Level 2 Algebra Courses for Children

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) = 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.

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^x, and f(x)=log_b (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) = b^x and f(x) = log_b (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 = ab^x 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.

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)=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.

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