ORCCAOpen Resources for Community College Algebra

Systems of Linear Equations in Two Variables

1. Solve and check systems of equations graphically and using the substitution and addition methods

2. Create and solve real-world models involving systems of linear equations in two variables

   1. Properly define variables; include units in variable definitions

   2. Apply dimensional analysis while solving problems

   3. State contextual conclusions using complete sentences

   4. Use estimation to determine reasonableness of solution

Working with Algebraic Expressions

1. Apply the rules for integer exponents

2. Work in scientific notation and demonstrate understanding of the magnitude of the quantities involved

3. Add, subtract, multiply, and square polynomials

4. Divide polynomials by a monomial

5. Understand nonvariable square roots

   1. Simplify using the product rule of square roots including complex numbers (e.g. \(\sqrt{-72}=6i\sqrt{2}\))

   2. Recognize like radical terms

   3. Rationalize denominators (e.g. \(\frac{1}{\sqrt{2}}\) but not \(\frac{1}{3+\sqrt{5}}\))

   4. Estimate square roots

Factoring Polynomials

1. Factor the greatest common factor from a polynomial

2. Factor a polynomial of four terms using the grouping method

3. Factor trinomials that have leading coefficients of \(1\)

4. Factor trinomials that have leading coefficients other than \(1\)

5. Factor differences of squares

6. Recognize and factor sums and differences of cubes

Quadratic Equations in One Variable

1. Solve quadratic equations using the zero product principle (factoring)

2. Solve quadratic equations using the square root property

3. Solve quadratic equations using the quadratic formula including complex solutions

4. Make choices about the appropriate method to use when solving a quadratic equation

5. Understand that the solutions satisfy the original equation by checking the solutions

6. Distinguish between a linear and a quadratic equation and be able to solve both kinds of equations when mixed up in a problem set

7. Create and solve real-world models involving quadratic equations

   1. Properly define variables; include units in variable definitions

   2. Apply dimensional analysis while solving problems

   3. Use the Pythagorean Theorem to find missing sides of a right triangle, then use the lengths to write the sine, cosine, and tangent of an angle within the triangle

   4. State contextual conclusions using complete sentences

   5. Use estimation to determine reasonableness of solution

Quadratic Equations in Two Variables

1. Identify a quadratic equation in two variables

2. Create a table of solutions for the equation of a quadratic function

3. Emphasize that the graph of a parabola is a visual representation of the solution set to a quadratic equation

4. Graph quadratic functions by finding the vertex and plotting additional points without using a graphing calculator

5. Algebraically find the vertex, axis of symmetry, and vertical and horizontal intercepts and graph them by hand

   1. The vertex as well as the vertical and horizontal intercepts should be written as ordered pairs

   2. The axis of symmetry should be written as an equation

6. Determine whether quadratic functions are concave up or concave down based on their equations

7. Create, use, and interpret quadratic models of real-world situations algebraically and graphically

   1. Evaluate the function at a particular input value and interpret its meaning

   2. Given a functional value (output), find and interpret the input

   3. Interpret the vertex, vertical intercept, and any horizontal intercept(s) using proper units

Relations and Functions

1. Use the definition of a function to determine whether a given relation represents a function

2. Determine the domain and range of functions given as a graph, given as a set of ordered pairs, and given as a table

3. Apply function notation in graphical, algebraic, and tabular settings

   1. Understand the difference between the input and output

   2. Identify ordered pairs from function notation

   3. Given an input, find an output

   4. Given an output, find input(s)

4. Interpret function notation in real world applications

   1. Evaluate the function at a particular input value and interpret its meaning

   2. Given a functional value (output), find and interpret the input