Attention: Be sure to try our new Radical Expression Calculator to simplify roots and radical expressions.
Quizzes serve as an important check of your progress, and here I stress important. In a math course, you want to make sure you are grasping the material and mastering it. Due to the cumlative nature of an algebra course, you don't want to fall behind and you want to know that you are ready for what is to come.
Below are a selection of quizzes that I gave when I taught college algebra at the University of Missouri. My students always found them challenging and I tried to test for common mistakes. The sooner you can spot your mathematical trouble spots and correct them the better. I hope these serve you well.
Several problems dealing with rational and radical equations. Rational equations are those that involve fractions and have unknowns in the denominator. Radical equations are ones that are just really cool! No, just kidding. These are equations that have radicals, or roots in them.
Polynomials in some respect are like numbers. You can add, subtract, multiply and divide them. It's also useful to know what happens at positive and negative infinity and be able to classify polyinomials as even, odd or neither.
Every function maps an input to one output. We could try to input into one function the output of another. This is exactly what happens when we compose functions. We could also try to reverse the map and try to link every output to its input. That's the inverse of a function.
Logs are just what you throw on the fire. When working with logs we are really working with exponents. There are a number of log properties that must be mastered to work effectively with logs and logarithm equations.
Sometimes one variable just isn't enought to describe the problem at hand. When this is the case, we need two or more unknowns and a system of equations or inequalities.
Just warmups here. You'll find the Pathagorian Theorem, standard form of a circle and simplifying with exponent rules.
Factoring is the process of rewriting an expression in terms of factors. We simply need to change an expression into product of several smaller expressions. There are a number of tricks that we can employ to do this.
When you see rational, think of ratio. Ratios are often written as fractions. Rational espressions then are just ugly looking fractions.
To simplify radical expressions, pull whatever you can out from underneth the radical. You also might need to put some radical rules to use.
Functions are maps, or rules, between two sets. They tell you how to get an output for every input. Make sure your clear on functional notation and how to interpret each point on the graph of a function.
It's ideal to be able to generalize data by means of a model. If your data is linear, this can be done with a line. From there, predicitions and inferences about the data can be made from your model.
A linear equality if fancy speak for a linear equation. Something along the lines of ax + b = y. An inequality is, as you would think, NOT an equality. Thus, it must be a statement where one expression is greater or less than another.
Equations and Inequalities with absolute values in them require special care. Steps must be taken to rewrite the equation or inequality with out the absolute value. From there, it's business as usual. Transformations of graphs involve rotations, streches, shifts and strinks. They usually prove to be more than trying.
The graph of a quadratic function has a distinctive U shape. This is evidence that every quadratic takes on a maximum or minimum value. Many simple optimization problems boil down to this fact. Quadratic functions can be used to model data that is not linear and U-like in nature.