MA2A1: Students will explore exponential functions.

MA2A1.a: Extend properties of exponents to include all integer exponents.

Dividing Exponential Expressions
Exponents and Power Rules

MA2A1.b: Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B

MA2A1.c: Graph functions as transformations of f(x) = a to the x power.

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Translating and Scaling Functions

MA2A1.d: Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

MA2A1.e: Understand and use basic exponential functions as models of real phenomena.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Half-life

MA2A1.f: Understand and recognize geometric sequences as exponential functions with domains that are sets of whole numbers.

Arithmetic and Geometric Sequences
Exponential Functions - Activity A
Geometric Sequences

MA2A1.g: Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.

Arithmetic and Geometric Sequences
Exponential Functions - Activity A
Geometric Sequences

MA2A2: Students will explore inverses of functions.

MA2A2.a: Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

Function Machines 3 (Functions and Problem Solving)

MA2A2.b: Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including the use of restricted domains.

Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic

MA2A2.c: Explore the graphs of functions and their inverses.

Cosine Function
Fourth-Degree Polynomials - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Translating and Scaling Functions

MA2A2.d: Use composition to verify that functions are inverses of each other.

Function Machines 3 (Functions and Problem Solving)

MA2A3: Students will analyze graphs of polynomial functions of higher degree.

MA2A3.a: Graph simple polynomial functions as translations of the function f(x) = ax to the n power.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Polynomials and Linear Factors
Translating and Scaling Functions

MA2A3.b: Understand the effects of the following on the graph of a polynomial function: degree, lead coefficient, and multiplicity of real zeros.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Parabolas - Activity A
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Translating and Scaling Functions

MA2A3.c: Determine whether a polynomial function has symmetry and whether it is even, odd, or neither.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A

MA2A3.d: Investigate and explain characteristics of polynomial functions, including domain and range, intercepts, zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Polynomials and Linear Factors

MA2A4: Students will explore logarithmic functions as inverses of exponential functions.

MA2A4.c: Define logarithmic functions as inverses of exponential functions.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Function Machines 3 (Functions and Problem Solving)
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

MA2A4.e: Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

MA2A4.g: Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Half-life
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

MA2A5: Students will solve a variety of equations and inequalities.

MA2A5.a: Find real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem, and fundamental theorem of algebra, incorporating complex and radical conjugates.

Dividing Polynomials Using Synthetic Division
Roots of a Quadratic

MA2A5.c: Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

MA2A5.d: Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology.

Modeling and Solving Two-Step Equations
Solving Two-Step Equations

MA2A7: Students will use matrices to formulate and solve problems.

MA2A7.c: Represent and solve realistic problems using systems of linear equations.

Modeling Linear Systems - Activity A
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

MA2A8: Students will solve linear programming problems in two variables.

MA2A8.a: Solve systems of inequalities in two variables, showing the solutions graphically.

Modeling Linear Systems - Activity A
Systems of Linear Inequalities (Slope-intercept form) - Activity A

MA2A8.b: Represent and solve realistic problems using linear programming.

Linear Programming - Activity A

MA2G2: Students will define and apply sine, cosine, and tangent ratios to right triangles.

MA2G2.a: Discover the relationship of the trigonometric ratios for similar triangles.

Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio

MA2G2.b: Explain the relationship between the trigonometric ratios of complementary angles.

Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio

MA2G2.c: Solve application problems using the trigonometric ratios.

Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio

MA2G3: Students will investigate the relationships between lines and circles.

MA2G3.a: Find equations of circles.

Circles

MA2G3.b: Graph a circle given an equation in general form.

Circles

MA2G3.d: Solve a system of equations involving a circle and a line.

Circles

MA2G3.e: Solve a system of equations involving two circles.

Circles

MA2G4: Students will recognize, analyze, and graph the equations of the conic sections (parabolas, circles, ellipses, and hyperbolas).

MA2G4.b: Graph conic sections, identifying fundamental characteristics.

Circles
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A

MA2G4.c: Write equations of conic sections given appropriate information.

Circles
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A

MA2G5: Students will investigate planes and spheres.

MA2G5.b: Apply the distance formula in 3-space.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

MA2D1: Using sample data, students will make informal inferences about population means and standard deviations.

MA2D1.b: Understand and calculate the means and standard deviations of sets of data.

Line Plots

MA2D1.c: Use means and standard deviations to compare data sets.

Line Plots
Populations and Samples

MA2D1.d: Compare the means and standard deviations of random samples with the corresponding population parameters. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

Polling: City
Polling: Neighborhood

MA2D2: Students will create probability histograms of discrete random variables, using both experimental and theoretical probabilities.

Geometric Probability - Activity A
Histograms
Populations and Samples
Probability Simulations
Theoretical and Experimental Probability