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Intermediate Algebra

Guiding Principle

A student at the proficient level in Intermediate Algebra will be able to demonstrate understanding of high school mathematics by solving problems, reasoning, communicating, representing, and making connections based on the following indicators:

Benchmark/Topics	As a result of studying Intermediate Algebra, I will be able to:
(1) Real Number System · Sets of Numbers · Properties/Identities · Order of Operations	2.1.1 Demonstrate an understanding of the real number system when I can o Classify real numbers as rational, irrational, integer, whole and/or natural o Apply and identify algebraic properties and identities of the real number system o Evaluate expressions using the order of operations
(2) Solving Linear Equations and Inequalities · Fractional Coefficients · Decimal Coefficients · Compound	3.3.2 Utilize algebraic methods to o Solve linear equations including those with fractional and decimal coefficients o Solve linear inequalities o Solve compound inequalities
(3) Exponents and Polynomials · Simplify · Basic Operations · Rules of Exponents	3.2.3 Show understanding of exponents and polynomials when I can o Simplify algebraic expressions o Perform basic operations on polynomials o Apply the rules of exponents
(4) Factoring · GCF · Trinomials · Difference of Squares	3.2.4 Factor polynomials completely using the following methods: o Greatest Common Factor o Trinomials factored into binomial factors o Difference of Squares
(5) Solving Systems (2 Equations 2 Unknowns) · Substitution · Elimination (Add/Subtract or Linear Combinations)	3.4.5 Solve systems of equations containing two variables using the following methods: o Substitution o Elimination (Add/Subtract or Linear Combinations)
(6) Introduction to Radicals · Basic Operation · Simplify · Rationalize (monomial denominators)	3.2.6 Show understanding of radicals when I can o Perform basic operations (add, subtract, multiply, divide) with radicals o Simplify radicals o Rationalize monomial denominators
(7) Quadratic Equations · Solving using Factoring · Solve using Quadratic Formula	3.3.7 Utilize the following methods to solve quadratic equations: o Factoring o Quadratic formula
(8) Lines and Angles · Midpoints · Distance formula · Parallel · Perpendicular	4.0.8 Demonstrate an understanding of basic geometric relationships when I can o Identify a midpoint o Apply the midpoint formula o Apply the distance formula o Determine relationships of parallel lines o Determine relationships of perpendicular lines
(9) Congruent Polygons · Definition · Proof	4.2.9 Demonstrate an understanding of the properties of congruent polygons when I can o Classify congruent polygons by definition o Show two polygons are congruent using formal proof
(10) Similar Polygons · Triangle Properties · Ratio/Proportion	5.1.10 Demonstrate knowledge of similar polygons when I can o Identify the properties of similar triangles o Apply properties of ratio and proportion to solve problems involving indirect measurement

(11) Quadrilaterals · Parallelograms · Trapezoids · Squares · Rectangles · Rhombus	4.2.11 Identify, state the properties and determine the relationships between each of the following quadrilaterals: o Parallelograms o Trapezoids o Squares o Rectangles o Rhombi
(12) Right Triangles · Pythagorean Theorem · Special Right Triangles	4.5.12 Apply right triangle properties to problem situations when I can o Apply the Pythagorean Theorem o State the properties of special right triangles o 30-60-90 triangle o 45-45-90 triangle
(13) Area and Volume	4.1.13 Define and use the appropriate formula for o Finding the area of o Triangles o Quadrilaterals o Regular Polygons o Circles o Finding the volume and surface area of o Right rectangular prisms o Right circular prisms o Right rectangular pyramids o Right cones
(14) Circles · Circumference · Area · Secants · Tangents · Chords	4.0.14 Demonstrate an understanding of circles and their properties when I can o Calculate the circumference o Determine the area o Define special cases of segments and lines related to circles and develop and use theorems about measures of the following o Secants o Tangents o Chords

12/30/03

*Benchmark Key – State Content Standard . State Benchmark . District Benchmark