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## End-of-Course - Algebra II

## Sites to help students practice skills needed for the Algebra II exam.

## Links being verified 1/28/2015

Standards Number & Operations | Algebra | Geometry | Measurement | Data Analysis and Probability

Virginia Standards of Learning - Select Algebra II and 10, 20 or 40 questions - Repeat for a new set of questions

SOL Algebra I & II resources - posted by Rockingham County Public Schools

FCAT Sample Test Book - [2008] sample questions and test taking tips

FCAT Sample Answer Book - [2008] sample questions and test taking tips

Texas Released Tests

Virginia DOE index of released testsreturn to the top of the page

Standard 1 - Number and Operations

Students will recognize, represent, model, and apply real numbers and operations and will demonstrate an understanding of properties and operations of the complex number system.Level 1 order a given set of real numbers

- Common Core Math Video 32 - [12:08] a You Tube video on comparing and ordering real numbers
- Comparing and Ordering Real Numbers - To determine which of two real numbers is greater, express each number as a decimal. Then compare the numbers
- Comparing and Ordering Real Numbers - [4 pages] several sets of problems, each followed by answers
- Comparing Seven Digit Numbers - practice area followed by an interactive game
- Ordering Numbers - elementary level explanation with ten questions at the bottom of the page
- Ordering Real Numbers From Least To Greatest - [4:53] You Tube video
- Properties of Real Numbers - intermediate algebra tutorial 5
- Rational and Irrational number review
identify the reciprocal of a real number

- Fractions: the Reciprocal - instructions followed by practice problems, reciprocal of real numbers practice is also available
- How do I find the reciprocal of a decimal mixed number? - an answer to a student's question
- Properties of Real Numbers - intermediate algebra tutorial 5 [provides practice with reciprocals
- Rational Number and its Reciprocal - a step-by-step examination of a problem by Dr. Math
- Reciprocal - explanation, examples, and review questions at the end [from Math is Fun]
- The Reciprocal of a Real Number - [37:25] You Tube video (
caution: some users complained that the video was too long)- The Reciprocal of a Real Number - [30 slides] PowerPoint show designed to teach about simplifying expressions involving reciprocals
- Reciprocal of a Real Number - [14 pages] lesson on the topic in the format of a slide show
multiply two polynomials with each factor having no more than two terms.

- Factoring Trinomials - practice exercises at Math Pinball [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.]
- "FOIL": A Special (and Misleading) Case - a special method, useful ONLY for a two-term polynomial times another two-term polynomial
- General Polynomial Multiplication - switch over to vertical multiplication once the polynomials get big
- Interactive Algebra Review - Multiplying Algebraic Expressions [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.]
- Interactive Algebra Review - Solving Polynomial Equations (see also part B of this tutorial ) [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.]
- Multiply Polynomials - this two page .pdf document could be printed as a student handout
- Multiply Polynomials - This WebMath page will show you how to multiply polynomials together
- Multiply Two Polynomials Using Algebra Tiles - multiple-choice question from IXL
- Multiplication of Polynomials - using the distributive property
- Multiplying Polynomials - this Math is Fun page has several animated explanations plus ten questions for students to check their understanding
- Multiplying Polynomials - a step-by-step explanation from PurpleMath
- Multiplying Polynomials - Beginning Algebra Tutorial 28 from West Texas A & M's Virtual Math Lab
- Multiplying Polynomials - following the explanation from Free Math Help you will find an interactive problem solver
- Multiplying Polynomials: an Example - video lesson from Khan Academy
- Multiplying Polynomials Calculator - the Wolfram calculator includes input interpretation and possible intermediate steps
- Solving Polynomial Equations - In algebra you spend lots of time solving polynomial equations or factoring polynomials (which is the same thing). This paper ties them all together in a coherent whole.
- Steps Required for Multiplying Polynomials - five examples followed by a link to practice problems
Level 2 perform basic operations using complex numbers (i.e., addition, subtraction, and multiplication)

