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Algebra 1 Help | Free Algebra 1 Lessons & Practice Problems
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Algebra 1: 01-Introduction to Algebra
Algebra 1: 02-solving equations, algebra 1: 03-solving inequalities, algebra 1: 04-functions, algebra 1: 05-linear functions, algebra 1: 06-systems of equations and inequalities, algebra 1: 07-exponents and exponential functions, algebra 1: 08-polynomials & factoring, algebra 1: 09-quadratic functions and equations, algebra 1: 10-radical expressions & functions, protected: order – march 16, 2020 @ 08:13 pm, algebra 1: 11-rational expressions & functions, algebra 1: 12-data analysis & probability, i. introduction to algebra, lesson: verbal to algebraic expressions & equations.
- Practice 01
- Practice 02
- Practice 03
- Practice 04
Lesson: Declaring Variables
Example: Mike is 3 inches taller than Semande. If Semande is s inches tall, express Mike’s height in terms of s .
Lesson: Order of Operations
Lesson: Real Numbers (Including Rational vs. Irrational Numbers)
Lesson: order of operations with substitution.
Lesson: Adding and Subtracting Real Numbers
Lesson: Multiplying and Dividing Real Numbers
Lesson: Properties of Real Numbers
Lesson: Distributive Property
Lesson: Finding the Solution to an Equation
II. Solving Equations
Lesson: solving algebraic equations (one-step).
Lesson: Solving Multi-Step Equations
Lesson: Multi-Step Equations (Variable on Both Sides)
Lesson: Linear Equations
Lesson: Solving Proportions
Lesson: Solving Complex Proportions
Lesson: Percents
Example: What is 48% of 30?
Lesson: Percent Change
Example: What is the percent change from 50 to 72?
III. Solving Inequalities
Lesson: graphing inequalities.
Lesson: Solving Inequalities Using Addition or Subtraction
Lesson: Solving Inequalities Using Multiplication or Division
Lesson: Solving Inequalities
Lesson: Solving Compound Inequalities
Lesson: Solving and Graphing Compound Inequalities
Lesson: Absolute Value Equations
Lesson: Absolute Value Inequalities
IV. Functions
Lesson: using graphs to relate two quantities.
Lesson: Patterns and Linear Functions
Lesson: Patterns and Non-Linear Functions
Example: For the set of ordered pairs, write the rule that represents the function. (0,1),(1,3),(2,9),(3,27),(4,81)
Lesson: Graphing a Function Rule
Lesson: Writing a Function Rule
Lesson: Formalizing Relations and Functions
Example: Is the following relation shown a function? (-2, 0.5), (0, 2.5), (4, 6.5), (5, 2.5)
V. Linear Functions
Lesson: slope.
- Practice 01 – Slope from a graph & from 2 points
- Practice 02 – Slope from a graph & from 2 points
- Practice 03 – Slope from 2 Points
- Practice 04 – Slope from 2 Points
Lesson: Equation of a Line
Lesson: point slope form, lesson: finding the equation of a line, given the slope and a point, lesson: standard form of the equations of a line.
Lesson: Finding the Equation of a Line, Given Two Points
Lesson: equations of parallel and perpendicular lines.
Lesson: Scatterplots and Trendlines
- If the trend continues, what is the expected y-value when x is 8, based on the scatterplot shown below?
Lesson: Graphing Absolute Value Functions
VI. Systems of Equations and Inequalities
Lesson: solving a system of equations graphically.
Lesson: Solving a System of Equations Using Substitution
Lesson: Solving a System of Equations Using Elimination
Lesson: Applications of Linear Systems
Lesson: word problems – system of equations, lesson: graphing linear inequalities.
- What system of inequalities is shown below?
Lesson: Solving a System of Linear Inequalities
VII. Exponents and Exponential Functions
Lesson: positive exponents.
Lesson: Negative Exponents
Lesson: Multiplying & Dividing Terms that have Exponents
Lesson: Graphs of Exponential Functions
Lesson: Exponential Growth
Lesson: exponential decay.
VIII. Polynomials and Factoring
Lesson: adding & subtracting polynomials.
