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1
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Geometry and Measurement
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- Construction and Measurement of Geometric Solids
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- Identify the characteristics of different geometric shapes.
- Apply formulas to measure geometric shapes.
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2
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Basic Algebraic Operations
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- Real Numbers and Polynomials
- Rational Expressions
- Rational Exponents and Radicals
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- Identify and use properties of real numbers.
- Simplify algebraic expressions.
- Write rational numbers in different formats.
- Identify and classify polynomial and Radicals expressions.
- Perform operations on polynomials.
- Factor polynomials.
- Write a rational expression in simplest form
- Compute rational expressions.
- Simplify radical expressions.
- Multiply and divide radical expressions.
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3
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Linear Equations and Inequalities in One Variable
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- Linear Equations and Applications
- Linear Inequalities and Applications
- Absolute Value in Equations and Inequalities
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- Solve linear equations by using all properties of equality and the rules.
- Solve word problems using linear equations.
- Solve and graph linear inequalities.
- Solve an application using inequalities.
- Solve absolute value equalities and inequalities.
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4
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Quadratic Equations
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- Factoring and solving Quadratic Equations using Factoring
- Completing the Square
- Quadratic Formula and Applications of the Quadratic Equations
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- Write a quadratic equation in the standard form.
- Solve quadratic equations by factoring.
- Solve quadratic equations by the square root property.
- Solve quadratic equations by completing the square.
- Solve quadratic equations by using the quadratic formula.
- Solve word problems involving quadratic equations.
- Use the discriminant to identify the number of solutions.
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5
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Polynomial and Other Equations
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- Polynomial Equations and Applications
- Equations Involving Radicals and Rational Exponents
- Complex Numbers
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- Solve polynomial equations using the zero factor property.
- Solve rational equations.
- Solve radical equations.
- Identify and simplify complex numbers.
- Add and subtract complex numbers.
- Multiply and divide complex numbers.
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6
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Functions and Graphs
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- Rectangular Coordinates and the Graph of a Line
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- Use a table of values to graph linear equations.
- Determine when lines are parallel or perpendicular.
- Use linear graphs in an applied context.
- Identify functions and state their domain and range.
- Use function notation.
- Write a linear equation in function form.
- Use function form to identify the slope.
- Use slope-intercept form to graph linear functions.
- Write a linear equation in point-intercept form.
- Use the function form, the slope-intercept form, and the point-intercept form to solve applications.
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7
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Operations and Functions
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- The Algebra and Composition Functions
- One-to-One and Inverse Functions
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- Compute a sum or difference of functions and determine the domain of the result.
- Compose two functions and find the domain.
- Identify one-to-one functions.
- Find inverse functions using an algebraic method.
- Graph a function and its inverse.
- Graph factorable quadratic equations.
- Graph the square root, cubic, and cube root functions.
- Compute a product or quotient of functions and determine the domain of the result.
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8
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Analyzing Graphs
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- Piecewise-Defined Functions
- Graphs and Symmetry
- Tranformations
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- State the domain of a piecewise-defined function.
- Evaluate piecewise-defined functions.
- Graph functions that are piece-wise defined.
- Identify different symmetry types.
- Use symmetry as an aid to graphing.
- Perform vertical and horizontal shifts of a basic graph.
- Perform vertical and horizontal reflections of a basic graph.
- Perform stretches and compressions on a basic graph.
- Transform the graph of a general function.
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9
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Graphing Polynomial Functions
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- Graphing General Quadratic Functions
- Graphing Polynomial Functions
- Applications of Polynomial Functions
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- Graph quadratic functions by completing the square and using transformations.
- Graph a general quadratic function using the vertex formula.
- Solve applications involving quadratic functions.
- Graph polynomial functions.
- Describe the end behavior of a polynomial graph.
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10
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Graphing Rational Functions
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- Asymptotes and Rational Functions
- Graphing Rational Functions
- Applications of Rational Functions
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- Graph the reciprocal and reciprocal quadratic functions.
- Identify horizontal and vertical asymptotes.
- Use asymptotes to graph transformations.
- Use asymptotes to determine the equation of a rational function from its graph.
- Find the domain of a rational function.
- Find the intercepts of a rational function.
- Graph general rational functions.
- Solve applications involving rational functions.
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11
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Exponential and Logarithmic Functions
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- Exponential Functions
- Logarithms and Logarithmic Functions
- The Exponential Function and Natural Logarithm
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- Evaluate an exponential function.
- Graph exponential functions.
- Solve certain exponential equations.
- Solve applications of exponential equations.
- Write exponential equations in logarithmic form.
- Graph logarithmic functions and find their domains.
- Solve applications of logarithmic functions.
- Evaluate and graph base exponential functions.
- Evaluate and graph the natural logarithm functions.
- Apply the properties of logarithms.
- Use the change-of-base formula.
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12
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Exponential and Logarithmic Equations
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- Exponential Equations
- Logarithmic Equations
- Applications of Exponential and Logarithmic Equations
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- Write logarithmic and exponential equations in simplified form.
- Solve exponential equations.
- Solve logarithmic equations.
- Solve applications involving exponential and logarithmic equations.
- Use exponential equations to find the interest compounded in times per year.
- Use exponential equations to find the interest compounded continuously.
- Solve exponential growth and decay problems.
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13
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Systems of Linear Equations in Two Variables
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- Solving Systems Graphically and by Substitution
- Solving Systems using Elimination
- Applications of Linear Systems
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- Verify ordered pair solutions.
- Solve linear systems by graphing.
- Solve linear systems by substitution.
- Solve linear systems by elimination.
- Recognize inconsistent systems (no solutions) and dependent systems (infinitely many solutions).
- Use a system of equations to mathematically model and solve applications.
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14
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Solving Linear Systems Using Augmented Matrices
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- Matrices
- Solving Linear Systems using Matrix Equations
- More Applications of Linear Systems
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- State the size of a matrix and identify entries in a specified row and column.
- Form the augmented matrix of a system of equations.
- Recognize inconsistent and dependent systems.
- Model and solve applications using linear systems.
- Solve a system of equations using row operations.
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15
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Sequences and Series
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- Sequences and Series
- Arithmetic Sequences
- Geometric Sequences
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- Write out the terms of a sequence given the general term.
- Determine the general term of a sequence.
- Find the partial sum of a series.
- Use summation notation to write and evaluate the series.
- Solve applications using mathematical sequences.
- Find the sum of a geometric series.
- Solve application problems involving geometric sequences and series.
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16
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Review and Graded Final Exam
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