Algebra 2 |
Timeline Block 8 Schedule | Units  | Learning Outcomes and Indicator |
About 1 Weeks | - Preparation for Algebra 2
- Review of Major Algebra 1 Based Topics which are fundamental to Algebra 2
| Students will: - Be able to work with basic algebra skills. A1.4.2, A1.4.5, A1.L.5
|
About 2 Weeks | - Expressions, Equations, & Inequalities
| Students will:Â - Represent real-world problems using linear equations and inequalities in one variable, including those with rational number coefficients and variables on both sides of the equal sign. Solve them fluently, explaining the process used and justifying the choice of a solution method. AI.L.1
- Solve compound linear inequalities in one variable, and represent and interpret the solution on a number line. Write a compound linear inequality given its number line representation. AI.L.2
- Represent linear functions as graphs from equations, equations from graphs, and equations from tables and other given information (e.g., from a given point on a line and the slope of the line). Find the equation of a line, passing through a given point, that is parallel or perpendicular to a given line. AI.L.3
- Represent real-world problems that can be modeled with a linear function using equations, graphs, and tables; translate fluently among these representations, and interpret the slope and intercepts. AI.L.4
- Translate among equivalent forms of equations for linear functions, including slope-intercept, point-slope, and standard. Recognize that different forms reveal more or less information about a given situation. AI.L.5
- Represent real-world problems using linear inequalities in two variables and solve such problems; interpret the solution set and determine whether it is reasonable. Graph the solutions to a linear inequality in two variables as a half-plane. AI.L.6
- Solve linear and quadratic equations and formulas for a specified variable to highlight a quantity of interest, using the same reasoning as in solving equations. AI.L.7
|
About 4 Weeks | - Functions, Equations, & Graphs
| Students will:Â - Understand composition of functions and combine functions by composition. AII.F.1
- Define and find the inverse of a function.  Verify functions are inverses algebraically and graphically. AII.F.2
- Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x. AII.F.3
- Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative). Find the value of k given the graph of f(x) and the graph of f(x) + k, k f(x), f(kx), or f(x + k). (Translations of graphs - vertical/horizontal shifts, stretch/compression, reflection) Â AII.F.4
|
About 5 Weeks | - Linear and Inequality Systems
| Students will:Â - Solve a system of equations consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. AII.SE.1
- Solve real-world systems of two or three linear equations in two or three variables algebraically. AII.SE.2
- Represent real-world problems using a system of linear equations in three variables and solve such problems. Interpret the solution and determine whether it is reasonable. AII.SE.3
|
About 6 Weeks | - Quadratic Functions & Equations
| Students will:Â - Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Interpret the solutions and determine whether they are reasonable. AII.Q.1
- Understand the different forms of a quadratic equation can provide different information. Â Use and translate quadratic functions between standard and vertex form to graph and identify key features, including intercepts, vertex, line of symmetry, end behavior, and domain and range. AII.Q.3
- Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a ± bi for real numbers a and b. AII.Q.4
|
About 12 Week | - Polynomial, Rational & Other Equations and Functions
| Students will:Â - Solve mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable. AII.PR.1
- Graph relations and functions including polynomial, square root, and absolute value functions. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry. AII.PR.2
- Solve mathematical problems involving rational and radical equations. Give examples showing how extraneous solutions may arise. AII.PR.3
- Solve absolute value linear equations and inequalities in one variable. AII.PR.4
- Explain how extending the properties of integer exponents to rational numbers allows for a notation for radicals in terms of rational exponents (e.g. 51/3) is defined to be the cube root of 5 because we want (51/3) 3 = 5(1/3)3 to hold, so (51/3) 3 must equal 5.) AII.ASE.1
- Rewrite expressions involving radicals and rational exponents using the properties of exponents. AII.ASE.2
- Rewrite algebraic rational expressions in equivalent forms (e.g., using properties of exponents and factoring techniques). Add, subtract, multiply, and divide algebraic rational expressions. AII.ASE.3
- Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x). Â AII.ASE.4
|
About 4 Weeks (Time Permitting) | - Exponential & Logarithmic  Equations & Functions
| Students will:Â - Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, and asymptotic and end behavior. AII.EL.2
- Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (0.97)^t, y = (1.01)12^t, y = (1.2)^t/10, and classify them as representing exponential growth or decay. AII.EL.3
- Use the properties of exponents to transform expressions for exponential functions (e.g., the expression 1.15^t can be rewritten as (1.15^1/12)^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%). AII.EL.4
- Know that the inverse of an exponential function is a logarithm. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship. AII.EL.5
- Use the laws of exponents to derive the laws of logarithms. Use the laws of logarithms and the inverse relationship between exponential functions and logarithms to evaluate expressions and solve equations in one variable. Â AII.EL.6
|