LEARN NC

K–12 teaching and learning · from the UNC School of Education

Advanced Functions and Modeling

All questions and comments about this curriculum should be directed to the North Carolina Department of Public Instruction.

Goal 1

Data Analysis and Probability - The learner will analyze data and apply probability concepts to solve problems.

Objective 1.01

Create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, and logarithmic functions of bivariate data to solve problems.

  • Interpret the constants, coefficients, and bases in the context of the data.
  • Check models for goodness-of-fit; use the most appropriate model to draw conclusions and make predictions.

Objective 1.02

Summarize and analyze univariate data to solve problems.

  • Apply and compare methods of data collection.
  • Apply statistical principles and methods in sample surveys.
  • Determine measures of central tendency and spread.
  • Recognize, define, and use the normal distribution curve.
  • Interpret graphical displays of univariate data.
  • Compare distributions of univariate data.

Objective 1.03

Use theoretical and experimental probability to model and solve problems.

  • Use addition and multiplication principles.
  • Calculate and apply permutations and combinations.
  • Create and use simulations for probability models.
  • Find expected values and determine fairness.
  • Identify and use discrete random variables to solve problems.
  • Apply the Binomial Theorem.

Goal 2

Algebra - The learner will use functions to solve problems.

Objective 2.01

Use logarithmic (common, natural) functions to model and solve problems; justify results.

  • Solve using tables, graphs, and algebraic properties.
  • Interpret the constants, coefficients, and bases in the context of the problem.

Objective 2.02

Use piecewise-defined functions to model and solve problems; justify results.

  • Solve using tables, graphs, and algebraic properties.
  • Interpret the constants, coefficients, and bases in the context of the problem.

Objective 2.03

Use power functions to model and solve problems; justify results.

  • Solve using tables, graphs, and algebraic properties.
  • Interpret the constants, coefficients, and bases in the context of the problem.

Objective 2.04

Use trigonometric (sine, cosine) functions to model and solve problems; justify results.

  • Solve using tables, graphs, and algebraic properties.
  • Create and identify transformations with respect to period, amplitude, and vertical and horizontal shifts.
  • Develop and use the law of sines and the law of cosines.

Objective 2.05

Use recursively-defined functions to model and solve problems.

  • Find the sum of a finite sequence.
  • Find the sum of an infinite sequence.
  • Determine whether a given series converges or diverges.
  • Translate between recursive and explicit representations.