Algebra Worksheets |
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Topic or Concept |
Handouts & Worksheets |
Solutions (if available) |
| Section-by-section class notes that refer to a specific book but can be used independent of it | Elementary Algebra Class Notes (First Half of Class) | |
| Section-by-section class notes that refer to a specific book but can be used independent of it | Elementary Algebra Class Notes (Second Half of Class) | |
| Section-by-section class notes that refer to a specific book but can be used independent of it | Intermediate Algebra Class Notes (First Half of Class) | |
| Section-by-section class notes that refer to a specific book but can be used independent of it | Intermediate Algebra Class Notes (Second Half of Class) | |
| Section-by-section class notes that refer to a specific book but can be used independent of it | College Algebra Class Notes (Current Sullivan book) | |
| Section-by-section class notes with accompanying videos that refer to a specific book but can be used independent of it | College Algebra Class Notes (Bittinger, et al book) | |
| Review document I wrote for College algebra covering how I think through problems ranging from solving equations to lines to asymptotes to exponential functions and more | Main points of discussion (31.2 KB) | |
| Complete semester of PowerPoints with audio | College Algebra Multimedia Tutorials | |
| Reviews finding equations of lines, slope, graphing, and x and y-intercepts | Review: Linear
relationships (PowerPoint presentation) |
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| Examples of analytic geometry problems involving maximums and minimums | Mathematical models (PowerPoint presentation) | |
| Quick linear application of revenue, cost, and profit; also analyze using the graphs | Candle Problem: Revenue and Cost | |
| Order of operations | PEMDAS | PEMDAS Solutions |
| This video is a story from TECH.BIN, our student television show from ISU. It introduces the Carchip that is featured in the following worksheet. | Carchip video (Dial-up speed modem - 1.48 MB) Carchip video (DSL speed modem - 10.7 MB) |
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| Explore and interpret basic graphs using software that evaluates a car's performance | Carchip worksheet | Carchip worksheet Solutions |
| Definitions of real numbers and integers, Closure, Commutative, Associative, and Distributive Properties, Factoring | Properties of real numbers 1 | Properties of real numbers 1 Solutions |
| Same as above but lots more discussion and pratice with algebraic fractions (rational expressions) | Properties of real numbers Solutions | |
| Investigate why you can cancel common factors from a fraction but not common terms; also defines these words | Factors versus terms | |
| Area model to help visualize why FOIL works | Understanding FOIL | |
| Acquaint yourself with the graphs of basic functions: square, cube, identity, absolute value, reciprocal, square root, and greatest integer functions | Library of functions | |
| Investigate slope and how linear relationships use it | Understanding slope | |
| Slope of parallel and perpendicular lines | Parallel and perpendicular lines | |
| Understand what a linear equation tells us about the variables x and y | Relationship between x and y | |
| Linear relationships of cost and revenue including break-even point | Linear function applications | Linear function applications Solutions |
| Solving linear equations by undoing what was done to the variable | Solving linear equations | Solving linear equations Solutions |
| Same as above but includes non-linear equations too | Solving equations | Solving equations Solutions |
| Using variables in beginning story problems | Story Problem Pieces | Story Problem Pieces Solutions |
| Using variables in more complex story problems | Story Problem Pieces | Story Problem Pieces Solutions |
| Story problems involving dimensions of a rectangle and split simple interest accounts | Group DoThis 1.4 | Group DoThis 1.4 Solutions |
| Assorted story problems including work-rate, mixture, percentages, simple interest, area of rectangles, and distance-rate | Story problems practice | Story problems practice Solutions |
| Guided examples os story problems including wage rate, rectangle perimeter, mixture, and simple interest | Story problems are my friends | |
| Use pictures to help understand what is going on in mixture problems | Mixture problems: Salt concentration | Mixture problems Solutions: Salt concentration |
| Covers the basic idea of function and function notation | Investigating functions Solutions | |
| Interpret functional notation, determine function values, and determine the domain and range of functions | Investigating functions 2 | Investigating functions 2 Solutions |
| Understand the formulas for simple and compound interest; practice problems too | Simple and compound interest | |
