Mathematics III

Basic Algebra

1. perform operations with real numbers including absolute value and exponential notation
2. simplify expressions using rules for order of operations and properties of exponents
3. translate common language into algebraic expressions
4. evaluate algebraic expressions by substitution
5. simplify algebraic expressions with nested parentheses

Linear Equations and Inequalities

1. solve first degree/linear equations in one variable
2. solve simple formulas for a given variable
3. solve and graph linear inequalities in one variable
4. write interval notation for the solution set or graph of an inequality
5. use linear equations, formulas and linear inequalities to solve applied problems
6. find the intersection of two sets
7. solve and graph compound inequalities (conjunctions only)

Graphing, Relations, and Functions

1. write linear equations in slope intercept form
2. graph linear equations and non-linear equations using a table of values
3. graph linear equations using the y-intercept and slope and using x- and y-intercepts
4. graph horizontal and vertical lines
5. find the slope of a line given two points on the line
6. find the equation of a line given graphic data: the slope and y-intercept, the slope and one point, or two points on the line
7. determine whether a pair of lines is parallel
8. find the equation of a line parallel to a given line and through a given point
9. use the definition of function and the vertical-line test to distinguish between functions and non-functions
10. use and interpret function notation to evaluate functions for given x-values and find x-values for given function values
11. determine the domain and range of a function
12. graph linear functions and non-linear functions such as quadratic, cubic, square root, reciprocal, exponential and absolute value functions
13. graph linear inequalities in two variables
14. analyze functions to determine line of symmetry, vertices, asymptotes, and intercepts
15. understand and demonstrate transformations in graphs resulting from the following changes in the defining equation: translation and dilation
16. use a graphing calculator or other appropriate technology to graph equations
17. identify an appropriate graph for a given relation
18. develop a model function from a given graph or set of data

Systems of Linear Equations and Inequalities

1. solve systems of linear equations in two variables by graphing, substitution and elimination methods
2. determine if a system of equations will have one/no solution or an infinite number of solutions
3. use systems of equations to solve applied problems

Polynomials and Polynomial Functions

1. determine the degree of a polynomial
2. distinguish between monomials, binomials, trinomials, and other polynomials
3. add, subtract, multiply polynomials
4. divide polynomials by monomials
5. factor polynomials using an appropriate strategy or a combination of techniques: common factors, difference of squares,  perfect square trinomials, general trinomials or grouping
6. solve polynomial equations using the principle of zero products
7. solve applied problems using polynomial equations/functions

Rational Expressions and Equations and Variation

1. identify situations and find values for which a rational expression will be undefined
2. simplify rational expressions
3. add, subtract, multiply and divide rational expressions
4. solve rational equations and check
5. solve formulas involving rational expressions for a given variable
6. solve applied problems that can be modeled with rational equations
7. simplify complex fractions
8. express variations in the form of equations (direct, inverse, joint, combined)
9. solve problems involving direct, inverse, joint and combined variation

Radical Expressions and Equations

1. write radicals as powers with rational exponents and vice versa
2. use rational exponents to simplify radical expressions
3. simplify, add, subtract, multiply and divide radical expressions (numeric or algebraic)
4. rationalize denominators in fractional expressions containing radicals
5. solve equations involving radical expressions or powers with rational exponents and check for extraneous roots
6. solve formulas involving powers and square roots for a given variable
7. solve applied problems which can be modeled by radical equations, and determine if solutions are reasonable given the context of the problem

Quadratic Equations and Quadratic Functions

1. solve quadratic equations by factoring, principle of square roots and the quadratic formula
2. solve rational and radical equations reducible to a quadratic pattern and check that answers are reasonable
3. solve selected polynomial equations that can be factored simplifying to linear and/or quadratic factors
4. graph quadratic functions of the form f(x) = a(x-h)² + k and demonstrate translations, reflections and stretching/shrinking resulting from changes in the function equation
5. find the vertex, line of symmetry, minimum or maximum values, x- and y-intercepts, domain and range, given the function f(x) = a(x-h)² + k
6. rewrite f(x) = ax² + bx + c as f(x) = a(x-h)² + k by completing the square
7. solve problems that can be modeled using quadratic equations including maximum and minimum problems
8. use a graphing calculator or other appropriate technology to graph and solve quadratic equations
9. solve quadratic inequalities by graphing

Trigonometry

1. label the sides of a right triangle with respect to a given angle
2. determine sine, cosine, and tangent ratios of an angle in a right triangle using the side lengths
3. use a scientific calculator to find the trigonometric value for a given angle and to find an angle given its trigonometric value
4. solve right triangles and applied problems using the basic trigonometric ratios, the Pythagorean theorem, and sum of the angles (180°)
5. use the Law of Sines and the Law of Cosines to solve non-right (oblique) triangles and applied problems