Algebra Homework Help Secrets
Better Algebra Grades-Less Effort
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We will take you through the basics of Algebra - from understanding unknowns, variables and constants to linear and quadratic algebraic expressions.
To help you understand our Algebra Homework Help Secrets we have put together an Algebra Dictionary of simple basic definitions of all the important terms and words you will need to understand and master basic algebra skills.
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The secret to understanding and mastering Algebra is to realize that Algebra is just arithmetic (adding, subtracting, multiplying, dividing...) using symbols that represent numbers instead of numbers alone. In algebra these symbols are usually letters such as x, y and z which we call variables. Other symbols typically represented by the letters a, b, c... are held at a constant value. In arithmetic we use actual numbers that have a fixed and known value. In algebra we use symbols that do not have a known value. If the unknown value of these symbols is fixed we call them constants. If the unknown value of these symbols can vary we call them variables.
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Order of Operations
One of the most basic issues we need to deal with in our Algebra Homework Help Secrets is the order in which we carry out operations. In arithmetic and in algebra there is a specific order in which we must do the basic operations of addition, subtraction, multiplication, etc. In this section we explain why this order is of critical importance and give you an easy way to remember the correct order of operations.
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Units of Measure
In many algebra problems, especially algebra word problems, each variable and constant has a specific unit of measure like centimeters, meters, feet, inches... It is of critical importance to understand how to convert from one unit of measure to another. In this section we show you a special Algebra Homework Help Secret we call the "Unit Equation Approach" where you treat units like numbers. When you master this equation you will be able to convert units of measure with ease.
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In algebra problems we frequently must use several different measurements in our calculations. Some measurements may be very accurate while others are just estimates. The accuracy of a given number is defined by the number of "significant figures" in that number. This section will clearly explain significant figures and give you rules for determining the significant figures of the answers.
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When a given number or variable is multiplied by itself multiple times we need to have shorthand method to represent this. For instance when 2 is multiplied by itself we represent this as 2 x 2 = 22 which is referred to as 2 "raised to the 2nd power". The superscripted 2 is called the exponent and stands for how many times two is multiplied by itself.
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Once you have mastered exponents you can use a really neat way of expressing very large and very small numbers called Scientific Notation.
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An Algebraic Expression is a combination of numbers, variables and/or constants combined with any of the operators from arithmetic such as 2*x2 + 4*x - 2. In algebra we typically use * for multiplication because we don't want to confuse the arithmetic operator for times (x) with the variable x. When the algebraic expression is set = to a number or another expression the result is an Algebra Equation such as 2*x2 + 4*x - 2 = 0.
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The simplest type of Algebra Equation is the Linear Equation or the equation of a straight line. This takes on the general form of y = ax + b. Linear equations describing a straight line can be derived in a number of ways. This page explains linear equations and how they are derived.
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Solving Linear Equations
In this section of Algebra Homework Help we discuss linear equations. These equations mainly contain either one variable (typically x) or two variables (typically x and y). Step-by-step procedures for solving both types of linear equations are discussed in detail in this section.
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A quadratic expression has the general form of ax2 + bx +c and a quadratic equation has the general form ax2 + bx +c = 0. This type of equation describes a curved line rather than a straight line. This page of our Algebra Homework Help defines and describes Quadratic Functions.
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Completing the Square
One specific method that solves many but not quadratic equations involves Completing the Square. This page gives a clear step-by-step explanation of Completing the Square.
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Another key Algebra Homework Help Secret is a general method that will work to solve any quadratic equation is to use the Quadratic Formula. In this section take the mystery out of the Quadratic Formula by showing you how it is derived. Once you learn this you will have no trouble remembering and applying this important formula.
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This very useful theorem or equation was first developed around 500 BC by the Greek philosopher Pythagoras. It establishes the relationship of sides of a very specific type of triangle called a right triangle in which one of the internal angles is 90 degrees. Once you know any two sides of a right triangle you can use the Pythagorean Theorem to calculate the other side. This has many applications in algebra, trigonometry and geometry and is use routinely in construction and surveying.
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A function is defined as an algebraic equation of two variables that expresses the dependence of one variable called the dependent variable (usually x) upon the other variable called the independent variable (usually). Generically this equation is expressed as y = f(x) which is read y equals a function of x. Examples of a function are the straight line equation y = ax + b and the general quadratic y = ax2 + bx + c.
The corresponding values of y for given values of x can be plotted on a piece of graph paper (paper with a grid of regularly spaced, intersecting lines). This plotting activity is called Graphing Functions and will give a visual representation of the shape of the function y=f(x).
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Unless you use a graphing calculator or graphing software, graph paper is necessary for graphing functions. This section of Algebra Homework Help provides a discussion of various kinds of graph paper, how to use them and links to several sites where you can download free graph paper.
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Algebra Word Problems
Using algebra to solve problems in the real world entails formulating algebraic equations based on word descriptions. These kind of problems are called Algebra Word Problems. The only way to get better at solving these types of problems is through practice. This sections gives you a step-by-step approach to solving these word problems and demonstrates this approach with examples.
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Even with the Algebra Homework Help Secrets we have shown you on this website, sometimes, you just need a little one-on-one personal coaching. This section reviews our options for online algebra tutors.
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