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Algebra 2

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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 This is an Adobe Acrobat document This link includes something for the teacher to print
FCAT Sample Answer Book - [2008] sample questions and test taking tips This is an Adobe Acrobat document This link includes something for the teacher to print
Texas Released Tests
Virginia DOE index of released tests This is an Adobe Acrobat document

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

  1. Comparing Seven Digit Numbers - practice area followed by an interactive game This site is interactive and allows students to play a game or input or collect data
  2. Rational and Irrational number review
identify the reciprocal of a real number
  1. Rational Number and its Reciprocal - a step-by-step examination of a problem by Dr. Math
  2. 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.
  1. 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.] This site is interactive and allows students to play a game or input or collect data
  2. Interactive Algebra Review - Multiplying Algebraic Expressions This site is interactive and allows students to play a game or input or collect data
  3. Interactive Algebra Review - Solving Polynomial Equations (see also part B of this tutorial ) This site is interactive and allows students to play a game or input or collect data
  4. Multiplying Polynomials - a step-by-step explanation from PurpleMath
  5. 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)

  1. A concentration type game from Quia using algebraic expressions - If d = 2 match the algebraic expressions to the correct answers. This site includes questions for your students to check their understanding
  2. Interactive Algebra Review - Rational Algebraic Expressions This site is interactive and allows students to play a game or input or collect data
select a graph that represents an absolute value equation on a coordinate plane
  1. Absolute Value lesson from Purple Math
  2. Simplifying Basic Absolute Value Expressions - practice exercises at Math Pinball This site is interactive and allows students to play a game or input or collect data
  3. 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
  1. Converting Numbers to Scientific Notation - AAA Math lesson and practice problems This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  2. Interactive Algebra Review on Integer Exponents This site is interactive and allows students to play a game or input or collect data
  3. Evaluating Exponents of Negative Numbers - AAA Math lesson and practice problems This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  4. 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. This site is interactive and allows students to play a game or input or collect data
  5. Exponents - Unit 3 from Ms. Glosser's Math Goodies
  6. Scientific Notation - interactive practice This site is interactive and allows students to play a game or input or collect data
  7. 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. This site includes questions for your students to check their understanding
  8. Use the Equation Calculator from Algebra Help This site is interactive and allows students to play a game or input or collect data
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

  1. 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.
  2. 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. This site is interactive and allows students to play a game or input or collect data
  3. Learn to solve word problems - This is a collection of word problem solvers that solve your problems and help you understand the solutions. This site is interactive and allows students to play a game or input or collect data
  4. 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)
  1. Solving Equations - illustrates the process of solving equations of various forms (from SOS Math)
  2. Solving Simple Linear Equations with Integer Coefficients - practice exercises at Math Pinball This site is interactive and allows students to play a game or input or collect data [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.]
  3. 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.] This site is interactive and allows students to play a game or input or collect data
select the graph that represents a given linear function expressed in slope-intercept form
  1. Algebra vs the Cockroaches - determine the slope of the line that cockroaches are crawling along to destroy them This site is interactive and allows students to play a game or input or collect data
  2. 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. This site is interactive and allows students to play a game or input or collect data
  3. A PowerPoint show related to this standardSlope 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
  1. Number Line Bounce - use all the arrows to bounce back and forth along the number line to reach a target number This site is interactive and allows students to play a game or input or collect data
  2. Visualizing Numbers on an Interactive Number Line - instructions for using this activity are included This site is interactive and allows students to play a game or input or collect data
Level 2

select functional notation to generalize a given numeric pattern

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

  2. Multiple-Choice Questions – twenty (20) questions on Patterns & Functions This site includes questions for your students to check their understanding
solve one-variable linear equations with rational expressions
  1. Solving Simple Linear Equations with Integer Coefficients - practice exercises at Math Pinball This site is interactive and allows students to play a game or input or collect data [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.]
  2. 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.] This site is interactive and allows students to play a game or input or collect data
select the graph of a two-variable inequality  
determine the domain of polynomial, rational, square root, exponential and logarithmic functions
  1. Simplifying Radical Expressions - Intermediate Algebra tutorial
  2. 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
  1. Properties of Logarithms from SOS Math
  2. College Algebra - a tutorial on Logarithmic Properties with several examples and practice problems
  3. 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

  1. Exponential functions - a review of logarithms from SOS Math
  2. 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

