PC.N: Number and Quantity

PC.N.1: Apply properties of complex numbers and the complex number system.

PC.N.1.1: Execute the sum and difference algorithms to combine complex numbers.

Points in the Complex Plane

PC.N.1.2: Execute the multiplication algorithm with complex numbers.

Points in the Complex Plane

PC.N.2: Apply properties and operations with matrices.

PC.N.2.1: Execute the sum and difference algorithms to combine matrices of appropriate dimensions.

Translations

PC.N.2.4: Execute properties of matrices to multiply a matrix by a scalar.

Dilations

PC.N.3: Understand properties and operations with vectors.

PC.N.3.1: Represent a vector indicating magnitude and direction.

Adding Vectors
Vectors

PC.N.3.2: Execute sum and difference algorithms to combine vectors.

Adding Vectors
Vectors

PC.A: Algebra

PC.A.1: Apply properties of solving inequalities that include rational and polynomial expressions in one variable.

PC.A.1.1: Implement algebraic (sign analysis) methods to solve rational and polynomial inequalities.

Quadratic Inequalities

PC.A.1.2: Implement graphical methods to solve rational and polynomial inequalities.

Quadratic Inequalities

PC.A.2: Apply properties of solving equations involving exponential, logarithmic, and trigonometric functions.

PC.A.2.1: Use properties of logarithms to rewrite expressions.

Cosine Function
Sine Function
Tangent Function

PC.A.2.2: Implement properties of exponentials and logarithms to solve equations.

Cosine Function
Sine Function
Tangent Function

PC.F: Functions

PC.F.2: Apply properties of a unit circle with center (0,0) to determine the values of sine, cosine, tangent, cotangent, secant, and cosecant.

PC.F.2.1: Use a unit circle to find values of sine, cosine, and tangent for angles in terms of reference angles.

Cosine Function
Sine Function
Tangent Function

PC.F.2.2: Explain the relationship between the symmetry of a unit circle and the periodicity of trigonometric functions.

Cosine Function
Sine Function
Tangent Function

PC.F.3: Apply properties of trigonometry to solve problems involving all types of triangles.

PC.F.3.3: Implement the Pythagorean identity to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle.

Cosine Function
Sine Function

PC.F.4: Understand the relationship of algebraic and graphical representations of exponential, logarithmic, rational, power functions, and conic sections to their key features.

PC.F.4.1: Interpret algebraic and graphical representations to determine key features of exponential functions. Key features include: domain, range, intercepts, intervals where the function is increasing, decreasing, positive or negative, concavity, end behavior, limits, and asymptotes.

Exponential Functions
Introduction to Exponential Functions

PC.F.4.2: Integrate information to build exponential functions to model phenomena involving growth or decay.

Exponential Growth and Decay

PC.F.4.3: Interpret algebraic and graphical representations to determine key features of logarithmic functions. Key features include: domain, range, intercepts, intervals where the function is increasing, decreasing, positive or negative, concavity, end behavior, continuity, limits, and asymptotes.

Logarithmic Functions
Logarithmic Functions: Translating and Scaling

PC.F.4.4: Implement graphical and algebraic methods to solve exponential and logarithmic equations in context with support from technology.

Logarithmic Functions

PC.F.4.5: Interpret algebraic and graphical representations to determine key features of rational functions. Key features include: domain, range, intercepts, intervals where the function is increasing, decreasing, positive or negative, concavity, end behavior, continuity, limits, and asymptotes.

General Form of a Rational Function
Rational Functions

PC.F.4.7: Construct graphs of transformations of power, exponential, and logarithmic functions showing key features.

Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions: Translating and Scaling

PC.F.4.8: Identify the conic section (ellipse, hyperbola, parabola) from its algebraic representation in standard form.

Ellipses
Hyperbolas
Parabolas
Quadratics in Vertex Form

PC.F.4.9: Interpret algebraic and graphical representations to determine key features of conic sections (ellipse: center, length of the major and minor axes; hyperbola: vertices, transverse axis; parabola: vertex, axis of symmetry).

Ellipses
Hyperbolas
Parabolas
Quadratics in Vertex Form

PC.F.6: Apply mathematical reasoning to build recursive functions to model and solve problems.

PC.F.6.1: Use algebraic representations to build recursive functions.

Arithmetic Sequences
Geometric Sequences

PC.F.6.2: Construct a recursive function for a sequence represented numerically.

Arithmetic Sequences
Geometric Sequences