# Level 2 Algebra Courses for Children

### Algebra 2 Scope and Sequence

**Students will be able to:**

- 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.

**Activities**

- Domain and Range
- Intro to Absolute Value
- Absolute Value FunctionTranslations
- Abs Value Eqs and Ineqs First Step Stop Activity

**Students will be able to:**

- 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.

**Activities**

- Airport Impact
- Calculator Exploration (Rational F'n Graphs)
- Hardly Working

**Students will be able to:**

- 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.

**Activities**

- Complex Numbers
- Factoring Polynomials Circuit Training
- Factoring Polynomials Puzzle
- Factoring Sum and Differences of Two Cubes

**Students will be able to:**

- 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) = ax*^{2}*+ 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.

**Activities**

- Extreme Punkin Chunkin
- General and VertexForm
- Problem Solving with Quadratics
- Applying Quadratics
- Solving Quadratic Inequalities

**Students will be able to:**

- 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.

**Activities**

- Instructions for Using Matrices to Solve Systems.pdf
- Candy Lab Solving Systems Using Matrices
- Quadratic and Linear System Task

**Students will be able to:**

- 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.

**Activities**

- Border Patrol
- Graph Attack – Cow Zapping
- Systems of Inequalities Scavenger Hunt

**Students will be able to:**

- 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.

**Activities**

- A Screeching Halt
- Firefighter
- Radical Transformations
- The Square Root Function

**Students will be able to:**

- Write the domain and range of a function in interval notation, inequalities, and set notation.
- Graph the functions
*f(x)= b*and^{x},*f(x)=log*where_{b}(x)*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) = b*and^{x}*f(x) = log*where_{b }(x)*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 = ab*where^{x}*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.

**Activities**

- 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

**Students will be able to:**

- 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.

**Activities**

- Inverse Functions PowerPoint
- Composing Functions Dice Game
- Intriguing Inverses
- Exponential Reflections
- Inverse Functions Identifying Pairs

**Students will be able to:**

- Write the domain and range of a function in interval notation, inequalities, and set notation.
- Graph the functions
*f(x)=x*^{3}*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) = x*^{3}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.

**Activities**

- Roots of Radical Equations
- Cubic Functions Matching

**Students will be able to:**

- 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.

**Activities**

- 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

**Students will be able to:**

- 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.

**Activities**

- And We Have Liftoff
- Bungee Bounce
- Chirp Jump and Scatter
- Quadratic Regression