- Basic Operations With Complex Numbers - topics covered are addition, multiplication and division, sample problems are given and answers are available
- Complex Number Operations - [9:56] a You Tube video
- Complex Numbers - explanation, examples and review questions at the bottom of this Math is Fun page
- Complex Numbers - rules of complex arithmetic
- Complex Numbers - online algebra notes
- Complex Numbers Primer - algebra notes
- A concentration type game from Quia using algebraic expressions - If d = 2 match the algebraic expressions to the correct answers.
- How To Perform Operations With Complex Numbers - explanation from the Dummies series
- Interactive Algebra Review - Rational Algebraic Expressions [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.]
- Operations on Complex Numbers - To simplify complex-valued expressions, you combine "like" terms and apply the various other methods you learned for working with polynomials.
- Operations With Complex Numbers - this Algebra Lab interactive page covers addition, multiplication and division and has sample problems for each operation
- Operations With Complex Numbers - [6:06] a You Tube video
- Operations With Complex Numbers - this worksheet has two pages of problems and is followed by two pages of answers
select a graph that represents an absolute value equation on a coordinate plane

- Absolute Value Inequalities - [5 pages] examples, exercises and a quiz
- Absolute Value lesson - from Purple Math
- Coordinate Graphs - extensive explanation from Cliffs Notes
- Coordinate Planes and Graphs - explanation with quite a few examples
- Graphing Absolute Value Expressions - [22 slides] several review questions for students included
- Graphing Absolute Value Functions - from the academic support center of Mercy High School in Michigan
- Graph Absolute Value Inequalities (Coordinate Plane) - [2:33] short video lesson
- Graphing Absolute Value Inequalities on the Coordinate Plane - [5:43] video lesson
- Graphing Inequalities - [8:04] video lesson from Khan Academy
- Graphing Inequalities - from Tutor Vista
- How to Graph Absolute Value Inequalities on a Coordinate Plane - step by step from eHow
- Length of a Line Segment (Distance) - When working with Coordinate Geometry, there are many ways to find distances (lengths) of line segments on graph paper.
- Linear Inequalities - How to graph the equation of a linear inequality. [includes an interactive linear inequality]
- Popular Tutorials - topics in ordered pairs, relations, and the coordinate plane at Virtual Nerd
- Practice Problems - fifty-three practice problems, with solutions available from Hotmath
- Simplifying Basic Absolute Value Expressions - practice exercises at Math Pinball
- Solving Absolute Value Equations - a lesson from Purple Math
- Solving Absolute Value Equations and Inequalities - includes a short video
identify the exponential form of a logarithmic expression and vice versa

- Changing from Exponential to Logarithmic Form - [4 pages] explanation, examples, and practice problems
- Convert Logarithms and Exponentials - explanation and examples
- Converting between Exponential and Logarithmic Equations - explanation including two graphs
- Exponential & Logarithmic Expressions - seventy-four question quiz
- How Can Your Rewrite a Logarithm Expression - explanation, examples, and practice problems
- How Do You Convert From Logarithmic Form to Exponential Form? - [3:12] short video from Virtual Nerd
- Logarithmic Expressions - explanation from the Regents Exam Prep Center
- Logarithm Worksheets - links to a large number of free worksheets, all in .pdf format
- Logarithms - In this section, you will learn a variety of properties and applications involving logarithms.
- Writing in Logarithmic and Exponential Form - [1:42] video lesson from Khan Academy
simplify expressions with rational and negative exponents

- Converting Numbers to Scientific Notation - AAA Math lesson and practice problems &
- Evaluating Exponents of Negative Numbers - AAA Math lesson and practice problems &
- Exponent Practice - Try a workout of 10 problems. If you get at least 8 correct on your first attempt, then you're ready to move on. If not, review "In Depth" and try again.
- Exponents - Unit 3 from Ms. Glosser's Math Goodies
- Fractional Exponent Expressions - [2:02] video lesson from Khan Academy
- How Do You Simplify an Expression With Negative Exponents? - [4:40] short video from Virtual Nerd
- Interactive Algebra Review on Integer Exponents [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.]
- Negative Fractional Exponents Examples - video lesson from Khan Academy
- Rational Expressions - lesson designed to help students convert radicals to expressions with rational exponents
- Rational Exponents - tutorial from the Virtual Math Lab at West Texas A & M University
- Scientific Notation - interactive practice
- Simplify Fraction Exponents - formula and examples of how to simplify fraction exponents
- Simplifying - Expressions that have had their like terms combined. Match each expression on the left with an expression on the right. Type the letter of the correct expression in the box.
- Simplifying Expressions - examples of mathematical expressions from Tutor Vista
- Simplifying Expressions with Exponents - Demonstrates how to simplify exponent expressions, including fractional ones.
- Simplifying Expressions with Negative Exponents - several examples from Purple Math
- Use the Equation Calculator from Algebra Help
add, subtract, and multiply algebraic expressions.

