Algebra Worksheets

Use CTRL-F to find specific topics. There are class notes from Intermediate algebra at the top of the page. If you print PowerPoint presentations, find, in the print dialog, where it says it will print "slides" and change that to "handouts". Then select "2 (or more) slides per page". This will save paper.
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  
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)
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)
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

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

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

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: Algebraic and graphical solutions

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