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) = 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)= 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.

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)= 3x, 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) = 3x when f(x) is replaced by af(x), f(bx), f(x - c), and f(x) + 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