of a regression model.
CB.Stats.VAR-7.MCalculate an appropriate test statistic for the slope of a regression model.
CB.Stats.VAR-8 Chi-square distributions and tests.
CB.Stats.VAR-8.ADescribe chi-square distributions.
CB.Stats.VAR-8.BIdentify the null and alternative hypotheses in a test for a distribution of proportions in a set of categorical data.
CB.Stats.VAR-8.CIdentify an appropriate testing method for a distribution of proportions in a set of categorical data.
CB.Stats.VAR-8.DCalculate expected counts for the chi-square test for goodness of fit.
CB.Stats.VAR-8.EVerify the conditions for making statistical inferences when testing goodness of fit for a chi-square distribution.
CB.Stats.VAR-8.FCalculate the appropriate statistic for the chi-square test for goodness of fit.
CB.Stats.VAR-8.GDetermine the p-value for the chi-square test for goodness of fit.
CB.Stats.VAR-8.HCalculate expected counts for two-way tables of categorical data.
CB.Stats.VAR-8.IIdentify the null and alternative hypotheses for a chi-square test for homogeneity or independence.
CB.Stats.VAR-8.JIdentify an appropriate testing method for comparing distributions in two-way tables of categorical data.
CB.Stats.VAR-8.KVerify the conditions for making statistical inferences when testing a chi-square distribution for independence or homogeneity.
CB.Stats.VAR-8.LCalculate the appropriate statistic for a chi-square test for homogeneity or independence.
CB.Stats.VAR-8.MDetermine the p-value for a chi-square test for independence or homogeneity.
CB.Stats.UNC Uncertainty and Inference
CB.Stats.UNC-1 Representing and describing categorical and quantitative data.
CB.Stats.UNC-1.ARepresent categorical data using frequency or relative frequency tables.
CB.Stats.UNC-1.BDescribe categorical data represented in frequency or relative tables.
CB.Stats.UNC-1.CRepresent categorical data graphically.
CB.Stats.UNC-1.DDescribe categorical data represented graphically.
CB.Stats.UNC-1.ECompare multiple sets of categorical data.
CB.Stats.UNC-1.FClassify types of quantitative variables.
CB.Stats.UNC-1.GRepresent quantitative data graphically.
CB.Stats.UNC-1.HDescribe the characteristics of quantitative data distributions.
CB.Stats.UNC-1.ICalculate measures of center and position for quantitative data.
CB.Stats.UNC-1.JCalculate measures of variability for quantitative data.
CB.Stats.UNC-1.KExplain the selection of a particular measure of center and/or variability for describing a set of quantitative data.
CB.Stats.UNC-1.LRepresent summary statistics for quantitative data graphically.
CB.Stats.UNC-1.MDescribe summary statistics of quantitative data represented graphically.
CB.Stats.UNC-1.NCompare graphical representations for multiple sets of quantitative data.
CB.Stats.UNC-1.OCompare summary statistics for multiple sets of quantitative data.
CB.Stats.UNC-1.PCompare numerical and graphical representations for two categorical variables.
CB.Stats.UNC-1.QCalculate statistics for two categorical variables.
CB.Stats.UNC-1.RCompare statistics for two categorical variables.
CB.Stats.UNC-1.SRepresent bivariate quantitative data using scatterplots.
CB.Stats.UNC-2 Probability and simulation.
CB.Stats.UNC-2.AEstimate probabilities using simulation.
CB.Stats.UNC-3 Random variables and sampling distributions.
CB.Stats.UNC-3.AEstimate probabilities of binomial random variables using data from a simulation.
CB.Stats.UNC-3.BCalculate probabilities for a binomial distribution.
CB.Stats.UNC-3.CCalculate parameters for a binomial distribution.
CB.Stats.UNC-3.DInterpret probabilities and parameters for a binomial distribution.
CB.Stats.UNC-3.ECalculate probabilities for geometric random variables.
CB.Stats.UNC-3.FCalculate parameters of a geometric distribution.
