# Pennsylvania Core Standards in Mathematics — Grade 12

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#### CC.2.1.HS.F.1

Apply and extend the properties of exponents to solve problems with rational exponents. A1.1.1.1.1, A1.1.1.1.2, A1.1.1.3.1, A2.1.2.1.1, A2.1.2.1.2, A2.1.2.1.3, A2.1.2.1.4

#### CC.2.1.HS.F.2

Apply properties of rational and irrational numbers to solve real world or mathematical problems. A1.1.1.1.1, A1.1.1.1.2, A1.1.1.3.1, A1.1.1.2.1

#### CC.2.1.HS.F.3

Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays. A1.1.2.1.1, A1.1.2.1.2, A1.1.2.1.3, A1.2.1.2.1, A1.2.1.2.2, A2.2.2.1.1, A2.2.2.1.2, A2.2.3.1.1, A2.2.3.1.2

#### CC.2.1.HS.F.4

Use units as a way to understand problems and to guide the solution of multi-step problems. A1.1.2.1.1, A1.1.2.1.2, A1.1.2.1.3, A1.2.1.2.1, A1.2.1.2.2, A2.2.2.1.1, A2.2.2.1.2

#### CC.2.1.HS.F.5

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. A1.1.2.1.1, A1.1.2.1.2, A1.1.2.1.3, A1.1.2.2.1, A1.1.2.2.2, A1.1.3.1.1, A1.1.3.1.2, A1.1.3.1.3, A1.1.3.2.1, A1.1.3.2.2, A2.2.3.1.1, A2.2.3.1.2

#### CC.2.1.HS.F.6

Extend the knowledge of arithmetic operations and apply to complex numbers.

#### CC.2.1.HS.F.7

Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems.

#### CC.2.2.HS.C.1

Use the concept and notation of functions to interpret and apply them in terms of their context.

#### CC.2.2.HS.C.2

Graph and analyze functions and use their properties to make connections between the different representations.

#### CC.2.2.HS.C.3

Write functions or sequences that model relationships between two quantities.

#### CC.2.2.HS.C.4

Interpret the effects transformations have on functions and find the inverses of functions

#### CC.2.2.HS.C.5

Construct and compare linear, quadratic, and exponential models to solve problems.

#### CC.2.2.HS.C.6

Interpret functions in terms of the situations they model.

#### CC.2.2.HS.C.7

Apply radian measure of an angle and the unit circle to analyze the trigonometric functions.

#### CC.2.2.HS.C.8

Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs.

#### CC.2.2.HS.C.9

Prove the Pythagorean identity and use it to calculate trigonometric ratios.

#### CC.2.2.HS.D.1

Interpret the structure of expressions to represent a quantity in terms of its context

#### CC.2.2.HS.D.10

Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

#### CC.2.2.HS.D.2

Write expressions in equivalent forms to solve problems.

#### CC.2.2.HS.D.3

Extend the knowledge of arithmetic operations and apply to polynomials.

#### CC.2.2.HS.D.4

Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs.

#### CC.2.2.HS.D.5

Use polynomial identities to solve problems

#### CC.2.2.HS.D.6

Extend the knowledge of rational functions to rewrite in equivalent forms.

#### CC.2.2.HS.D.7

Create and graph equations or inequalities to describe numbers or relationships.

#### CC.2.2.HS.D.8

Apply inverse operations to solve equations or formulas for a given variable.

#### CC.2.2.HS.D.9

Use reasoning to solve equations and justify the solution method.

#### CC.2.3.HS.A.1

Use geometric figures and their properties to represent transformations in the plane.

#### CC.2.3.HS.A.10

Translate between the geometric description and the equation for a conic section.

#### CC.2.3.HS.A.11

Apply coordinate geometry to prove simple geometric theorems algebraically.

#### CC.2.3.HS.A.12

Explain volume formulas and use them to solve problems.

#### CC.2.3.HS.A.13

Analyze relationships between two-dimensional and three-dimensional objects.

#### CC.2.3.HS.A.14

Apply geometric concepts to model and solve real world problems.

#### CC.2.3.HS.A.2

Apply rigid transformations to determine and explain congruence.

#### CC.2.3.HS.A.3

Verify and apply geometric theorems as they relate to geometric figures.

#### CC.2.3.HS.A.4

Apply the concept of congruence to create geometric constructions.

#### CC.2.3.HS.A.5

Create justifications based on transformations to establish similarity of plane figures.

#### CC.2.3.HS.A.6

Verify and apply theorems involving similarity as they relate to plane figures.

#### CC.2.3.HS.A.7

Apply trigonometric ratios to solve problems involving right triangles.

#### CC.2.3.HS.A.8

Apply geometric theorems to verify properties of circles.

#### CC.2.3.HS.A.9

Extend the concept of similarity to determine arc lengths and areas of sectors of circles.

#### CC.2.4.HS.B.1

Summarize, represent, and interpret data on a single count or measurement variable.

#### CC.2.4.HS.B.2

Summarize, represent, and interpret data on two categorical and quantitative variables.

#### CC.2.4.HS.B.3

Analyze linear models to make interpretations based on the data.

#### CC.2.4.HS.B.4

Recognize and evaluate random processes underlying statistical experiments.

#### CC.2.4.HS.B.5

Make inferences and justify conclusions based on sample surveys, experiments, and observational studies.

#### CC.2.4.HS.B.6

Use the concepts of independence and conditional probability to interpret data.

#### CC.2.4.HS.B.7

Apply the rules of probability to compute probabilities of compound events in a uniform probability model.