Mathematics III

Upon completion of this course, students will be able to:

1. Use, simplify, evaluate and perform operations with real numbers and expressions

1.1 perform operations with real numbers including the use of absolute value and exponential notation
1.2 simplify expressions using rules for order of operations and properties of exponents
1.3 translate common language into algebraic expressions
1.4 evaluate algebraic expressions by substitution
1.5 simplify algebraic expressions with nested parentheses

2.     Solve linear equations, inequalities and formulas and graph linear equations and inequalities

       2.1 solve first degree/linear equations in one variable
       2.2 solve simple formulas for a given variable
       2.3 solve and graph linear inequalities in one variable
       2.4 write the solution set of a linear inequality in set builder or interval notation
       2.5 use linear equations, formulas and inequalities to solve applied problems
       2.6 find the intersection of two sets
       2.7 solve and graph compound inequalities (conjunctions and disjunctions)
       2.8 solve absolute value equations

3.           Graph, interpret and analyze relations and functions

3.1 write linear equations in slope-intercept form
3.2 graph linear equations and non-linear equations using a table of values
3.3 graph linear equations using the y-intercept and slope or using x- and y-intercepts
3.4 graph horizontal and vertical lines
3.5 find the slope of a line given two points on the line
3.6 find the equation of a line given the following information: graphical data, slope and y-intercept, slope and one point, or two points on the line
3.7 determine whether a pair of lines is parallel, perpendicular or neither
3.8 find the equation of a line parallel to or perpendicular to a given line and through a given point
3.9 use the definition of function and the vertical-line test to distinguish between functions and non-function relations
3.10 use and interpret function notation to evaluate functions for given x-values and find x-values for given function values
3.11 determine the domain and range of a function
3.12 graph linear functions and non-linear functions, including quadratic, cubic, square root, reciprocal, exponential and absolute value functions
3.13 graph linear inequalities in two variables
3.14 analyze functions to determine line of symmetry, vertices, asymptotes, and intercepts
3.15 understand and demonstrate transformations in graphs resulting from the following changes in the defining equation: translation and dilation
3.16 use a graphing calculator or other appropriate technology to graph equations
3.17 identify an appropriate graph for a given relation
3.18 develop a model function from a given graph or set of data

4.      Solve systems of linear equations, inequalities and applied problems

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

5.      Classify, evaluate, factor  and  perform operations on polynomial expressions and solve polynomial equations

5.1 determine the degree of a polynomial
5.2 distinguish between monomials, binomials, trinomials, and other polynomials
5.3 add, subtract, multiply polynomials
5.4 divide polynomials by monomials
5.5 factor polynomials using an appropriate strategy or a combination of techniques: common factors, difference of squares,  perfect square trinomials, general trinomials or grouping
5.6 solve polynomial equations using the principle of zero products
5.7 solve applied problems using polynomial equations/functions

6.     Interpret, simplify and perform operations on rational expressions and solve rational equations

6.1 identify situations and find values for which a rational expression will be undefined
6.2 simplify rational expressions
6.3 add, subtract, multiply and divide rational expressions
6.4 solve rational equations and check that the solutions are valid
6.5 solve formulas involving rational expressions for a given variable
6.6 solve applied problems that can be modeled with rational equations
6.7 simplify complex fractions
6.8 express variations in the form of equations (direct, inverse, joint, combined)
6.9 solve problems involving direct, inverse, joint and combined variation

7.     Interpret and perform operations on radical expressions and solve radical equations

7.1 write radicals as powers with rational exponents and vice versa
7.2 use rational exponents to simplify radical expressions
7.3 simplify, add, subtract, multiply and divide radical expressions (numeric or algebraic)
7.4 rationalize denominators in fractional expressions containing radicals (including the use of conjugates)
7.5 solve equations involving radical expressions or powers with rational exponents and check for extraneous roots
7.6 solve formulas involving powers and square roots for a given variable
7.7 solve applied problems which can be modeled by radical equations, and determine if solutions 
are reasonable given the context of the problem

8.      Interpret and graph quadratic functions and solve quadratic equations

8.1 solve quadratic equations by factoring, principle of square roots and the quadratic formula
8.2 use the discriminant to identify the number and type of solutions of a quadratic equations
8.3 write a quadratic equation given its solutions
8.4 solve rational and radical equations reducible to a quadratic form and check that answers 
are reasonable
8.5 solve selected polynomial equations that can be factored into linear and/or quadratic factors
8.6 graph quadratic functions of the form f(x) = a(x-h)² + k. Demonstrate translations, reflections and stretching/shrinking resulting from changes in the function equation
8.7 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
8.8 rewrite f(x) = ax² + bx + c as f(x) = a(x-h)² + k by completing the square
8.9 solve problems that can be modeled using quadratic equations including maximum and minimum problems
8.10 use a graphing calculator or other appropriate technology to graph and solve quadratic equations
8.11 solve quadratic inequalities by graphing

9.     Solve right and non-right angle triangles

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