North Carolina State Standards for Mathematics: Grade 12

NC.IM. Introductory Mathematics

1 The learner will understand and compute with real numbers.

1.01. Develop number sense for the real numbers.

1.01.a. Define and use irrational numbers.

1.01.b. Compare and order.

1.01.c. Use estimates of irrational numbers in appropriate situations.

1.02. Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.

2 The learner will use properties and relationships in geometry and measurement concepts to solve problems.

2.01. Determine the effect on perimeter, area or volume when one or more dimensions of two- and three-dimensional figures are changed.

2.02. Apply and use concepts of indirect measurement.

2.03. Represent problem situations with geometric models.

2.04. Apply geometric properties and relationships, including the Pythagorean theorem, to solve problems.

2.05. Identify, predict, and describe dilations in the coordinate plane.

3 The learner will understand and use graphs and data analysis.

3.01. Collect, organize, analyze, and display data (including scatterplots) to solve problems.

3.02. Approximate a line of best fit for a given scatterplot; explain the meaning of the line as it relates to the problem and make predictions.

3.03. Identify misuses of statistical and numerical data.

4 The learner will understand and use linear relations and functions.

4.01. Develop an understanding of function.

4.01.a. Translate among verbal, tabular, graphic, and algebraic representations of functions.

4.01.b. Identify relations and functions as linear or nonlinear.

4.01.c. Find, identify, and interpret the slope (rate of change) and intercepts of a linear relation.

4.01.d. Interpret and compare properties of linear functions from tables, graphs, or equations.

4.02. Write an equation of a linear relationship given: two points, the slope and one point on the line, or the slope and y-intercept.

4.03. Solve problems using linear equations and inequalities; justify symbolically and graphically.

4.04. Solve problems using the inverse relationships of addition and subtraction, multiplication and division, squares and square roots, and cubes and cube roots.

NC.AI. Algebra I

1.03. Model and solve problems using direct variation.

3.03.a. Interpret constants and coefficients in the context of the data.

3.03.b. Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.

NC.G. Geometry

2.03.a. Triangles.

2.03.b. Quadrilaterals.

2.03.c. Other polygons.

2.03.d. Circles.

NC.AII. Algebra II

1.04. Operate with matrices to model and solve problems.

1.05. Model and solve problems using direct, inverse, combined and joint variation.

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

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

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

2.04.b. Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.

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

2.05.b. Interpret the constants and coefficients in the context of the problem.

2.05.c. Identify the asymptotes and intercepts graphically and algebraically.

2.06. Use cubic equations to model and solve problems.

2.06.a. Solve using tables and graphs.

2.06.b. Interpret constants and coefficients in the context of the problem.

2.07. Use equations with radical expressions to model and solve problems; justify results.

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

2.07.b. Interpret the degree, constants, and coefficients in the context of the problem.

2.08. Use equations and inequalities with absolute value to model and solve problems; justify results.

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

2.08.b. Interpret the constants and coefficients in the context of the problem.

2.09. Use the equations of parabolas and circles to model and solve problems; justify results.

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

2.09.b. Interpret the constants and coefficients in the context of the problem.

2.10. Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix operations, and algebraic properties.

NC.TMI. Technical Mathematics I

1.01.d. Choose or create appropriate representations of two- and three-dimensional figures.

NC.TMII. Technical Mathematics II

1.02.a. Triangles.

1.02.b. Quadrilaterals.

1.02.c. Other polygons.

1.02.d. Circles.

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

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

NC.AFM. Advanced Functions and Modeling (AFM)

1.02.e. Interpret graphical displays of univariate data.

1.02.f. Compare distributions of univariate data.

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.

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

2.05.d. Translate between recursive and explicit representations.

NC.DM. Discrete Mathematics

2.01.c. Determine measures of central tendency and spread.

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

2.01.e. Interpret graphical displays of data.

2.01.f. Compare distributions of data.

2.02.c. Create and use simulations for probability models.

2.02.d. Find expected values and determine fairness.

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

2.02.f. Apply the Binomial Theorem.

3.01.a. Find the sum of a finite sequence.

3.01.b. Find the sum of an infinite sequence.

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

3.01.d. Write explicit definitions using iterative processes, including finite differences and arithmetic and geometric formulas.

3.01.e. Verify an explicit definition with inductive proof.

NC.PC. Pre-Calculus

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

2.07.d. Translate between recursive and explicit representations.

NC.IMI. Integrated Mathematics I

3.02.a. Use addition and multiplication principles.

3.02.b. Calculate and apply permutations and combinations.

3.02.c. Create and use simulations for probability models.

3.02.d. Find expected values and determine fairness.

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

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

NC.IMII. Integrated Mathematics II

3.01.f. Compare distributions of data.

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

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

NC.IMIII. Integrated Mathematics III

3.03.c. Identify the asymptotes and intercepts graphically and algebraically.

3.04. Use equations and inequalities with absolute value to model and solve problems; justify results.

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

3.04.b. Interpret the constants and coefficients in the context of the problem.

3.05. Transform functions in two dimensions; describe the results algebraically and geometrically.

NC.IMIV. Integrated Mathematics IV

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

4.02.d. Translate between recursive and explicit representations.

4.04.a. Solve using graphs and algebraic properties.

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

4.05. Use polar equations to model and solve problems.

4.05.a. Solve using graphs and algebraic properties.

4.05.b. Interpret the constants and coefficients in the context of the problem.

4.06. Use parametric equations to model and solve problems.

4.07. Find the rate of change at any point of a function.

NC.APS. Advanced Placement Statistics

3.06. Use normal distributions as a model for distribution.

3.06.a. Investigate the properties of the normal distribution.

3.06.b. Use the table of standard normal distribution (Z).

3.07. Simulate sampling distributions.

3.08. Use simulations to develop an understanding of the Central Limit Theorem and its importance in confidence intervals and tests of significance.

3.09. Recognize, construct and interpret results using confidence intervals in the context of a problem.

3.10. Perform tests of significance and interpret results in the context of a problem.

NC.APC. Advanced Placement Calculus

2.06.c. Model rates of change, including related rates problems.

2.06.d. Use implicit differentiation to find the derivative of an inverse function.

2.06.e. Interpret the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration.

2.06.f. Interpret differential equations geometrically via slope fields and the relationship between slope fields and solution curves for differential equations.

3.04.c. Set up and use an approximating Riemann sum or trapezoidal sum and represent its limit as a definite integral.

3.04.d. Find the area of a region.

3.04.e. Find the volume of a solid with known cross sections.

3.04.f. Find the average value of a function.

3.04.g. Find the distance traveled by a particle along a line.

3.04.h. Solve separable differential equations and use them in modeling. In particular, study the equation y' = ky and exponential growth.