STANDARD COMPETENCIES:

 

 1. Demonstrate knowledge of and the ability to perform algebraic manipulations with radicals, complex numbers, polynomials, and rational expressions.

 2. Demonstrate knowledge of and the ability to solve quadratic equations, absolute value equations and inequalities, and systems of linear equations.

 3. Demonstrate the use of critical thinking skills to solve application problems.

 TOPICAL OUTLINE:

 

 I. Demonstrate knowledge of and the ability to perform algebraic manipulations with radicals, complex numbers, polynomials, and rational expressions.

 a. Write a radical expression in simplest form.

 b. Determine the domain for radical expressions.

 c. Write radical expressions as an expression with a rational exponent and vice versa.

 d. Apply the properties of exponents to expressions with rational exponents.

 e. Simplify radical expressions using rational exponents.

 f. Add, subtract, multiply and divide radical expressions using radical properties and/or rational exponents.

 g. Rationalize denominators.

 h. Determine the square roots of a negative number and simplify powers of i.

 i. Add, subtract, multiply and divide complex numbers in the form a+bi.

 j.      Determine the domain of rational expressions.

 k. Add, subtract, multiply, and divide rational expressions.

 l. Divide polynomials by binomials using long division.

 m. Factor out the greatest common monomial factor.

 n. Factor the difference of two squares.

 o. Factor the difference and sum of two cubes.

 p. Factor trinomials of the form ax2 + bx + c.

 

 II. Demonstrate knowledge of and the ability to solve quadratic equations, absolute value equations and inequalities, and systems of linear equations.

 a. Apply the zero product property when factoring to solve quadratic equations.

 b. Solve quadratic equations by using the square root property, completing the square, and using the quadratic formula.

 c. Use the discriminant to determine the types of solutions of a quadratic equation.

 d. Solve equations that are reducible to quadratic equations.

 e. Graph basic quadratic functions.

 f. Solve radical equations with one radical expression that simplify to linear equations. (Example:  √(3x-7)=5)

 g. Solve rational equations that simplify to linear equations.  (Example:  (x+5)/(x-2)=5, ((x+1)(x-2))/((x-2))=5)

 h. Solve absolute value equations and inequalities that contain one absolute value expression.

 i.      Review linear equations in two variables.

 j.      Determine whether a system of equations is dependent, inconsistent or consistent.

 k.     Solve 2 by 2 linear system of equations by substitution elimination (addition), and graphing.

 

 III. Demonstrate the use of critical thinking skills to solve application problems.

 a. Model real-world application problems, interpret results, and summarize using complete sentences.

 b. Create and use graphs, tables, and equations to solve real-world application problems relating to quadratic equations and systems of equations.

 c. Identify academic support resources.

 d. Engage in appropriate math learning and testing strategies.

 e. Effectively use calculators and other appropriate technology.