Level 3 determine the conjugate of a complex number Sample Task design and build a simple fractal from available materials

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Standard 2 Algebra

Students will describe, extend, analyze, and create a wide variety of patterns and functions using appropriate materials and representations in real-world problem solving, and will demonstrate an understanding of the behavior of a variety of functions and their graphs.Level 1 translate a verbal sentence into an algebraic equation and vice versa

- Word Problems For Kids - This is a set of carefully selected problems (grade 5 to Grade 12) which can help you improve your problem solving skills.
- Ms. Lindquist: The Tutor - A free, web-delivered, intelligent tutoring system for tutoring students in writing expressions for algebra word problems. This site is sponsored by NSF.
- Learn to solve word problems - This is a collection of word problem solvers that solve your problems and help you understand the solutions.
- Solving Equations - illustrates the process of solving equations of various forms (from SOS Math)
select the algebraic equation that generalizes the pattern represented by data in a given table solve multi-step (more than two steps) linear equations (one set of parentheses on each side of the equations and/or variables on both sides)

- Solving Equations - illustrates the process of solving equations of various forms (from SOS Math)
- Solving Simple Linear Equations with Integer Coefficients - practice exercises at Math Pinball [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.]
- Solving More Complicated Linear Equations with Integer Coefficients - practice exercises at Math Pinball [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.]
select the graph that represents a given linear function expressed in slope-intercept form

- Algebra vs the Cockroaches - determine the slope of the line that cockroaches are crawling along to destroy them
- Equation of a Line: Slope-Intercept Form - An interactive applet that will help you visualize how changing the values for the slope, m, and the y-intercept, b, will affect the graph of the equation y = mx + b.
- Slope Intercept Jeopardy review game in the form of a PowerPoint show
select the graph that models a given real-world situation (i.e., linear and non-linear) identify the graphical representation of the solution to a one-variable inequality on a number line

- Number Line Bounce - use all the arrows to bounce back and forth along the number line to reach a target number
- Visualizing Numbers on an Interactive Number Line - instructions for using this activity are included
Level 2 select functional notation to generalize a given numeric pattern

Calculating the nth Term - how to develop a formula that can be used to calculate these terms

- Multiple-Choice Questions ? twenty (20) questions on?Patterns & Functions
solve one-variable linear equations with rational expressions

- Solving Simple Linear Equations with Integer Coefficients - practice exercises at Math Pinball [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.]
- Solving More Complicated Linear Equations with Integer Coefficients - practice exercises at Math Pinball [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.]
select the graph of a two-variable inequality determine the domain of polynomial, rational, square root, exponential and logarithmic functions

- Simplifying Radical Expressions - Intermediate Algebra tutorial
- Simplifying Radicals - explanation and practice problems
determine the range of a wide variety of functions given a graph solve a system of linear equations with 2 variables (e.g. substitution, elimination, Cramer?s Rule, and graphing) apply properties of logarithms to simplify a logarithmic expression

- Properties of Logarithms from SOS Math
- College Algebra - a tutorial on Logarithmic Properties with several examples and practice problems
- Basic Log Rules from Purple Math
identify matrices that model given real-world situations

Level 3 determine the inverse of a logarithmic function given its graph

- Exponential functions - a review of logarithms from SOS Math
- Inverse, Exponential and Logarithmic functions - five practice problems from Spark Notes
Sample Task examine patterns found in Pascal?s Triangle return to the top of the page

Standard 3 Geometry

Students will investigate, model, and apply geometric properties and relationshipsLevel 1 apply the given Pythagorean Theorem to real-world problems

