Level 2 Algebra Courses
for Children
Algebra 2 Scope and Sequence
| Unit Title | Students will be able to: | Activities |
|---|---|---|
| Unit 1 Absolute Value Functions | Graph the function f(x)=|x| and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval. Write the domain and range of a function in interval notation, inequalities, and set notation. Analyze the effect on the graph of f(x) = |x| when f(x) is replaced by af(x), f(bx), f(x - c), and f(x) + d for specific positive and negative real values of a, b, c, and d. Formulate absolute value linear equations. Solve absolute value linear equations. Solve absolute value linear inequalities. | Domain and Range Intro to Absolute Value Absolute Value Function Translations Abs Value Eqs and Ineqs First Step Stop Activity |
| Unit 2 Inverse Variation F’ns | Graph the function f(x)=1/x and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval. Write the domain and range of a function in interval notation, inequalities, and set notation. Analyze the effect on the graph of f(x) = 1/x when f(x) is replaced by af(x), f(bx), f(x - c), and f(x) + d for specific positive and negative real values of a, b, c, and d. Formulate and solve equations involving inverse variation. | Airport Impact Calculator Exploration (Rational F'n Graphs) Hardly Working |
| Unit 3 Polynomials | Add, subtract, and multiply polynomials. Determine the quotient of a polynomial of degree three and of degree four when divided by a polynomial of degree one and of degree two. Determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods. Determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping. Add, subtract, and multiply complex numbers. | Complex Numbers Factoring Polynomials Circuit Training Factoring Polynomials Puzzle Factoring Sum and Differences of Two Cubes |
| Unit 4 Quadratic Functions | Write the quadratic function given three specified points in the plane. Write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening. Given a table of data, formulate quadratic equations using technology. Transform a quadratic function f(x) = ax2 + bx + c to the form f(x) = a(x - h)2 + k to identify the different attributes of f(x). Solve quadratic equations. Solve quadratic inequalities. | Extreme Punkin Chunkin General and Vertex Form Problem Solving with Quadratics Applying Quadratics Solving Quadratic Inequalities |
| Unit 5 Systems of Equations | Formulate systems of equations, including systems consisting of three linear equations in three variables and systems consisting of two equations, the first linear and the second quadratic. Solve systems of three linear equations in three variables by using Gaussian elimination, technology with matrices, and substitution. Solve, algebraically, systems of two equations in two variables consisting of a linear equation and a quadratic equation. Determine the reasonableness of solutions to systems of a linear equation and a quadratic equation in two variables. | Instructions for Using Matrices to Solve Systems.pdf Candy Lab Solving Systems Using Matrices Quadratic and Linear System Task |
| Unit 6 Systems of Inequalities | Formulate systems of at least two linear inequalities in two variables. Solve systems of two or more linear inequalities in two variables. Determine possible solutions in the solution set of systems of two or more linear inequalities in two variables. | Border Patrol Graph Attack – Cow Zapping Systems of Inequalities Scavenger Hunt |
| Unit 7 Square Root Functions | Rewrite radical expressions that contain variables to equivalent forms. Graph the function f(x)= √x and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval. Write the domain and range of a function in interval notation, inequalities, and set notation. Determine the effect on the graph of f(x) = √x when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x – c) for specific positive and negative values of a, b, c, and d. Given a table of data, formulate square root equations using technology. Solve square root equations. Identify extraneous solutions of square root equations. | A Screeching Halt Firefighter Radical Transformations The Square Root Function |
| Unit 8 Exponential and Logarithmic Functions | Write the domain and range of a function in interval notation, inequalities, and set notation.
Graph the functions f(x)= bx, and f(x)=logb (x) where b is 2, 10, and e, and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval.
Determine the effects on the key attributes on the graphs of f(x) = bx and f(x) = logb (x) where b is 2, 10, and e when f(x) is replaced by af(x), f(x) + d, and f(x - c) for specific positive and negative real values of a, c, and d. Solve equations involving rational exponents. Formulate exponential and logarithmic equations that model real-world situations, including exponential relationships written in recursive notation. Rewrite exponential equations as their corresponding logarithmic equations and logarithmic equations as their corresponding exponential equations. Solve exponential equations of the form y = abx where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutions. Determine the reasonableness of a solution to a logarithmic equation. | Attach of the Buzz Bugs Where did the Buzz Bugs Go? Intro To Exponential Functions Radioactive Decay Definition of Logarithm with Applications Intro to Logs Log Equations Maze Graphs of Log Functions |
| Unit 9 Inverses of Functions | Graph and write the inverse of a function using notation such as f -1(x). Describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), including the restriction(s) on domain, which will restrict its range. Use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each other. | Inverse Functions PowerPoint Composing Functions Dice Game Intriguing Inverses Exponential Reflections Inverse Functions Identifying Pairs |
| Unit 10 Cubic and Cube Root F’ns | Write the domain and range of a function in interval notation, inequalities, and set notation. Graph the functions f(x)=x3 and f(x)= 3√x, and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval. Analyze the effect on the graphs of f(x) = x3 and f(x) = 3√x when f(x) is replaced by af(x), f(bx), f(x - c), and f(x) + d for specific positive and negative real values of a, b, c, and d. Solve cube root equations that have real roots. | Roots of Radical Equations Cubic Functions Matching |
| Unit 11 Rational Functions | Determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and of degree two. Determine the asymptotic restrictions on the domain of a rational function and represent domain and range using interval notation, inequalities, and set notation. Formulate rational equations that model real-world situations. Solve rational equations that have real solutions. Determine the reasonableness of a solution to a rational equation. | Asymptotes and Zeros of Rational Functions Finding Vertical Asymptotes The Trick for Finding Horizontal Asymptotes Mirror Mirror on the Floor Rational Functions Four-Square Activity Simplifying Rational Expressions |
| Unit 12 Modeling Data | Analyze data to select the appropriate model from among linear, quadratic, and exponential models. Use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data. Predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models. | And We Have Liftoff Bungee Bounce Chirp Jump and Scatter Quadratic Regression |