Lesson: Multiplying a Polynomial by a Monomial
Lesson: Dividing a Polynomial by a Monomial
Lesson: Factor Out the Greatest Common Factor
Lesson: Multiplying Binomials
Lesson: Multiplying a Binomial by a Trinomial
Lesson: Multiplying a Trinomial by a Binomial
Lesson: Multiplying Binomials (Special Cases)
Lesson: Factoring Quadratics
Lesson: Difference of Perfect Squares
Lesson: Factoring by Grouping
IX. Quadratic Functions and Equations
Lesson: evaluating quadratic functions.
Lesson: Properties of Quadratic Functions
Lesson: Solving Quadratic Equations by Taking Square Roots
Lesson: Solving Equations by Factoring
Lesson: Completing the Square
Lesson: Solve Equations by Completing the Square
Lesson: Vertex Form of a Quadratic Function by Completing the Square
Lesson: Solving a System of Equations Graphically (Linear & Quadratic)
Lesson: Solving a System of Equations Using Substitution (Linear & Quadratic)
X. Radical Expressions and Functions
Lesson: pythagorean theorem, lesson: simplifying radical expressions.
Lesson: Adding and Subtracting Radical Expressions
Lesson: Multiplying Radical Expressions
Lesson: Dividing Radical Expressions
Lesson: Solving Equations That Have Radical Terms
Lesson: Graphing Square Root Functions
Lesson: SOHCAHTOA (sine, cosine, tangent)
Lesson: Inverse Trigonometric Functions
XI. Rational Expressions and Functions
Lesson: simplifying rational expressions.
Lesson: Multiplying and Dividing Rational Expressions
Lesson: Dividing Polynomials
Lesson: Adding and Subtracting Rational Expressions
Lesson: Fractional Equations
Lesson: Solving Rational Equations
Lesson: Inverse Variation
Lesson: Graphing Rational Functions
XII. Data Analysis and Probability
Lesson: matrices.
- What are the dimensions of this matrix?
Lesson: Frequency, Cumulative Frequency, & Histograms
Lesson: measures of central tendency & dispersion, lesson: box & whisker plot, lesson: samples and surveys, lesson: permutations and combinations.
Lesson: Theoretical vs. Experimental Probability
Lesson: probability of compound events.
Sign up for a free membership on our algebra 1 lessons & start learning today. Learn about the importance of learning algebra here .
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Algebra Help
In this chapter, we will be discussing Algebra. Algebra is the branch of mathematics that uses symbols to represent numerical values or members of a set of numbers. This representation is called an algebraic expression. Algebra is a powerful tool for solving mathematical problems.
- Polynomials
- Factoring Polynomials
- Division of Polynomials
- Solving Equations
- Solving Inequalities
- Solving Quadratics
- Complex Numbers
- Graphing Quadratics (Parabolas)
- Systems of Equations (2x2s)
- Systems of Equations (3x3s)
- Determinants and Cramer's Rule
- Inverse Functions
- Exponentials and Logarithms
- Absolute Value Equations and Inequalities
- Sequences and Series
- Combinatorics
- Advanced Graphing
- Graphing Polynomials
- Graphing Rational Functions
- Conic Sections
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The Best Free Algebra Homework Help Websites
The grade level where children make the transition from math to algebra can be very easy for some students, but difficult and confusing for others. Math concepts that are centered on clearly defined numbers and with all "factors" within the problem typically defined, are usually fairly easy for most students to follow and understand.
However, algebra concepts insert "unknowns" into equations and formulas that can really throw many students for a loop. Solving an equation for a factor that appears to be on the "wrong side" of the equal sign can feel like a very strange and impossible premise for those students.
As usual, help is available on the Internet, and the following list are some of the best free algebra homework help websites that can make the process of learning algebra a whole lot easier .
MyAlgebra - A Free Algebra Problem Solver
A very simple and useful resource is the MyAlgebra online problem solver application. While this isn't the first place a student should go for help, because it simply provides the answer to the equation, it is an excellent website for students to check their work.
Students can work through their algebra problems, and when they've come up with a solution that they feel is correct, they can simply enter in the equation and click "Answer." Of course, solving for equations isn't the only thing the application can do - there is a long list of funcions in the drop-down list to choose from.
Obviously, the most common choice will be to "solve the equation," and the nice thing about this online application is that it converts both the problem and the solution into the same sort of format that it would appear in the textbook.
Unfortunately, "show steps" isn't really a legitimate option, as it takes you to a website for Bagatrix, where you can purchase Algebra solving software that provides step-by-step solutions. Regardless, as an answer-checker the free online app proves very useful.
