Algebra

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Algebra

How to Add and Subtract with Powers

To add or subtract with powers, both the variables and the exponents of the variables must be the same. You perform the required operations on the coefficients, leaving the variable and exponent as they are. When adding or subtracting with powers, the terms that combine always have exactly the same variables with exactly the same powers. [more…]

Algebra

How to Write Numbers in Scientific Notation

Scientific notation is a standard way of writing very large and very small numbers so that they're easier to both compare and use in computations. [more…]

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Algebra Basics

How to Use the Order of Operations

Follow the order of operations with each algebra problem you solve. The order of operations in algebra is important if you want to find the correct answer. You first work through any grouping symbols, [more…]

Quadratics in Algebra

Standard Equations of Algebraic Conics

Conics are curved algebraic forms that come from slicing a cone with a plane. Use these equations to graph algebraic conics, such as circles, ellipses, parabolas, and hyperbolas: [more…]

Linear Equations in Algebra

Cramer’s Rule for Linear Algebra

Named for Gabriel Cramer, Cramer’s Rule provides a solution for a system of two linear algebraic equations in terms of determinants — the numbers associated with a specific, square matrix. [more…]

Counting Techniques

Algebraic Permutations and Combinations

In algebra, you use permutations to count the number of subsets of a larger set. Use permutations when order is necessary. With combinations, you can count the number of subsets when order doesn't matter [more…]

Algebra Basics

Eight Basic Algebraic Curves

Algebra is all about graphing relationships, and the curve is one of the most basic shapes used. Here's a look at eight of the most frequently used graphs. [more…]

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Algebra II: What Is the Binomial Theorem?

A binomial is a mathematical expression that has two terms. In algebra, people frequently raise binomials to powers to complete computations. The binomial theorem says that if [more…]

Use the Properties of Proportions to Simplify Fractions

In algebra, the properties of proportions come in handy when solving equations involving fractions. When you can, change an algebraic equation with fractions in it to a proportion for easy solving. [more…]

Algebra II: Raise Binomials to a Power

A binomial is a mathematical expression that has two terms. In algebra, people frequently raise binomials to powers in order to solve equations. Here are some examples: [more…]

Algebra II: Basics of Logarithms and Exponents

Before handheld calculators, students used tables of logarithms (or logs) to do calculations in physics and other science classes. Those tables of logarithms allowed you to do multiplication or division [more…]

Algebra II: Making Matrices Work for You

A matrix is a rectangular array of numbers. Each row has the same number of elements, and each column has the same number of elements. Matrices can be classified as: square, identity, zero, column, and [more…]

10 Pitfalls to Avoid When Working with Exponents

In algebra, the rules used when working with exponents are straightforward and consistent. Challenges arise, though, when applying the rules or knowing how to apply the rules in situations where the problem [more…]

Algebra II: Hidden Intersections of Curves

When solving systems of equations, you have several options at your disposal for finding those common solutions. Linear systems can be solved by hand, algebraically, using elimination, or substitution [more…]

Algebra II Workbook For Dummies Cheat Sheet

Learning some algebraic rules for various exponents, radicals, laws, binomials, formulas, and equations will help you successfully study and solve problems in an Algebra II course. You should also be able [more…]

10 Basic Algebraic Graphs

Graphing is one way of getting the characteristics of a function out there for everyone to see. The basic graphs are just that — basic. They’re centered at the origin and aren’t expanded or shrunken or [more…]

Using the Multiplication Property in Sets

When you want to count up how many things are in a set, you have quite a few options. When the set contains too many elements to count accurately, you look for some sort of pattern or rule to help out. [more…]

How to Graph Parabolas

The graph of a quadratic function is a smooth, U-shaped curve that opens either upward or downward, depending on the sign of the coefficient of the x2 term. The vertex and intercepts offer the quickest [more…]

Hyperbola: Standard Equations and Foci

Of the four types of conic sections, the hyperbola is the only conic that seems a bit disconnected. The graph of a hyperbola is two separate curves seeming to face away from one another. The standard forms [more…]

Systems with Three Linear Equations

When working with systems of equations, you can solve for one variable at a time. So, if a third linear equation comes along (bringing, of course, its variable [more…]

Finding the Intersections of Lines and Parabolas

A line can cut through a parabola in two points, or it may just be tangent to the parabola and touch it at one point. And then, sadly, a line and a parabola may never meet. When solving systems of equations [more…]

Crossing Curves: Finding the Intersections of Parabolas and Circles

When a parabola and circle intersect, the possibilities for their meeting are many and varied. The two curves can intersect in as many as four different points, or maybe three, or just two or even just [more…]

Operations on Complex Numbers

A complex number has the standard form a + bi, where a and b are real numbers. You can add, subtract, and multiply complex numbers using the same algebraic rules as those for real numbers and then simplify [more…]

“Dividing” Complex Numbers with a Conjugate

Mathematicians (that’s you) can add, subtract, and multiply complex numbers. Technically, you can’t divide complex numbers — in the traditional sense. You divide complex numbers by writing the division [more…]

Applying Quadratics to Real-Life Situations

Quadratic equations lend themselves to modeling situations that happen in real life, such as the rise and fall of profits from selling goods, the decrease and increase in the amount of time it takes to [more…]

Digging Up Polynomial Roots with Factoring

When solving for roots (x-intercepts of a polynomial), you usually need to factor the function rule and set it equal to 0. The factorization can be simple and obvious or complicated and obscure. You always [more…]

Solving Two Linear Equations Algebraically

A solution of a system of two linear equations consists of the values of x and y that make both of the equations true — at the same time. Graphically, the solution is the point where the two lines intersect [more…]

Simplifying Powers of i

Performing operations on complex numbers requires multiplying by i and simplifying powers of i. By definition, i = the square root of –1, so i2 = –1. If you want [more…]

Solving Equations with Complex Solutions

You often come across equations that have no real solutions — or equations that have the potential for many more real solutions than they actually have. For instance, the equation [more…]

5 Basic Sequences and Their Sums

A sequence is a list of terms that has a formula or pattern for determining the numbers to come. A series is the sum of the terms in a sequence. Many sequences of numbers are used in financial and scientific [more…]

5 Special Sequences and Their Sums

Arithmetic sequences are very predictable. The terms are always a constant difference from one another. The terms in an arithmetic sequence are a1, a2, [more…]

How to Write the Elements of a Set from Rules or Patterns

You can describe the elements in a set in several different ways, but you usually want to choose the method that’s quickest and most efficient and/or clearest to the reader. The two main methods for describing [more…]

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