  1. Animated Proof of the Pythagorean Theorem
  2. Demonstrate the Pythagorean Theorem - from NOVA This site is interactive and allows students to play a game or input or collect data
  3. 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. This site is interactive and allows students to play a game or input or collect data
  4. Nineteen Pythagorean Theorem applets This site is interactive and allows students to play a game or input or collect data
  5. Pythagorean theorem - In this session, you will look at a few proofs and several applications of one of the most famous theorems in mathematics A lesson plan can be found at this site
  6. Proof of the theorem is demonstrated through a Quicktime animation
  7. Pythagorean Theorem - a java applet that allows students to investigate this theorem This site is interactive and allows students to play a game or input or collect data
  8. Pythagorean Theorem and its many proofs (43 to be precise)
  9. The Pythagorean Theorem, Distance Formula and Intro to Trigonometry - other practice activities
  10. 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
  1. Geometry Java Applets - Similar Figures This site is interactive and allows students to play a game or input or collect data
  2. A Mathematical Droodle - Two Triples of Similar Triangles This site is interactive and allows students to play a game or input or collect data
  3. Percent and Proportion - unit 10 from Ms. Glosser's Math Goodies
  4. Plane Math - Nine activities involving aviation and mathematic This site is interactive and allows students to play a game or input or collect data
  5. Proportional Thinking and Probability - here you will find the Customizable Proportion Problems and much more
  6. 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
  1. Determining The Height Of A Waterfall - In research on waterfalls often the most confusing aspect has been determining the true height of a waterfall.
  2. How to use the distance formula to find distances between (x,y) points
  3. 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. This site is interactive and allows students to play a game or input or collect data
  4. 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.
  5. Measured Altitude of a Model Rocket - a simple way to determine the maximum altitude the rocket reaches at the end of the coasting flight
  6. 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
  1. Lesson on Circumference of a Circle - a quiz is included at the bottom of the page
  2. Lesson on the Area of a Circle This site is interactive and allows students to play a game or input or collect data
  3. Circle, Sphere & Cylinder Calculator This site is interactive and allows students to play a game or input or collect data
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

  1. Graphs and charts - four different graphs and charts for you to consider This site is interactive and allows students to play a game or input or collect data
  2. Math in Daily Life: How do numbers affect everyday decisions? - A unit from Annenberg CPB which includes several hands-on activities. A lesson plan can be found at this site
  3. Plane Math - Nine activities involving aviation and mathematic This site is interactive and allows students to play a game or input or collect data
  4. Using Data and Statistics - good graphs, however they are not interactive
  5. Fun and Sun Rent-a-Car - students use tables, graphs, linear functions to solve a real-world problem A lesson plan can be found at this site
  6. 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. A lesson plan can be found at this site
  7. What Percentage of your Class is Right or Left Handed? - a data collection and analysis class experiment A lesson plan can be found at this site
  8. 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. This site is interactive and allows students to play a game or input or collect data
determine the measures of central tendency for a given set of real-world data
  1. Central Tendency - explanation of this concept and related concepts
  2. Measures of Central Tendency - tutorial and examples
  3. 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)

  1. Creating an Excel XY (Scatter) Plot - simple explanation
  2. 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
  3. Explanation of Scatter Plot s from the Engineering Statistics Handbook
  4. 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. This site is interactive and allows students to play a game or input or collect data
  5. Using Excel to create a Scatter Plot - an Internet4Classrooms module
  6. Weather and Spreadsheets - Java applet which allows you to enter data and display a scatter plot or a column chart of the data entered This site is interactive and allows students to play a game or input or collect data
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
  1. Probabilistic Situations - a short slide show on the topic
  2. Coin Flipping - Flip the coin and calculate the probability of flipping heads or tails. This site is interactive and allows students to play a game or input or collect data
  3. 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. This site is interactive and allows students to play a game or input or collect data
  4. Interactive Probability Tutorials: Sample Spaces and Events , Estimated Probability , Empirical Probability , Abstract Probability and Conditional Probability and Independence This site is interactive and allows students to play a game or input or collect data
  5. 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. This site is interactive and allows students to play a game or input or collect data
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
  1. 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.
  1. 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.
  2. List of Data Sources on the Internet4Classrooms Project page
  3. Review of tables, charts and graphs - an index of topics
  4. 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. A lesson plan can be found at this site




A resource for the teacher to use in planning their lessons site for teachers | A PowerPoint show related to this standard PowerPoint show | An Adobe Acrobat document in .pdf format Acrobat document | A Microsoft Word document to be downloaded Word document | This interactive site would work well on an interactive whiteboard whiteboard resource | This resource includes voice instructions for students sound | A video is available through this link video format | This site is interactive and allows students to play a game or input or collect data interactive lesson | This site includes questions for your students to check their understanding a quiz | A lesson plan can be found at this site lesson plan | This link includes something for the teacher to print to print

 


Multiple
Review
Activities
  1. SOS Mathematics - Algebra lessons
  2. AAA Math offers a large number of math review topics , each one supported by an interactive practice page (8th grade level)
  3. 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.]
  4. Practical Algebra Lessons from PurpleMath - The lessons give practical tips, hints, and examples, and point out common mistakes.
  5. Practice Tests from Virginia State Standards of Learning - Select Algebra I or II , and then select 10, 20, or 40 questions. This site is interactive and allows students to play a game or input or collect data
  6. 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
  7. National Library of Virtual Manipulatives - Virtual manipulatives related to the NCTM Number & Operations standard.

 

 

Internet4classrooms is a collaborative effort by Susan Brooks and Bill Byles.
 

  

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