Illuminations - Cool Algebra Activities and Lessons
Nothing is quite as frustrating for many students as trying to understand abstract concepts, and learning to do so by reading drab and boring textbooks that make you want to go to sleep. Luckily, the National Council of Teachers of Mathematics in the U.S. understands this problem and created a website called Illuminations that brings the subject (including algebra) to life for students.
The site includes high quality activities and lessons that cover all aspects of both math and algebra. Of all available free algebra homework help websites, this is definitely the one that's the most fun and interesting. For lessons, you select grade levels and topics (one area is devoted to just algebra), and you get access to dozens of valuable lessons that teach important algebra concepts. However, my favorite part of the site is the "activities" area that offers some really high quality and valuable online applications that graphically show algebraic principles, such as this "pan balance" app that graphically displays what happens when you change different elements of equations.
Tutorvista - Free Lessons
While Tutorvista isn't technically a free site, because the primary aim is to get parents to sign up their children for an online tutor, the website does offer an entire algebra help section with well formatted lessons that teach students about the many elements of algebra, from foundation principles all the way to the more advanced topics.
Of course, if you do need tutoring for your child, you can actually submit an assignment and for an average fee of $5, a tutor will actually send back the answer in a fully worked-out step-by-step solution. However, before you start dishing out your cash for any paid tutoring, make sure to check out the next free Algebra homework help website that actually does offer many tutoring services for free.
Algebra.com - Math Tutors Who Just Can't Get Enough
Of course, the best place to get some free algebra tutoring is Algebra.com , an online community of mathematicians who are obsessed with the topic. You can turn their obsession into your child's advantage by posting problems for the tutor community to answer. The website itself offers more lessons and information than probably any other algebra help website out there.
Just the algebra section includes pre-algebra, algebra I and algebra II - and of course there's a quick and easy "Universal Simplifier and Solver" at the top that will either simplify or solve your algebra equations. At the top of the site, there's a "Free Tutors" menu option that'll take you to a section where you can either sign up to be a free tutor (a public service which gives you exposure for your tutoring business), or you can submit your own algebra questions to the tutors. There are almost a thousand active tutors - and the question/answer area is a huge community of fantastic tutors who are eager to help kids with their algebra problems.
Math.com - Interactive Algebra Help
Another valuable site filled with step-by-step instructions and lessons for students to learn the most important algebra concepts is Math.com . This site covers both the basics as well as advanced concepts under categories like "The Language of Algebra", "Equations and Inequalities" and "Graphing Equations and Inequalities."
The lessons at Math.com take students through an easy step-by-step "wizard," and on each step there's often a "show me" option students can click where the application offers examples or additional information that better explains a specific topic. It's just like having a teacher available with instant answers to the typical questions that students often ask.
Drexel University - The Math Forum
The Math Forum is a valuable public service offered by Drexel University that offers both students and teachers dozens of resources. Many of the resources are buried within internal links, but the Algebra Section alone offers classroom materials for teachers, Internet projects, public forums and even links to algebra software throughout the net.
The Math Forum is one of the largest math & algebra resources on the net, and if you can afford to donate it would be a valuable and worthy cause to contribute. Mathematics, and algebra in particular are critical skills for students to learn early on that can tremendously simplify their lives later on. Any free algebra homework help websites that exist on the Internet are very positive resources that should be promoted and applauded by everyone.
Do you know of any additional algebra resources for teachers, parents or students on the Internet? Share them in the comments section below.
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- Solve equations and inequalities
- Simplify expressions
- Factor polynomials
- Graph equations and inequalities
- Advanced solvers
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- Arithmetics
- Determinant
- Percentages
- Scientific Notation
- Inequalities
What can QuickMath do?
QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.
- The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
- The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
- The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
- The calculus section will carry out differentiation as well as definite and indefinite integration.
- The matrices section contains commands for the arithmetic manipulation of matrices.
- The graphs section contains commands for plotting equations and inequalities.
- The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.
Math Topics
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College Algebra
Also known as "High School Algebra"
OK. So what are you going to learn here?
You will learn about Numbers, Polynomials, Inequalities, Sequences and Sums, many types of Functions, and how to solve them.
You will also gain a deeper insight into Mathematics, get to practice using your new skills with lots of examples and questions, and generally improve your mind.
