Heart of Algebra

Linear equations, inequalities, functions, and graphs:

• Solving linear equations and linear inequalities (in these expressions, x is a constant or the product of a constant)

• Interpreting linear functions

• Linear inequality and equation word problems

• Graphing linear equations

• Linear function word problems

• Systems of linear inequalities word problems

• Solving systems of linear equations

Summary of Tasks

• Use multiple steps to simplify an expression or equation or solve for a variable.

• Solve for a variable within functions or systems of inequalities with two variables (usually x and y).

• Determine whether a given point is in a solution set or what value would make an expression have no solution.

• Select a graph that shows an algebraic equation, or, on the flip side, choose the equation that describes a graph.

• Indicate how a graph would be affected by a given change in its equation.

Passport to Advanced Math

Nonlinear expressions:  These questions will ask you to work with quadratic equations, exponential expressions, and word problems.  

Official Topics

• Solving quadratic equations

• Interpreting nonlinear expressions

• Quadratic and exponential word problems

• Radicals and rational exponents

• Operations with rational expressions and polynomials

• Polynomial factors and graphs

• Nonlinear equation graphs

• Linear and quadratic systems

• Structure in expressions

• Isolating quantities

• Functions

Summary of Tasks

• Solve equations by factoring or using other methods to rewrite them in another form.

• Add, subtract, multiply, or divide two rational expressions or divide two polynomial expressions and simplify your results.

• Select a graph that matches a nonlinear equation or an equation that corresponds to a graph.

• Determine the equation of a curve from a description of a graph.

• Figure out how a graph would change if its equation changed.