### 12: Mathematics

#### 12.N: Number Sense and Operations

12.N.1: Define complex numbers (e.g., a + bi) and operations on them, in particular, addition, subtraction, multiplication, and division. Relate the system of complex numbers to the systems of real and rational numbers.

12.N.2: Simplify numerical expressions with powers and roots, including fractional and negative exponents.

#### 12.P: Patterns, Relations, and Algebra

12.P.4: Demonstrate an understanding of the trigonometric, exponential, and logarithmic functions.

12.P.5: Perform operations on functions, including composition. Find inverses of functions.

12.P.6: Given algebraic, numeric and/or graphical representations, recognize functions as polynomial, rational, logarithmic, exponential, or trigonometric.

12.P.7: Find solutions to quadratic equations (with real coefficients and real or complex roots) and apply to the solutions of problems.

12.P.8: Solve a variety of equations and inequalities using algebraic, graphical, and numerical methods, including the quadratic formula; use technology where appropriate. Include polynomial, exponential, logarithmic, and trigonometric functions; expressions involving absolute values; trigonometric relations; and simple rational expressions.

12.P.11: Solve everyday problems that can be modeled using polynomial, rational, exponential, logarithmic, trigonometric, and step functions, absolute values, and square roots. Apply appropriate graphical, tabular, or symbolic methods to the solution. Include growth and decay; joint (e.g., I = Prt, y = k(w log 1 + w log 2)) and combined (F = G(m log 1 x m log 2)/d²) variation, and periodic processes.

12.P.13: Describe the translations and scale changes of a given function f(x) resulting from substitutions for the various parameters a, b, c, and d in y = af (b(x + c/b)) + d. In particular, describe the effect of such changes on polynomial, rational, exponential, logarithmic, and trigonometric functions.

#### 12.G: Geometry

12.G.1: Define the sine, cosine, and tangent of an acute angle. Apply to the solution of problems.

12.G.3: Use the notion of vectors to solve problems. Describe addition of vectors and multiplication of a vector by a scalar, both symbolically and geometrically. Use vector methods to obtain geometric results.

12.G.4: Relate geometric and algebraic representations of lines, simple curves, and conic sections.

12.G.5: Apply properties of angles, parallel lines, arcs, radii, chords, tangents, and secants to solve problems.

#### 12.M: Measurement

12.M.1: Describe the relationship between degree and radian measures, and use radian measure in the solution of problems, in particular, problems involving angular velocity and acceleration.

#### 12.D: Data Analysis, Statistics, and Probability

12.D.1: Design surveys and apply random sampling techniques to avoid bias in the data collection.

12.D.2: Select an appropriate graphical representation for a set of data and use appropriate statistics (e.g., quartile or percentile distribution) to communicate information about the data.

12.D.3: Apply regression results and curve fitting to make predictions from data.

12.D.4: Apply uniform, normal, and binomial distributions to the solutions of problems.

12.D.5: Describe a set of frequency distribution data by spread (i.e., variance and standard deviation), skewness, symmetry, number of modes, or other characteristics. Use these concepts in everyday applications.

12.D.6: Use combinatorics (e.g., "fundamental counting principle," permutations, and combinations) to solve problems, in particular, to compute probabilities of compound events. Use technology as appropriate.

12.D.7: Compare the results of simulations (e.g., random number tables, random functions, and area models) with predicted probabilities.

### AII: Algebra II

#### AII.N: Number Sense and Operations

AII.N.1: Define complex numbers (e.g., a + bi) and operations on them, in particular, addition, subtraction, multiplication, and division. Relate the system of complex numbers to the systems of real and rational numbers.

AII.N.2: Simplify numerical expressions with powers and roots, including fractional and negative exponents.

#### AII.P: Patterns, Relations, and Algebra

AII.P.4: Demonstrate an understanding of the exponential and logarithmic functions.

AII.P.5: Perform operations on functions, including composition. Find inverses of functions.

AII.P.6: Given algebraic, numeric and/or graphical representations, recognize functions as polynomial, rational, logarithmic, or exponential.

AII.P.7: Find solutions to quadratic equations (with real coefficients and real or complex roots) and apply to the solutions of problems.

AII.P.8: Solve a variety of equations and inequalities using algebraic, graphical, and numerical methods, including the quadratic formula; use technology where appropriate. Include polynomial, exponential, and logarithmic functions; expressions involving the absolute values; and simple rational expressions.

AII.P.9: Use matrices to solve systems of linear equations. Apply to the solution of everyday problems.

AII.P.11: Solve everyday problems that can be modeled using polynomial, rational, exponential, logarithmic, and step functions, absolute values and square roots. Apply appropriate graphical, tabular, or symbolic methods to the solution. Include growth and decay; logistic growth; joint (e.g., I = Prt, y = k(w log 1 + w log 2)), and combined (F = G(m log 1 x m log 2)/d²) variation.

AII.P.13: Describe the translations and scale changes of a given function f(x) resulting from substitutions for the various parameters a, b, c, and d in y = af (b(x + c/b)) + d. In particular, describe the effect of such changes on polynomial, rational, exponential, and logarithmic functions.

#### AII.G: Geometry

AII.G.1: Define the sine, cosine, and tangent of an acute angle. Apply to the solution of problems.

AII.G.3: Relate geometric and algebraic representations of lines, simple curves, and conic sections.

#### AII.D: Data Analysis, Statistics, and Probability

AII.D.1: Select an appropriate graphical representation for a set of data and use appropriate statistics (e.g., quartile or percentile distribution) to communicate information about the data.

AII.D.2: Use combinatorics (e.g., "fundamental counting principle," permutations, and combinations) to solve problems, in particular, to compute probabilities of compound events. Use technology as appropriate.

### PC: Precalculus

#### PC.N: Number Sense and Operations

PC.N.1: Plot complex numbers using both rectangular and polar coordinates systems. Represent complex numbers using polar coordinates, i.e., a + bi = r (cos theta + i sin theta). Apply DeMoivre's theorem to multiply, take roots, and raise complex numbers to a power.

#### PC.P: Patterns, Relations, and Algebra

PC.P.2: Relate the number of roots of a polynomial to its degree. Solve quadratic equations with complex coefficients.

PC.P.3: Demonstrate an understanding of the trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent). Relate the functions to their geometric definitions.

PC.P.8: Identify and discuss features of conic sections: axes, foci, asymptotes, and tangents. Convert between different algebraic representations of conic sections.

PC.P.9: Relate the slope of a tangent line at a specific point on a curve to the instantaneous rate of change. Explain the significance of a horizontal tangent line. Apply these concepts to the solution of problems.

#### PC.G: Geometry

PC.G.2: Use the notion of vectors to solve problems. Describe addition of vectors, multiplication of a vector by a scalar, and the dot product of two vectors, both symbolically and geometrically. Use vector methods to obtain geometric results.

PC.G.3: Apply properties of angles, parallel lines, arcs, radii, chords, tangents, and secants to solve problems.

#### PC.M: Measurement

PC.M.1: Describe the relationship between degree and radian measures, and use radian measure in the solution of problems, in particular problems involving angular velocity and acceleration.

#### PC.D: Data Analysis, Statistics, and Probability

PC.D.1: Design surveys and apply random sampling techniques to avoid bias in the data collection.

PC.D.2: Apply regression results and curve fitting to make predictions from data.

PC.D.3: Apply uniform, normal, and binomial distributions to the solutions of problems.

PC.D.4: Describe a set of frequency distribution data by spread (variance and standard deviation), skewness, symmetry, number of modes, or other characteristics. Use these concepts in everyday applications.

Correlation last revised: 5/14/2018

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.