With your new skills you will be able to put together mathematical models so you can find good quality solutions to many tricky real world situations.
Near the end of most pages is a "Your Turn" section ... do these! You need to balance your reading with doing . Answering questions helps you sort things out in your mind. And don't guess the answer: use pen and paper and try your best before seeing the solution.
So what is this thing called Mathematics? And how do you go about learning it?
- Welcome to Mathematics
- Learning Mathematics
- The Language of Mathematics
- Symbols in Algebra
Next, we need to think about mathematics in terms of sets .
- Introduction to Sets
Now we know what a set is, let us look at different sets of numbers that are useful:
- The Evolution of Numbers
- Prime and Composite Numbers
- Fundamental Theorem of Arithmetic
- Whole Numbers and Integers
- Rational Numbers
- Using Rational Numbers
- Irrational Numbers
- 0.999... = 1
- Real Numbers
- Imaginary Numbers
- Complex Numbers
- Multiplying Complex Numbers
- The Complex Plane
- Common Number Sets
Inequalities
"Equal To" is nice but not always available. Maybe we only know that something is less than, or greater than. So let's learn about in equalities.
- Introduction to Inequalities
- Properties of Inequalities
- Solving Inequalities
- Solving Inequality Word Questions
We will be using exponents a lot, so let's get to know them well.
- Variables with Exponents
- Using Exponents in Algebra
- Squares and Square Roots
- Squares and Square Roots in Algebra
- Fractional Exponents
- Laws of Exponents
- Exponents of Negative Numbers
Polynomials
Polynomials were some of the first things ever studied in Algebra. They are simple, yet powerful in their ability to model real world situations.
- What is a Polynomial?
- Adding And Subtracting Polynomials
- Multiplying Polynomials
- Polynomials - Long Multiplication
- Dividing Polynomials
- Polynomials - Long Division
- Degree (of an Expression)
- Special Binomial Products
- Difference of Two Cubes
- Factoring in Algebra
- Solving Polynomials
- Roots of Polynomials: Sums and Products
- Rational Expressions
- Using Rational Expressions
- Fundamental Theorem of Algebra
- Remainder Theorem and Factor Theorem
- General Form of a Polynomial
Graphing Polynomials
- How Polynomials Behave
- Polynomials: The Rule of Signs
- Polynomials: Bounds on Zeros
And, of course, we need to know about equations ... and how to solve them.
- Equations and Formulas
- Solving Equations
- Solving Word Questions
- Zero Product Property
- Implication and Iff
- Theorems, Corollaries, Lemmas
Graphs can save us! They are a great way to see what is going on and can help us solve many things. But we need to be careful, as they sometimes don't give the full story.
- Cartesian Coordinates
- Pythagoras' Theorem
- Distance Between 2 Points
- Graph of an Equation
- Finding Intercepts From an Equation
- Symmetry in Equations
- Linear Equations
They are just equations for lines. But they come in many forms.
- Equation of a Straight Line
- Point-Slope Equation of a Line
- General Form of Equation of a Line
- Equation of a Line from 2 Points
- Midpoint of a Line Segment
- Parallel and Perpendicular Lines
A function relates an input to an output. But from that simple foundation many useful things can be built.
- What is a Function?
- Domain, Range and Codomain
- Evaluating Functions
- Increasing and Decreasing Functions
- Maxima and Minima of Functions
- Even and Odd Functions
- Set-Builder Notation
Common Functions Reference :
- Square Function
- Square Root Function
- Cube Function
- Reciprocal Function
- Absolute Value Function
- Floor and Ceiling Function
- Function Transformations
- Equation Grapher
- Operations with Functions
- Composition of Functions
- Inverse Functions
Equations of Second Degree
"Second degree" just means the variable has an exponent of 2, like x 2 . It is the next major step after linear equations (where the exponent is 1, like x).
- Quadratic Equations
- Factoring Quadratics
- Completing the Square
- Derivation of Quadratic Formula
- Graphing Quadratic Equations
- Quadratic Equations in the Real World
- Circle Equations
We already have experience in solving, but now we can learn more!
- Mathematical Models and Mathematical Models 2
- Approximate Solutions
- Intermediate Value Theorem
- Solving Radical Equations
- Change of Variables
- Algebra Mistakes
We learned about inequalities above, now let's learn how to solve them.
