Algebra II is a full-year, high school math course intended for the student who has successfully completed the prerequisite course Algebra I. This course focuses on algebraic techniques and methods in order to develop student understanding of advanced number theory and concepts involving linear, quadratic, exponential, rational, radical, and polynomial functions. Students also explore statistical concepts, applying their understanding of functions to solve problems.
- Structure and Functions: Student will review the properties of functions, determine the domain, range, and inverse of a function, and simplify expressions by combining like terms and applying rules for exponents.
- Linear Functions: Student will determine the slope of a line and use that information to write an equation, compare lines, and solve a system of equations using the addition property of equality, the substitution property of equality, and graphical methods.
- Inequalities and Absolute Value: Student will solve and graph inequalities, including absolute value inequalities in one or two variables.
- Polynomials: Student will factor polynomials, including applying their understanding of the difference of two squares, perfect square trinomials, and the difference of two cubes. The student will also solve problems involving direct variation, inverse variation, and joint or combination variation.
- Algebraic Fractions: Student will add, subtract, multiply, and divide with rational expressions, as well as solve and graph rational equations and functions that model mathematical and real-world situations.
- Real Numbers: Student will evaluate and simplify expressions containing radicals and fractional exponents and solve quadratic equations and systems of quadratic equations using a variety of methods. The student is also introduced to the concept of imaginary numbers and complex solutions.
- Functions: Student will explore a variety of functions and systems of equations, including exponential, absolute value, radical, and piece-wise defined functions.
- More Functions: Student will deepen the understanding of inverse functions, understanding the inverse relationship of exponential and logarithmic functions.
- Statistics: Student will algebraically represent sequences and series, including arithmetic and geometric, and distinguish between permutations and combinations. The student will also describe properties of normal distributions and solve statistical problems with linear, quadratic, and exponential models.
Curriculum Content and Skill Focus
UNIT 1: STRUCTURE AND FUNCTIONS
- Identify functions and relations and describe the difference between them.
- Find the domain and range of a function and determine whether or not a given graph represents a function.
- Evaluate a function at any point and operate with functions, including composition.
- Evaluate expressions, including negative and zero exponents, and simplify them, combining like terms.
- Review exponent rules for multiplication and division of like bases and exponentiation of powers.
UNIT 2: LINEAR FUNCTIONS
- Identify linear and non-linear equations.
- Determine if two lines are parallel or perpendicular or if a line is horizontal or vertical.
- Write the point-slope form of parallel lines, perpendicular lines, a line given the slope and a point on the line, and a line that passes through two given points.
- Write equations of a line in general form, point-slope, and slope-intercept form.
- Find the x- and y-intercepts by inspecting the general form of a line.
- Solve a system of two equations by using the addition property of equality, the substitution property of equality, and graphical methods.
UNIT 3: INEQUALITIES AND ABSOLUTE VALUE
- Solve and graph linear inequalities using multiplication, addition, and distributive properties.
- Solve and graph absolute value and compound equations and inequalities.
- Express the solutions of one- and two-variable inequalities using a line graph or coordinate plane.
UNIT 4: POLYNOMIALS
- Add, subtract, multiply, and divide with polynomial expressions.
- Find special products such as the perfect square trinomial.
- Factor polynomials, including using the difference of two squares, perfect square trinomials, and the difference of two cubes.
- Graph polynomial functions on the coordinate plane.
- Solve word problems that involve direct variation of two quantities, inverse variation of two quantities, and joint or combination variation of three quantities.
UNIT 5: ALGEBRAIC FRACTIONS
- Simplify rational expressions.
- Add, subtract, multiply, and divide rational expressions.
- Solve mathematical and real-world problems that can be modeled by rational equations and functions.
- Graph rational functions on the coordinate plane.
UNIT 7: REAL NUMBERS
- Evaluate, simplify, and rewrite radical expressions and expressions containing fractional exponents.
- Add, subtract, multiply, and divide with radical expressions.
- Use conjugates to rationalize the denominator of an algebraic expression.
- Solve quadratic equations by factoring, completing the square, or using the square root method or quadratic formula.
- Graph quadratic functions on the coordinate plane.
- Determine the sum and product of the roots of a quadratic equation.
- Find the discriminant of a quadratic equation and use it to determine what kinds of solutions a quadratic equation has.
- Perform operations on complex numbers and rewrite expressions using properties of imaginary numbers.
- Solve systems of quadratic equations.
UNIT 8: FUNCTIONS
- Simplify expressions with fractional exponents and solve exponential equations.
- Solve mathematical and real-world problems that can be modeled by exponential, absolute value, radical, and piece-wise defined functions.
- Graph exponential, absolute value, radical, and piece-wise defined functions.
UNIT 9: MORE FUNCTIONS
- Express an exponential equation in logarithmic form and a logarithmic function in exponential form.
- Evaluate logarithmic functions.
- Use logarithmic properties to evaluate and calculate common and natural logarithms.
- Solve mathematical and real-world problems that can be modeled by exponential and logarithmic functions.
- Graph exponential and logarithmic functions on the coordinate plane.
- Determine the inverse of a function.
- Solve systems of equations including linear, quadratic, rational, radical, exponential, and logarithmic relationships.
UNIT 10: STATISTICS
- Indicate the general term of a sequence and find the nth term.
- Differentiate between a finite and an infinite series and between an arithmetic and a geometric series.
- Use summation notation and evaluate factorial expressions.
- Calculate the number of permutations or combinations of r elements from a set of n elements.
- Demonstrate knowledge of the pattern of Pascal’s triangle and use it to find powers of binomials.
- Determine normal distribution from a histogram and/or a data table and calculate the variance and standard deviation of a data set.
- Use a normal distribution to determine probabilities and make decisions.
- Use a table or graph to determine the appropriate model for the data.
- Use regression methods available through technology to write linear functions, quadratic functions, and exponential functions from a set of data.
- Make predictions and solve problems with linear, quadratic, and exponential models created by technology.
Some assignments in this course require the use of resources that must be supplied by the user. These outside resources are listed by assignment.
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