| Complete to make cheatsheet for interest and annuities formulas, including effective rate of interest | Interest and annuities | |
| Exponent rules | Discovering the rules of exponents | |
| Rules for telling if a number is divisible by another | Rules for Divisibility | |
| General tips for factoring trinomials | Tips for factoring trinomials of the form x^2 + bx + c | |
| Better understand the factoring process by creating your own trinomial | PairDoThis 6.2 | |
| A good introduction to what factoring does for us and the second most popular method for factoring trinomials | Factoring trinomials: Part 1: Introduction, Factoring by grouping, and A-C Method | |
| The most common way to factor a trinomial; also called Trial-and-error | Factoring trinomials: Part 2: Reverse FOIL Method | |
| Similar to the Reverse FOIL method but written differently | Factoring trinomials: Part 3: Cross-product method and Wrap-up | |
| Wacky but neat | Factoring trinomials: Part 4: Upside Down method | |
| Use the calculator to find the numbers needed for the A-C method | Factoring trinomials: Using the Calculator (TI-82, 83, and 84) to Help with the AC Method | |
| Practice solving quadratic equations by factoring | Practice solving by factoring problems | Practice solving by factoring problems Solutions |
| Investigates the quadratic relationship in Can you figire the initial velocity of the ball? including how to answer the question on the Flash problem | Quadratic equations practice | Quadratic equations practice Solutions |
| Investigate the connection between a function's discriminant and the number of x-intercepts its graph has by creating your own examples | Discriminants and x-intercepts | Discriminants and x-intercepts Solutions |
| Investigate the values and number of solutions of a quadratic equation; refers to the calculator program QUADRATC found under Calculator Worksheets; also practice finding the solutions by hand using the quadratic formula | Three possibilities for a quadratic equation | Three possibilities for a quadratic equation Solutions |
| Step-by-step example of using the quadratic formula to solve an equation | Quadratic Formula Example: Solving a quadratic equation | |
| Quick practice solving inequalities | Practice solving inequality problems | Practice solving inequality problems Solutions |
| Solving linear inequalities and using interval notation for solutions | Inequalities and you 1 | Inequalities and you 1 Solutions |
| Solve inequalities both algebraically and graphically | Inequalities and you 2 Solutions | |
| Solve inequalities that involve absolute value, rational, and polynomial expressions including graphical solutions | Inequalities and you 3 | Inequalities and you 3 Solutions |
| Investigates x and y-intercepts, vertex, and if parabola opens up or down (orientation) for quadratic functions | Quadratic functions: Orientation, vertex, and y-intercept | Quadratic functions: Orientation, vertex, and y-intercept Solutions |
| Practice finding vertices and orientation of parabolas (graphs of quadratic functions) including an application problem | Quadratic functions: Maximums and minimums practice | Quadratic functions: Maximums and minimums practice Solutions |
| Practice finding x and y-intercepts, vertex, and orientation for quadratic functions; also practice graphically solving quadratic equations | Quadratic functions practice | Quadratic functions practice Solutions |
| An introduction to the transformation worksheets that follow | Transformations (PowerPoint presentation) | |
| Explore the vertical and horizontal shifts, vertical stretch and compression, and reflections about the x or y axes transformations through graphing | Transformations | |
| Practice some individual and one combined transformations | Transformations 2 | |
| Quick practice for recalling basic functions and transformations | Library of functions and transformations 2 | |
| Practice adding, subtracting, dividing, and composing two functions; also investigate domains | Functions: Composition and operations | Functions: Composition and operations Solutions |
| Practice problems including an application of the composition of functions | Composition of functions | |
| Given two or more equations, you need to find the point that satisfies all equations | Solving linear systems graphically (Includes a discussion of how to write infinite solutions) | |
| Same worksheet as above but skips over how to write infinite solutions | Solving linear systems graphically | |
| How to use the calculator to find solutions to these systems | Solving systems of equations graphically: Calculator worksheet | |
| Understand why simplifying fractions works and when not to do it | Simplifying rational expressions: Cancelling common factors | |
| Example of a complicated multiplication problem involving radicals | Explanation of Radical Multiplication Problem | |
| Solving radical equations, focusing on the order you do the steps | Radical equations: Verbal model worksheet | |
