End-of-Course - Algebra II

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

Links verified 3/13/2012

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 tests

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	Comparing Seven Digit Numbers - practice area followed by an interactive game Rational and Irrational number review
identify the reciprocal of a real number	Rational Number and its Reciprocal - a step-by-step examination of a problem by Dr. Math How do I find the reciprocal of a decimal mixed number? - an answer to a student's question
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.] Interactive Algebra Review - Multiplying Algebraic Expressions Interactive Algebra Review - Solving Polynomial Equations (see also part B of this tutorial ) Multiplying Polynomials - a step-by-step explanation from PurpleMath 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.
Level 2
perform basic operations using complex numbers (i.e., addition, subtraction, and multiplication)	A concentration type game from Quia using algebraic expressions - If d = 2 match the algebraic expressions to the correct answers. Interactive Algebra Review - Rational Algebraic Expressions
select a graph that represents an absolute value equation on a coordinate plane	Absolute Value lesson from Purple Math Simplifying Basic Absolute Value Expressions - practice exercises at Math Pinball Solving Absolute Value Equations - a lesson from Purple Math
identify the exponential form of a logarithmic expression and vice versa
simplify expressions with rational and negative exponents	Converting Numbers to Scientific Notation - AAA Math lesson and practice problems & Interactive Algebra Review on Integer Exponents 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 Scientific Notation - interactive practice 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. 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

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Standard 3 Geometry Students will investigate, model, and apply geometric properties and relationships
Level 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.

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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	see a list above
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.

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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.