North Carolina

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Skills available for North Carolina high school math standards

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North Carolina Standard Course of Study: Discrete Math for Computer Science North Carolina Standard Course of Study: Discrete Math for Computer Science
North Carolina Standard Course of Study: Math 4 North Carolina Standard Course of Study: Math 4
North Carolina Standard Course of Study: Precalculus North Carolina Standard Course of Study: Precalculus
North Carolina Standard Course of Study: Advanced Functions and Modeling North Carolina Standard Course of Study: Advanced Functions and Modeling
North Carolina Standard Course of Study: Math 1 North Carolina Standard Course of Study: Math 1
North Carolina Standard Course of Study: Math 2 North Carolina Standard Course of Study: Math 2
North Carolina Standard Course of Study: Math 3 North Carolina Standard Course of Study: Math 3

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Data Analysis and Probability

1 The learner will analyze data and apply probability concepts to solve problems.
- 1.01 Create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, and logarithmic functions of bivariate data to solve problems.
  - Find the equation of a regression line (PC-Z.8)
  - Analyze a regression line of a data set (PC-Z.10)
  - 1.01.a Interpret the constants, coefficients, and bases in the context of the data.
  - 1.01.b Check models for goodness-of-fit; use the most appropriate model to draw conclusions and make predictions.
- 1.02 Summarize and analyze univariate data to solve problems.
  - 1.02.a Apply and compare methods of data collection.
  - 1.02.b Apply statistical principles and methods in sample surveys.
    - Identify biased samples (PC-Z.1)
    - Experiment design (PC-Z.15)
  - 1.02.c Determine measures of central tendency and spread.
  - 1.02.d Recognize, define, and use the normal distribution curve.
    - Find z-values (PC-Y.14)
    - Find values of normal variables (PC-Y.15)
  - 1.02.e Interpret graphical displays of univariate data.
  - 1.02.f Compare distributions of univariate data.
- 1.03 Use theoretical and experimental probability to model and solve problems.
  - 1.03.a Use addition and multiplication principles.
  - 1.03.b Calculate and apply permutations and combinations.
  - 1.03.c Create and use simulations for probability models.
    - Find probabilities using two-way frequency tables (PC-X.5)
    - Find conditional probabilities using two-way frequency tables (PC-X.9)
  - 1.03.d Find expected values and determine fairness.
  - 1.03.e Identify and use discrete random variables to solve problems.
  - 1.03.f Apply the Binomial Theorem.
    - Binomial Theorem I (PC-D.19)
    - Binomial Theorem II (PC-D.20)

Functions

2 The learner will use functions to solve problems.
- 2.01 Use logarithmic (common, natural) functions to model and solve problems; justify results.
  - 2.01.a Solve using tables, graphs, and algebraic properties.
  - 2.01.b Interpret the constants, coefficients, and bases in the context of the problem.
    - Domain and range of exponential and logarithmic functions (PC-F.1)
    - Describe linear and exponential growth and decay (PC-F.15)
- 2.02 Use piecewise-defined functions to model and solve problems; justify results.
  - 2.02.a Solve using tables, graphs, and algebraic properties.
    - Determine the continuity of a piecewise function at a point (C-I.6)
    - Make a piecewise function continuous (C-I.7)
  - 2.02.b Interpret the constants, coefficients, and bases in the context of the problem.
- 2.03 Use power functions to model and solve problems; justify results.
  - 2.03.a Solve using tables, graphs, and algebraic properties.
  - 2.03.b Interpret the constants, coefficients, and bases in the context of the problem.
- 2.04 Use trigonometric (sine, cosine) functions to model and solve problems; justify results.
  - 2.04.a Solve using tables, graphs, and algebraic properties.
  - 2.04.b Create and identify transformations with respect to period, amplitude, and vertical and horizontal shifts.
  - 2.04.c Develop and use the law of sines and the law of cosines.
    - Law of Sines (PC-M.15)
    - Law of Cosines (PC-M.16)
- 2.05 Use recursively-defined functions to model and solve problems.
  - 2.05.a Find the sum of a finite sequence.
    - Find the sum of a finite geometric series (PC-W.12)
  - 2.05.b Find the sum of an infinite sequence.
    - Find the value of an infinite geometric series (PC-W.18)
  - 2.05.c Determine whether a given series converges or diverges.
    - Convergent and divergent geometric series (PC-W.17)
  - 2.05.d Translate between recursive and explicit representations.

North Carolina

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Data Analysis and Probability

1 The learner will analyze data and apply probability concepts to solve problems.

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

1.01.a Interpret the constants, coefficients, and bases in the context of the data.

1.01.b Check models for goodness-of-fit; use the most appropriate model to draw conclusions and make predictions.

1.02 Summarize and analyze univariate data to solve problems.

1.02.a Apply and compare methods of data collection.

1.02.b Apply statistical principles and methods in sample surveys.

1.02.c Determine measures of central tendency and spread.

1.02.d Recognize, define, and use the normal distribution curve.

1.02.e Interpret graphical displays of univariate data.

1.02.f Compare distributions of univariate data.

1.03 Use theoretical and experimental probability to model and solve problems.

1.03.a Use addition and multiplication principles.

1.03.b Calculate and apply permutations and combinations.

1.03.c Create and use simulations for probability models.

1.03.d Find expected values and determine fairness.

1.03.e Identify and use discrete random variables to solve problems.

1.03.f Apply the Binomial Theorem.

Functions

2 The learner will use functions to solve problems.

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

2.01.a Solve using tables, graphs, and algebraic properties.

2.01.b Interpret the constants, coefficients, and bases in the context of the problem.

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

2.02.a Solve using tables, graphs, and algebraic properties.

2.02.b Interpret the constants, coefficients, and bases in the context of the problem.

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

2.03.a Solve using tables, graphs, and algebraic properties.

2.03.b Interpret the constants, coefficients, and bases in the context of the problem.

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

2.04.a Solve using tables, graphs, and algebraic properties.

2.04.b Create and identify transformations with respect to period, amplitude, and vertical and horizontal shifts.

2.04.c Develop and use the law of sines and the law of cosines.

2.05 Use recursively-defined functions to model and solve problems.

2.05.a Find the sum of a finite sequence.

2.05.b Find the sum of an infinite sequence.

2.05.c Determine whether a given series converges or diverges.

2.05.d Translate between recursive and explicit representations.