| Explore why we algebraically solve absolute value equations the way we do | Solving absolute value equations | |
| Explore the methods for solving absolute value and radical equations including graphically | Solving absolute value and radical equations | Solving absolute value and radical equations Solutions |
| Find where a graph's y-values increase or decrease, writing the answers in interval notation | Increasing and decreasing functions | Increasing and decreasing functions Solutions (Solutions to older version but still useful for most of worksheet) |
| Understand and denote the four types of end behavior for power functions | Power functions: End behavior | |
| Understand why you can find the end behavior of a polynomial function by looking at its leading term which is a power function | Connection between polynomial and power functions | |
| Understand and denote the four types of end behavior for polynomial functions | Polynomial functions: End behavior | Polynomial functions: End behavior Solutions |
| Create cheatsheet for the Remainder Theorem, Factor Theorem, Descartes' Rule of Signs, and other | Zeroes of polynomial functions | |
| Understand why and where vertical asymptotes exist on the graphs of rational functions | Rational functions: Vertical asymptotes | |
| Understand why and where horizontal (and oblique) asymptotes occur on the graphs of rational functions | Rational functions: Horizontal and oblique asymptotes | |
| Connects the solutions to an equation gotten by algebraic or graphical means; also investigates the difference between finding roots (or zeros) versus the intersections for an equation | Making connections Solutions: Algebraic and graphical solutions | |
| Operating with complex numbers and using them for the solution to a quadratic equation | Manipulating Complex Numbers | Manipulating Complex Numbers Solutions |
| Powers of i and operating with complex numbers | Manipulating Complex Numbers 2 | Manipulating Complex Numbers 2 Solutions |
| Understanding and finding the inverse of a function, including restricting its domain | Inverses of functions | |
| same as above | Inverses of functions 2 | |
| Understand how the idea of inverses can be used in solving equations | Solving equations using inverses | |
| Practice interpreting logarithms | DoThis 4.4 | DoThis 4.4 Solutions |
| Work through deriving the logarithm rules | Logarithm rules worksheet | Logarithm rules worksheet Solutions |
| Develop the log functions by seeing them as the inverse of exponential functions; also work through understanding the rules of logarithms | Visiting with exponential and logarithmic functions | |
| Explores a Flash problem (accessed from home page) concerning a geometric sequence and its exponential graph | Limits and the Bouncing Ball | |
| Explore different methods of solving an exponential equation | DoThis 4.6 | |
| Explores what makes an exponential function increase or decrease; also practices rules of exponents and using e on the calculator | Working with exponential functions | Working with exponential functions Solutions |
| Plot an exponential function and then find its inverse | Logarithmic / Exponential relationship | |
| Derive the equation of an exponential function from a table of values | Additional Examples of Exponential Functions | |
| Explores the intensity of sound, a logarithm application | Logarithmic and exponential applications: Intensity of sound | Logarithmic and exponential applications: Intensity of sound Solutions |
| Exploration of the continuous compounding interest formula; guided examples for solving compound interest problems | Logarithmic / Exponential applications: Compound interest | |
| Explores exponential decay and growth, an application of exponential functions | Logarithmic and exponential applications: Exponential decay and growth | Logarithmic and exponential applications: Exponential decay and growth Solutions |
| Solve exponential applications involving radioactive decay | DoThis 4.8 | |
| Practice solving log equations by using the log rules with step-by-step instructions; also practice solving by graphical means | Using log rules to solve equations | |
| Compare and contrast solving exponential and logarithmic equations by different methods | Solving exponential and logarithmic equations | Solving exponential and logarithmic equations Solutions |
| Practice operating with matrices | DoThis 5.4: Matrix arithmetic | |
| Practice verifying a matrix' inverse | DoThis 10.4: Matrix inverses | |
| Guided practice using partial fraction decomposition to rewrite a rational expression | Partial fraction decomposition | |
| Explore the graphical natures of the parabola, elllipse, and hyperbola | Conic Sections Worksheet (271 KB) | |
| Explores an exponential relationship (found under Flash Problems from the home page of this website) using the language and notation of sequences and series | Sequences and series | |