- Animated Proof of the Pythagorean Theorem
- Demonstrate the Pythagorean Theorem - from NOVA
- Interactive Proof of Pythagoras' theorem - This Java applet was written by Jim Morey. It won grand prize in Sun Microsystem's Java programming contest in the Summer of 1995.
- Nineteen Pythagorean Theorem applets
- Pythagorean theorem - In this session, you will look at a few proofs and several applications of one of the most famous theorems in mathematics
- Proof of the theorem is demonstrated through a Quicktime animation
- Pythagorean Theorem - a java applet that allows students to investigate this theorem
- Pythagorean Theorem and its many proofs (43 to be precise)
- The Pythagorean Theorem, Distance Formula and Intro to Trigonometry - other practice activities
- Using the Pythagorean Theorem Once you know the equation a 2 + b 2 = c 2 is true, then you can use it to solve all kinds of problems. Try the Pythagorean theorem with two other examples given on this page
Level 2 predict the graphical transformation that occurs when coefficients and/or constants of given function are changed (no trigonometric or logarithmic functions)

apply proportion and the concepts of similar triangles to solve real world problems

- Geometry Java Applets - Similar Figures
- A Mathematical Droodle - Two Triples of Similar Triangles
- Percent and Proportion - unit 10 from Ms. Glosser's Math Goodies
- Plane Math - Nine activities involving aviation and mathematic
- Proportional Thinking and Probability - here you will find the Customizable Proportion Problems and much more
- Ratio and Proportion - four stage lesson includes examples and a set of workout problems
Level 3 describe the transformation that has changed a ?parent function? to the given related function (e.g., right shift of 3 units, reflection in the x-axis)

Sample Task use properties of similar triangles to determine the height of objects that are difficult to measure

- Determining The Height Of A Waterfall - In research on waterfalls often the most confusing aspect has been determining the true height of a waterfall.
- How to use the distance formula to find distances between (x,y) points
- Object Height Calculator - Use the SCSA Object Height Calculator to calculate the height of tall shadow-casters, e.g., buildings, flagpoles, utility poles, trees, etc.
- Out of the Shadows: The Problem of Slopes - Knowing the sun's elevation is not enough to determine the height of an object from the length of its shadow; the slope of the surface on which the shadow is being cast must also be known.
- Measured Altitude of a Model Rocket - a simple way to determine the maximum altitude the rocket reaches at the end of the coasting flight
- Measured Altitude of a Kite - a simple way to determine the altitude of a flying kite
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Standard 4 Measurement

The student will understand and be able to apply the units, systems and processes of measurement.Level 1 select the area representation for a given product of two binomials

Level 2 apply the given formula to find area and circumference of circles, area and perimeter of polygons, and volume of regular solids

- Lesson on Circumference of a Circle - a quiz is included at the bottom of the page
- Lesson on the Area of a Circle
- Circle, Sphere & Cylinder Calculator
Level 3 solve real world problems given logarithmic and exponential formulas (e.g. Ph scale, Richter scale.)

Sample Task Students construct designs using basic geometric constructions. Then they transfer the design to a piece of 8" X 11" pane of plexiglas and paint the pane to create a ?stained glass.? Students construct one of the? regular 3-dimensional solid and compute the volume and surface area.

Standard 5 Data Analysis and Probability

The student will collect, organize, represent, and interpret data; make and evaluate inferences and predictions; present and evaluate arguments based on data analysis; and model situations to determine theoretical and experimental probabilities.Level 1 make a prediction from the graph of a real-world data set

- Graphs and charts - four different graphs and charts for you to consider
- Math in Daily Life: How do numbers affect everyday decisions? - A unit from Annenberg CPB which includes several hands-on activities.
- Plane Math - Nine activities involving aviation and mathematic
- Using Data and Statistics - good graphs, however they are not interactive
- Fun and Sun Rent-a-Car - students use tables, graphs, linear functions to solve a real-world problem
- Hand Squeeze - (a data collection and analysis class experiment) - Pass a "hand squeeze" around a circle and measure the amount of time that it takes for the hand squeeze to complete the circle.
- What Percentage of your Class is Right or Left Handed? - a data collection and analysis class experiment
- What are Your Chances - What many people refer to as 'good luck' can actually be explained by a little knowledge about probability and statistics. Our dice game allows you to see how increasing or decreasing the number of dice rolls effects an outcome.
determine the measures of central tendency for a given set of real-world data

