This course builds on the knowledge and skills from Integrated Algebra I and Integrated Geometry.  It introduces new topics such as functions, quadratics, more complex equations, and matrices.  Prerequisites are the successful completion of Integrated Algebra I and Integrated Geometry.

Learning Objectives
    The student will:
        Demonstrate the following skills

Functions
    The student will:
        Understand the definition of a function.
        Recognize linear and nonlinear functions.
        State the domain and range of a function.
        Use a mathematical model of a real world situation.

Quadratic Functions
    The student will:
        Recognize linear and nonlinear functions by their equations.
        Create mathematical models to solve real world problems.
        Use algebraic methods to establish the maximum or minimum values of quadratic functions.
        Use graphical methods to establish the maximum or minimum values of quadratic functions.

Critical Values of Quadratic Functions
    The student will:
        Solve quadratic equations graphically.
        Solve quadratic equations algebraically.
        Demonstrate understanding of the geometrical interpretation of the roots of a quadratic equation.
        Determine the nature of the roots of a quadratic equation.
        Use the quadratic equation formula to solve real world problems.

Finding the coordinates of the vertex
    The student will:
         State the coordinates of the vertex for the function y = ax² + bx +c.
        State the equation of the axis of symmetry of the function y = ax² + bx +c.
        Apply these ideas to the solution of optimization problems.

Transformations of Quadratic Functions
    The student will:
        Demonstrate the role of transformations on the quadratic equation and graph.
        State the vertex, axis of symmetry, and the direction of opening for the graphs of transformed quadratic equations.
        Fit a quadratic function to a given set of data points.
        Construct mathematical models to fit data.

More Polynomial Functions
    The student will:
        Use graphical techniques to find the max/min values of cubic functions.
        Recognize the characteristics of the graphs of cubic functions.
        Recognize the characteristics of the graphs of higher polynomial functions.
        Predict the number of turning points for a polynomial function.
        Predict the maximum number of intersection points with the x-axis for a polynomial function.

Finding the Inverse
    The student will:
        Demonstrate understanding of the concept of the inverse of a function.
        Find the inverse of a function algebraically.
        Find the inverse of a function graphically.
        Decide if the inverse of a function is a function.
        Apply the concept of inverse to real life situations.

Reciprocal and Absolute Value Functions
    The student will:
        Identify the graphs of reciprocal.
        Identify the graphs of absolute value functions.
        Apply transformations to the graphs of these functions.
        Develop a mathematical model for the relationship between sales and profits.

Introduction Exponential Function and Logarithms
    The student will:
        Recognize an exponential function.
        Identify some of the properties of an exponential function.
        Describe the features of an exponential curve.

Working with Exponents
    The student will:
        Work with integer exponents.
        Interpret the meaning of positive, negative, and zero exponents.
        Work with fractional exponents.
        Interpret the meaning of fractional exponents.
        Translate fractional exponents into other equivalent representations.

Exponential Growth
    The student will:
        Find the amount of money invested at any compound interest rate.
        Explain the link between compound interest and exponential growth.
        Interpret and compare features of various exponential graphs.
        Convert compound interest formula to a formula based on doubling.

Exponential Decay
    The student will:
        Recognize the difference between exponential growth and decay curves.
        Recognize the difference between exponential growth and decay equations.
        Evaluate quantities based on both between exponential growth and decay functions.
        Relate the depreciation equation to one based on halving.

Continuous Growth Models
    The student will:
        Compare continuous and discrete growth models.
        Explain the concept of limiting value.
        Describe the role played by the number e in exponential models of growth and decay.

Inverses of Exponential Functions
    The student will:
        Recognize the inverse of a function graphically and by its equation.
        Establish the inverse equation for a given function.
        Relate the inverse of an exponential function to its logarithmic function and graph them.
        Use a calculator to find the log of any positive number.
        Estimate the log of any positive number.
        Relate logs to exponents.

Properties of Logarithms
    The student will:
        Transform the log of a product into a sum.
        Transform the log of a quotient into a difference.
        Transform the log of a power into the product of a number and a log.
        Establish power functions to fit given data.

Applications of Logarithms
    The student will:
        Use logs to solve exponential equations.
        Demonstrate understanding of the application of logs in the measurement of earthquakes, sound intensity, and acidity.
        Apply the Rule of 72 to make judgments about interest rates.

Trigonometric Functions as Cyclic Events
    The student will:
        Recognize the graph of a periodic function.
        State the period of a periodic function.
        Give examples of things that behave in a periodic way in the natural world.