- Graphing Linear Inequalities
- Inequality Graphing Tool
- Solving Quadratic Inequalities
- Solving Rational Inequalities
- Absolute Value in Algebra
Exponents and Logarithms
We already know about exponents ... well logarithms just go the other way. And together they can be very powerful.
- Introduction to Logarithms
- Exponents, Roots and Logarithms
- Working with Exponents and Logarithms
- Exponential Function
- Logarithmic Function
- Exponential Growth and Decay
- Systems of Linear Equations
What happens when we have two or more linear equations that work together? They can often be solved! It isn't very hard but can take a lot of calculations.
- Types of Matrix
- How to Multiply Matrices
- Determinant of a Matrix
- Inverse of a Matrix:
- Using Elementary Row Operations (Gauss-Jordan)
- Using Minors, Cofactors and Adjugate
- Scalar, Vector, Matrix and Vectors
- Matrix Calculator
- More at Matrix Index
- Solving Systems of Linear Equations Using Matrices
- Systems of Linear and Quadratic Equations
- Probability
Is it likely? You be the judge!
- The Basic Counting Principle
- Combinations and Permutations
Sequences, Series and Partial Sums
A Sequence is a set of things (usually numbers) that are in order. We can also sum up a series, where Sigma Notation is very useful.
- Sequences - Finding A Rule
- Sigma Notation
- Partial Sums
- Arithmetic Sequences and Sums
- Geometric Sequences and Sums
These last few subjects use what we have learned above.
- Partial Fractions
- Mathematical Induction
- Pascal's Triangle
- Binomial Theorem
And that is all!
But there are many other interesting algebra topics such as:
- Euler's Formula for Complex Numbers
- Taylor Series (needs a basic understanding of derivatives )
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Number line, algebra calculator.
The Algebra Calculator is a versatile online tool designed to simplify algebraic problem-solving for users of all levels. Here's how to make the most of it:
- Begin by typing your algebraic expression into the above input field, or scanning the problem with your camera.
- After entering the equation, click the 'Go' button to generate instant solutions.
- The calculator provides detailed step-by-step solutions, aiding in understanding the underlying concepts.
- -x+3\gt 2x+1
- (x+5)(x-5)\gt 0
- 10^{1-x}=10^4
- \sqrt{3+x}=-2
- 6+11x+6x^2+x^3=0
- factor\:x^{2}-5x+6
- simplify\:\frac{2}{3}-\frac{3}{2}+\frac{1}{4}
- x+2y=2x-5,\:x-y=3
- How do you solve algebraic expressions?
- To solve an algebraic expression, simplify the expression by combining like terms, isolate the variable on one side of the equation by using inverse operations. Then, solve the equation by finding the value of the variable that makes the equation true.
- What are the basics of algebra?
- The basics of algebra are the commutative, associative, and distributive laws.
- What are the 3 rules of algebra?
- The basic rules of algebra are the commutative, associative, and distributive laws.
- What is the golden rule of algebra?
- The golden rule of algebra states Do unto one side of the equation what you do to others. Meaning, whatever operation is being used on one side of equation, the same will be used on the other side too.
- What are the 5 basic laws of algebra?
- The basic laws of algebra are the Commutative Law For Addition, Commutative Law For Multiplication, Associative Law For Addition, Associative Law For Multiplication, and the Distributive Law.
algebra-calculator
- High School Math Solutions – Inequalities Calculator, Exponential Inequalities Last post, we talked about how to solve logarithmic inequalities. This post, we will learn how to solve exponential...
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The Algebra 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; and Quadratic equations, functions, and graphs. Khan Academy's Algebra 1 course is built to deliver a comprehensive, illuminating, engaging, and Common Core aligned experience!
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Unit 1 Introduction to algebra. Unit 2 Solving basic equations & inequalities (one variable, linear) Unit 3 Linear equations, functions, & graphs. Unit 4 Sequences. Unit 5 System of equations. Unit 6 Two-variable inequalities. Unit 7 Functions. Unit 8 Absolute value equations, functions, & inequalities. Unit 9 Quadratic equations & functions.
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The Algebra Calculator is a versatile online tool designed to simplify algebraic problem-solving for users of all levels. Here's how to make the most of it: Begin by typing your algebraic expression into the above input field, or scanning the problem with your camera.