- Central Tendency - explanation of this concept and related concepts
- Measures of Central Tendency - tutorial and examples
- Running and Weighted Averages - tutorial and examples
choose the matching linear graph when given a set of ordered pairs representing real-world data

Level 2 categorize the correlation of a scatter plot using real-world data (i.e., positive, negative, strong, or weak)

- Creating an Excel XY (Scatter) Plot - simple explanation
- Creating a Scatter Plot in Excel - two elaborate examples of scatter plots; Beer's law scatter plot and linear regression, and creating a scatter plot of titration data
- Explanation of Scatter Plot s from the Engineering Statistics Handbook
- Scatter Plot Applet - This applet draws a scatter plot of points (a,b), where the data is taken from an input table. The table is on the left side of the applet and can be edited by the user.
- Using Excel to create a Scatter Plot - an Internet4Classrooms module
- Weather and Spreadsheets - Java applet which allows you to enter data and display a scatter plot or a column chart of the data entered
determine the number of possible outcomes for a given experiment (i.e. the multiplication counting principle, permutations, or combinations)

determine the theoretical probability of a simple event for a given situation

- Probabilistic Situations - a short slide show on the topic
- Coin Flipping - Flip the coin and calculate the probability of flipping heads or tails.
- Ken White's Coin Flipping page - flip up to 100 coins and see the total number of heads and tails. Excellent for teaching about probability.
- Interactive Probability Tutorials: Sample Spaces and Events , Estimated Probability , Empirical Probability , Abstract Probability and Conditional Probability and Independence
- What are Your Chances - What many people refer to as 'good luck' can actually be explained by a little knowledge about probability and statistics. Our dice game allows you to see how increasing or decreasing the number of dice rolls effects an outcome.
determine the theoretical probability of a compound event (i.e., dependent or independent, union and intersection)

Level 3 find the equation for the line of best fit given a scatter plot depicting real-world data Sample Task Students analyze real-world data collected from the newspaper and explore and report the uses, misuses, and abuses of reported statistical data.? Students search the internet to collect age and market value of a selected vehicle over a specific period of time.? They use a graphing calculator to create a scatter plot and construct a line of best fit to predict the depreciation of the vehicle.

- Finding Data on the Internet - You'll soon be checking facts and downloading reputable data on everything from public safety to education to agriculture to crime to economics ... you name it. This site is intended as a resource for journalists, but why not make this a source for projects. Your students can find raw data related to: aviation, demographics, weather, energy, health, immigration and more.
- List of Data Sources on the Internet4Classrooms Project page
- Review of tables, charts and graphs - an index of topics
- Using Graphs, Equations, and Tables to Investigate the Elimination of Medicine from the Body - This three-part example illustrates the use of iteration, recursion, and algebra to model and analyze the changing amount of medicine in an athlete's body.

site for teachers | PowerPoint show | Acrobat document | Word document | whiteboard resource | sound |video format | interactive lesson |a quiz | lesson plan | to print

Multiple

Review

Activities

- SOS Mathematics - Algebra lessons
- AAA Math offers a large number of math review topics , each one supported by an interactive practice page (8th grade level)
- Interactive online End of Course Algebra Review - [This expired link is available through the Wayback Machine Internet Archive. If the page doesn't load quickly click on Impatient? at the bottom right of the page.]
- Practical Algebra Lessons from PurpleMath - The lessons give practical tips, hints, and examples, and point out common mistakes.
- Practice Tests from Virginia State Standards of Learning - Select Algebra I or II , and then select 10, 20, or 40 questions.
- Algebra Help - in-depth algebra help through algebra history, an online textbook, and various articles covering everything from basic algebra fundamentals to the latest-and-greatest algebra software help available
- National Library of Virtual Manipulatives - Virtual manipulatives related to the NCTM Number & Operations standard.

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