Angles and Trigonometry
    The student will:
        Draw and identify positive, negative, and coterminal angles of rotation.
        Calculate equivalent rotation angles in both degree and radian measure.
        Identify common rotation angles in degree and radian measure.
        Convert between degrees and radians.

Generating Circular Functions
    The student will:
        Recognize the graph of the sine, cosine, and tangent functions.
        State the max, min, and period of the sine, cosine, and tangent function as appropriate.
        Generate the graph of each function from circular motion.
        Generate the graph of each function with a graphing calculator.
        Establish ordered pairs for each function by using the graphing calculator, their graphs, or the unit circle.

Transforming the Trigonometric Functions
    The student will:
        Sketch the graph of a transformed trigonometric function and state the period and amplitude of the new function.
        State the equation of a trigonometric function given its graph.

Fitting Function to Data
    The student will:
        Fit an appropriate trigonometric function to cyclical data.
        Use mathematical modeling to describe real world phenomena.

Inverses of Three Trigonometric Functions
    The student will:
        Determine the inverse of the sine, cosine, and tangent functions.
        Graph the inverse of these three functions.
        Identify the relationship between the graphs of the functions and their inverses.
        Evaluate the inverse functions using a calculator.

Counting, Probability, and Statistics
    The student will:
        Count the number of paths in small block diagrams.
        Compute the number of additions required to solve problems involving small block diagrams.
        Find the quickest route(s) in small block diagrams.
        Estimate the number of paths in large block diagrams.

Permutations
    The student will:
        Use the Fundamental Counting Principle to solve counting problems.
        Use permutations to solve counting problems.
        Find relations between factorials.
        Explain the difficulties in using permutations to solve block diagram problems.

Identical Objects
    The student will:
        Solve counting problems where some elements are alike.
        Determine the number of paths in a block diagram.
        Explain the limitations of computers in solving large problems involving block diagrams.

Combinations
    The student will:
        Solve counting problems where order is not important.
        Define what is meant by a combination of n objects taken r at a time.
        Use factorials to enumerate combinations.
        Use combinations to solve problems involving block diagrams.

Probability
    The student will:
        Use probability to solve problems involving uncertainty.
        Use conditional probabilities to solve problems with partial information.
        Determine whether or not two events are independent.
        Find the probability of the intersection of two events.

Binomial Distributions
    The student will:
        Explain the binomial probability distribution.
        Construct graphical representations of binomial distributions.
        Relate probabilities to areas of rectangles.

Normal Curves
    The student will:
        List the important properties of a normal curve.
        Relate the normal curve to binomial probabilities.
        Use the normal curve to compute probabilities.
        Relate probabilities to areas under a curve.
        Approximate binomial probabilities by using normal probabilities.

Dynamic Programming
    The student will:
        Use Dynamic Programming to solve block diagram problems.
        Compare the time required for a computer using the Exhaustive Search method versus Dynamic Programming.
        Explain how working backwards can be an efficient problem solving tool.

Introduction to Linear Programming
    The student will:
        Explain the importance of scheduling problems.
        Find acceptable solutions to scheduling problems.
        Explain the importance of blending problems.
        Find acceptable solutions to blending problems.

Linear Programming - Graphical Approach .
    The student will:
        Explain the terms decision variables, feasible solutions, optimal feasible solutions, and objective functions.
        Explain what is meant by a linear programming model.
        Use the graphs of feasible regions and profit lines to solve linear programming problems with two variables.

Linear Programming - Algebraic Approach .
    The student will:
        Explain the meaning of slack in linear programming problems.
        Solve linear programming problems with more than 2 variables.

Rational Number Properties
    The student will:
        Demonstrate understanding the historical development of the sets of natural numbers, the integers and the rational numbers.
        Recognize to which number set(s) various numbers belong.
        Describe the relationship that the three sets have to each other.
        Identify the group properties of the sets of natural numbers, the integers and the rational numbers.

Rational Numbers
    The student will:
        Locate rational numbers on the number line in both fractional form and decimal form.
        Change rational fractions to decimal form.
        Locate infinite repeating decimals on the number line.
        Explain how a repeating decimal is the result of an infinite process.

Irrational Numbers and Reals
    The student will:
        Describe irrational numbers.
        Find the position of irrational numbers on the number line in decimal and radical form.
        Explain the relationship of the sets of the rational and irrational numbers to the set of real numbers.