CB.Stats.UNC-3.GInterpret probabilities and parameters for a geometric distribution.
CB.Stats.UNC-3.HEstimate sampling distributions using simulation.
CB.Stats.UNC-3.IExplain why an estimator is or is not unbiased.
CB.Stats.UNC-3.JCalculate estimates for a population parameter.
CB.Stats.UNC-3.KDetermine parameters of a sampling distribution for sample proportions.
CB.Stats.UNC-3.LDetermine whether a sampling distribution for a sample proportion can be described as approximately normal.
CB.Stats.UNC-3.MInterpret probabilities and parameters for a sampling distribution for a sample proportion.
CB.Stats.UNC-3.NDetermine parameters of a sampling distribution for a difference in sample proportions.
CB.Stats.UNC-3.ODetermine whether a sampling distribution for a difference of sample proportions can be described as approximately normal.
CB.Stats.UNC-3.PInterpret probabilities and parameters for a sampling distribution for a difference in proportions.
CB.Stats.UNC-3.QDetermine parameters of a sampling distribution for a sample mean.
CB.Stats.UNC-3.RDetermine whether a sampling distribution of a sample mean can be described as approximately normal.
CB.Stats.UNC-3.SInterpret probabilities and parameters for a sampling distribution for a sample mean.
CB.Stats.UNC-3.TDetermine parameters of a sampling distribution for a difference in sample means.
CB.Stats.UNC-3.UDetermine whether a sampling distribution of a difference in sample means can be described as approximately normal.
CB.Stats.UNC-3.VInterpret probabilities and parameters for a sampling distribution for a difference in sample means.
CB.Stats.UNC-4 Confidence intervals for proportions and means.
CB.Stats.UNC-4.AIdentify an appropriate confidence interval procedure for a population proportion.
CB.Stats.UNC-4.BVerify the conditions for calculating confidence intervals for a population proportion.
CB.Stats.UNC-4.CDetermine the margin of error for a given sample size and an estimate for the sample size that will result in a given margin of error for a population proportion.
CB.Stats.UNC-4.DCalculate an appropriate confidence interval for a population proportion.
CB.Stats.UNC-4.ECalculate an interval estimate based on a confidence interval for a population proportion.
CB.Stats.UNC-4.FInterpret a confidence interval for a population proportion.
CB.Stats.UNC-4.GJustify a claim based on a confidence interval for a population proportion.
CB.Stats.UNC-4.HIdentify the relationships between sample size, width of a confidence interval, confidence level, and margin of error for a population proportion.
CB.Stats.UNC-4.IIdentify an appropriate confidence interval procedure for a comparison of population proportions.
CB.Stats.UNC-4.JVerify the conditions for calculating confidence intervals for a difference between population proportions.
CB.Stats.UNC-4.KCalculate an appropriate confidence interval for a comparison of population proportions.
CB.Stats.UNC-4.LCalculate an interval estimate based on a confidence interval for a difference of proportions.
CB.Stats.UNC-4.MInterpret a confidence interval for a difference of proportions.
CB.Stats.UNC-4.NJustify a claim based on a confidence interval for a difference of proportions.
CB.Stats.UNC-4.OIdentify an appropriate confidence interval procedure for a population mean, including the mean difference between values in matched pairs.
CB.Stats.UNC-4.PVerify the conditions for calculating confidence intervals for a population mean, including the mean difference between values in matched pairs.
CB.Stats.UNC-4.QDetermine the margin of error for a given sample size for a one-sample t-interval.
CB.Stats.UNC-4.RCalculate an appropriate confidence interval for a population mean, including the mean difference between values in matched pairs.
CB.Stats.UNC-4.SInterpret a confidence interval for a population mean, including the mean difference between values in matched pairs.
CB.Stats.UNC-4.TJustify a claim based on a confidence interval for a population mean, including the mean difference between values in matched pairs.
CB.Stats.UNC-4.UIdentify the relationships between sample size, width of a confidence interval, confidence level, and margin of error for a population mean.
