Released Test
Math III

Math III


Math II and Math III


Major Work of NC Local Option Math II


High School

Major Clusters
Supporting/Additional Clusters
The Real Number System
  • Extend the properties of exponents to rational exponents.

Quantities
  • Reason quantitatively and use units to solve problems.

Seeing the Structure in Expressions
  • Interpret the structure of expressions.
  • Write expressions in equivalent forms to solve problems. 


Arithmetic with Polynomials and Rational Expressions
  • Understand the relationship between zeros and factors of polynomials.

Creating Equations
  • Create equations that describe numbers or relationships.

Reasoning with Equations and Inequalities
  • Understand solving equations as a process of reasoning and explain the reasoning.
  • Represent and solve equations and inequalities graphically.

Interpreting Functions
  • Understand the concept of a function and understand function notation.
  • Interpret functions that arise in applications in terms of the context.
  • Analyze functions using different representations.

Building Functions
  • Build a function that models a relationship between two quantities.


Congruence
  • Prove geometric theorems.
Similarity, Right Triangles, and Trigonometry
  • Define trigonometric ratios and solve problems involving right triangles.

Modeling with Geometry
  • Apply geometric concepts in modeling situations.
Making Inferences and Justifying Conclusions
  • Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
Arithmetic with Polynomials and Rational Expressions
  • Perform arithmetic operations on polynomials.

Reasoning with Equations and Inequalities
  • Solve equations and inequalities in one variable.
  • Solve systems of equations.

Building Functions
  • Build new functions from existing functions.

Congruence
  • Experiment with transformations in the plane.
  • Understand congruence in terms of rigid motions.
  • Make geometric constructions.


Similarity, Right Triangles, and Trigonometry
  • Apply trigonometry to general triangles.

Expressing Geometric Properties with Equations
  • Translate between the geometric description and the equation for a conic section. (Here because of circles.)


Geometric Measurement and Dimension
  • Visualize relationships between two‐dimensional and three‐dimensional objects.

Making Inferences and Justifying Conclusions
  • Understand and evaluate random processes underlying statistical experiments.

Conditional Probability and the Rules of Probability
  • Understand independence and conditional probability and use them to interpret data.
  • Use the rules of probability to compute probabilities of compound events in a uniform probability model.


Major Work of NC Local Option Math III



High School

Major Clusters
Supporting/Additional Clusters
Quantities
  • Reason quantitatively and use units to solve problems.

Seeing the Structure in Expressions
  • Interpret the structure of expressions.
  • Write expressions in equivalent forms to solve problems. 


Arithmetic with Polynomials and Rational Expressions
  • Understand the relationship between zeros and factors of polynomials.

Creating Equations
  • Create equations that describe numbers or relationships.

Reasoning with Equations and Inequalities
  • Understand solving equations as a process of reasoning and explain the reasoning.
  • Represent and solve equations and inequalities graphically.

Interpreting Functions
  • Understand the concept of a function and understand function notation.
  • Interpret functions that arise in applications in terms of the context.
  • Analyze functions using different representations.



Building Functions
  • Build a function that models a relationship between two quantities.

Linear, Quadratic and Exponential Models
  • Construct and compare linear, quadratic, and exponential models and solve problems.

Congruence
  • Prove geometric theorems.
Modeling with Geometry
  • Apply geometric concepts in modeling situations.
Interpreting Categorical and Quantitative Data
  • Summarize, represent, and interpret data on a single count or measurement variable.

Making Inferences and Justifying Conclusions
  • Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
The Real Number System
  • Use properties of rational and irrational numbers.

The Complex Number System
  • Perform arithmetic operations with complex numbers.
  • Use complex numbers in polynomial identities and equations.

Arithmetic with Polynomials and Rational Expressions
  • Perform arithmetic operations on polynomials.
  • Use polynomial identities to solve problems.
  • Rewrite rational expressions.

Reasoning with Equations andInequalities
  • Solve equations and inequalities in one variable.

Building Functions
  • Build new functions from existing functions.

Trigonometric Functions
  • Extend the domain of trigonometric functions using the unit circle.
  • Model periodic phenomena with trigonometric functions.
  • Prove and apply trigonometric identities.


Congruence
  • Experiment with transformations in the plane.
  • Make geometric constructions.


Similarity, Right Triangles, and Trigonometry
  • Understand similarity in terms of similarity transformations.
  • Prove theorems involving similarity.

Expressing Geometric Properties with Equations
  • Translate between the geometric description and the equation for a conic section. (Here because of circles.)

Circles
  • Understand and apply theorems about circles.
  • Find arc lengths and areas of sectors of circles. 


Making Inferences and Justifying Conclusions
  • Understand and evaluate random processes underlying statistical experiments.

Using Probability to Make Decisions
  • Use probability to evaluate outcomes of decisions.