# Algebra 2 Curriculum

## Quarterly Overview of Algebra 2

The objectives and outcomes for each unit are common across FCPS and based on the Virginia Standards of Learning. The pacing by quarter and by week provides an example of how the curriculum can be organized throughout the year. Teacher teams may adjust the pacing or order of units to best meet the needs of students.

Week 1Week 2Week 3 Week 4Week 5Week 6 Week 7Week 8Week 9

## Units and Details

### Unit 1: Functions

Students will:

• Solve absolute value linear equations and inequalities.
• Recognize the general shape of the absolute value function family.
• Use knowledge of transformations to convert between equations and the corresponding graphs of absolute value functions.
• Investigate and analyze linear and absolute value function families algebraically and graphically. Key concepts include domain, range, and continuity, intervals in which a function is increasing or decreasing, extrema, zeros, intercepts, values of a function for elements in its domain, and end behavior.
• Make connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs.
• Find the inverse of a linear function.
• Investigate and analyze composition of functions, algebraically and graphically.

### Unit 2: Factoring and Quadratic Functions

Students will:

• Factor polynomials completely in one or two variables.
• Solve quadratic equations over the set of complex numbers.
• Recognize the general shape of the quadratic function family.
• Use knowledge of transformations to convert between equations and the corresponding graphs of quadratic functions.
• Investigate and analyze quadratic function family algebraically and graphically. Key concepts include domain, range, and continuity, intervals in which a function is increasing or decreasing, extrema, zeros, intercepts, values of a function for elements in its domain, and end behavior.
• Investigate and describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, and factors of a polynomial expression.

### Unit 3: Applications of Quadratics

Students will:

• Solve systems of linear-quadratic and quadratic-quadratic algebraically and graphically.
• Collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of quadratic functions.
• Make predictions, using data, scatterplots, or the equation of the curve of best fit
Solve practical problems involving an equation of the curve of best fit.

### Unit 4: Polynomial Expressions and Functions

Students will:

• Recognize the general shape of polynomial function families and identify the graph of a function from the equation.
• Use knowledge of transformations to convert between equations and the corresponding graphs of polynomial functions.
• Investigate and analyze polynomial function families algebraically and graphically. Key concepts include domain, range, and continuity, intervals in which a function is increasing or decreasing, extrema, zeros, intercepts, values of a function for elements in its domain, and end behavior.
• Define a polynomial function in factored form, given its zeros.
• For a function, identify zeros of multiplicity greater than 1 and describe the effect of those zeros on the graph of the function.
• Given a polynomial equation, determine the number and type of solutions.

### Unit 5: Exponents and Radicals

Students will:

• Add, subtract, multiply, divide, and simplify radical expressions containing rational numbers and variables, and expressions containing rational exponents.
• Solve equations containing radical expressions.
• Recognize the general shape of the square root and cube root function families.
• Use knowledge of transformations to convert between equations and the corresponding graphs of square root and cube root functions.
• Investigate and analyze square root and cube root function families algebraically and graphically. Key concepts include domain, range, and continuity, intervals in which a function is increasing or decreasing, extrema, zeros, intercepts, values of a function for elements in its domain, and end behavior.
• Find the inverse of square and cube root functions.

### Unit 6: Exponential and Logarithmic Functions

Students will:

• Recognize the general shape of the exponential and logarithmic function families.
• Use knowledge of transformations to convert between equations and the corresponding graphs of exponential and logarithmic functions.
• Investigate and analyze exponential and logarithmic function families algebraically and graphically. Key concepts include domain, range, and continuity, intervals in which a function is increasing or decreasing, extrema, zeros, intercepts, values of a function for elements in its domain, vertical and horizontal asymptotes and end behavior.
• Find the inverse of exponential and logarithmic functions.
• Collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of exponential functions.

### Unit 7: Rational Expressions and Functions

Students will:

• Add, subtract, multiply, divide, and simplify rational algebraic expressions.
• Solve equations containing rational algebraic expressions.
• Recognize the general shape of the rational function family.
• Use knowledge of transformations to convert between equations and the corresponding graphs of rational functions.
• Investigate and analyze rational function family algebraically and graphically. Key concepts include domain, range, and continuity, intervals in which a function is increasing or decreasing, extrema, zeros, intercepts, values of a function for elements in its domain, vertical and horizontal asymptotes and end behavior.
• Represent and solve problems, including practical problems, involving inverse variation, joint variation, and a combination of direct and inverse variations.

### Unit 8: Sequences and Series

Students will:

• Distinguish between a sequence and a series.
• Generalize patterns in a sequence using explicit and recursive formulas.
• Use and interpret the notations å, n, nth term, and an.
• Given the formula, determine an (the nth term) for an arithmetic or a geometric sequence.
• Given formulas, write the first n terms and determine the sum, Sn, of the first n terms of an arithmetic or geometric series.
• Given the formula, determine the sum of a convergent infinite series.
• Model practical situations using sequences and series.

### Unit 9: Probability and Statistics

Students will:

• Identify and describe properties of a normal distribution
• Interpret and compare z-scores for normally distributed data
• Apply properties of normal distributions to determine probabilities associated with areas under the standard normal curve
• Compute and distinguish between permutations and combinations

### SOL Review and Remediation

Students will:

• Make connections between big ideas learned throughout the course.
• Deepen and extend skills learned during the course.

## Assessments

Student assessments are part of the teaching and learning process.

• Teachers give assessments to students on an ongoing basis to
• Check for understanding
• Gather information about students' knowledge or skills.
• Assessments provide information about a child's development of knowledge and skills that can help families and teachers better plan for the next steps in instruction.

For testing questions or additional information about how schools and teachers use test results to support student success, families can contact their children's schools.

In Fairfax County Public Schools (FCPS), tests focus on measuring content knowledge and skill development.

EPF

English 9
English 10
English 11
English 12

Health 9
Health 10