CB.Stats.UNC-4.VIdentify an appropriate confidence interval procedure for a difference of two population means.
CB.Stats.UNC-4.WVerify the conditions for calculating confidence intervals for the difference of two population means.
CB.Stats.UNC-4.XDetermine the margin of error for the difference of two population means.
CB.Stats.UNC-4.YCalculate an appropriate confidence interval for a difference of two population means.
CB.Stats.UNC-4.ZInterpret a confidence interval for a difference of population means.
CB.Stats.UNC-5 Errors in statistical inference.
CB.Stats.UNC-5.AIdentify Type I and Type II errors.
CB.Stats.UNC-5.BCalculate the probability of a Type I and Type II errors.
CB.Stats.UNC-5.CIdentify factors that affect the probability of errors in significance testing.
CB.Stats.UNC-5.DInterpret Type I and Type II errors.
CB.Stats.DAT Data Analysis
CB.Stats.DAT-1 Bivariate data analysis and linear regression.
CB.Stats.DAT-1.ADescribe the characteristics of a scatter plot.
CB.Stats.DAT-1.BDetermine the correlation for a linear relationship.
CB.Stats.DAT-1.CInterpret the correlation for a linear relationship.
CB.Stats.DAT-1.DCalculate a predicted response value using a linear regression model.
CB.Stats.DAT-1.ERepresent differences between measured and predicted responses using residual plots.
CB.Stats.DAT-1.FDescribe the form of association of bivariate data using residual plots.
CB.Stats.DAT-1.GEstimate parameters for the least-squares regression line model.
CB.Stats.DAT-1.HInterpret coefficients for the least-squares regression line model.
CB.Stats.DAT-1.IIdentify influential points in regression.
CB.Stats.DAT-1.JCalculate a predicted response using a least-squares regression line for a transformed data set.
CB.Stats.DAT-2 Studies, sampling, and sources of bias.
CB.Stats.DAT-2.AIdentify the type of a study.
CB.Stats.DAT-2.BIdentify appropriate generalizations and determinations based on observational studies.
CB.Stats.DAT-2.CIdentify a sampling method, given a description of a study.
CB.Stats.DAT-2.DExplain why a particular sampling method is or is not appropriate for a given situation.
CB.Stats.DAT-2.EIdentify potential sources of bias in sampling methods.
CB.Stats.DAT-3 Interpreting and justifying conclusions from significance tests.
CB.Stats.DAT-3.AInterpret the p-value of a significance test for a population proportion.
CB.Stats.DAT-3.BJustify a claim about the population based on the results of a significance test for a population proportion.
CB.Stats.DAT-3.CInterpret the p-value of a significance test for a difference of population proportions.
CB.Stats.DAT-3.DJustify a claim about the population based on the results of a significance test for a difference of population proportions.
CB.Stats.DAT-3.EInterpret the p-value of a significance test for a population mean, including the mean difference between values in matched pairs.
CB.Stats.DAT-3.FJustify a claim about the population based on the results of a significance test for a population mean.
CB.Stats.DAT-3.GInterpret the p-value of a significance test for a difference of population means.
CB.Stats.DAT-3.HJustify a claim about the population based on the results of a significance test for a difference of two population means in context.
CB.Stats.DAT-3.IInterpret the p-value for the chi-square test for goodness of fit.
CB.Stats.DAT-3.JJustify a claim about the population based on the results of a chi-square test for goodness of fit.
CB.Stats.DAT-3.KInterpret the p-value for the chi-square test for homogeneity or independence.
CB.Stats.DAT-3.LJustify a claim about the population based on the results of a chi-square test for homogeneity or independence.
CB.Stats.DAT-3.MInterpret the p-value of a significance test for the slope of a regression model.
CB.Stats.DAT-3.NJustify a claim about the population based on the results of a significance test for the slope of a regression model.

Standards on this page are sourced from published state frameworks. Goblins aligns tutoring to these standards.