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natirs
11/27/2025
Algebra 1
High School Algebra: Evaluating Expressions, Linear Equations, Systems, Polynomials, Quadratic Equations, and Functions
590
•
Nov 27, 2025
•
Mastering High School Algebra: Expressions, Equations, and Functions
natirs
@natirs
1 / 5
Overview of High School Algebra
Algebra 1 introduces you to the world of abstract math through several key concepts. Instead of just working with numbers, you'll learn to use variables (letters that represent unknown values) and solve different types of equations.
The course typically covers seven main topics: variables and expressions, linear equations and inequalities, systems of equations, polynomials, factoring, quadratic equations, and functions. These concepts build on each other, so understanding earlier topics makes later ones easier.
In Unit 1, you'll start with the basics - learning what variables are, how to create expressions, and mastering the order of operations (PEMDAS). You'll also practice simplifying expressions to their clearest form.
Quick Tip: When you see an expression with multiple operations, remember "Please Excuse My Dear Aunt Sally" (PEMDAS) - Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
Key Units in Algebra 1
In Unit 2, you'll tackle linear equations and inequalities. You'll learn to solve equations like 2x + 3 = 7, graph lines using the slope-intercept form , and work with inequalities that use symbols like < and >.
Unit 3 introduces systems of equations - where you'll find values that make two or more equations true at the same time. You'll learn multiple methods including elimination, substitution, and graphing to find solutions where lines intersect.
Units 4 and 5 focus on more complex expressions: polynomials and quadratic equations. You'll learn to add, subtract, multiply, divide and factor polynomials. Then you'll solve quadratic equations using methods such as factoring, completing the square, and the quadratic formula.
Unit 6 explores functions - mathematical relationships that connect inputs to outputs. You'll learn about different function types including linear, quadratic, exponential, and logarithmic functions.
Remember: When you graph a linear equation , "m" represents the slope (steepness) and "b" shows where the line crosses the y-axis.
Important Formulas and Practice
Algebra 1 introduces several formulas you'll use throughout your math career. The slope-intercept form helps you graph lines, while the quadratic formula solves quadratic equations that can't be factored easily.
Other important formulas include the distance formula for finding the distance between two points, and formulas for exponential functions and logarithmic functions , which model growth and decay.
Practice is essential for mastering algebra. Try simplifying expressions like 2x + 3y - 5x + 2y, solving equations like 2x - 5 = 7, or graphing lines like y = 3x + 1. As you progress, you'll solve more complex problems like factoring x² + 5x + 6 or finding where two lines intersect.
Challenge Yourself: When practicing, don't just solve the problem. Explain each step to yourself or a friend to make sure you truly understand the concept.
Practice Problems and Vocabulary
For systems of equations, try solving problems like "x + y = 5, 2x - y = 1" using substitution or elimination. When working with polynomials, practice multiplying expressions like and factoring quadratics like x² + 4x + 3 = 0.
Function problems might ask you to find the slope of y = 2x - 1, graph f(x) = x² + 2x - 1, or determine the domain and range of logarithmic functions. These problems build your skills gradually from simple to complex.
Understanding algebra vocabulary is crucial for success. A variable represents an unknown value, while an expression combines numbers, variables, and operations. An equation shows that two expressions are equal , but an inequality shows when one value is greater or less than another (using <, >, ≤, or ≥).
Functions create relationships between inputs (the domain) and outputs (the range), with each input giving exactly one output. The slope measures how steep a line is, while the y-intercept shows where a line crosses the y-axis.
Test Prep Tip: Make flashcards for key vocabulary terms and formulas. Review them regularly so you can quickly recall important concepts during tests.
More Vocabulary and Study Tips
Quadratics have special terms like vertex (the highest or lowest point on a parabola) and the standard form of linear equations. You'll also use slope-intercept form for graphing lines and the quadratic formula for solving complex quadratic equations.
Exponential functions show growth or decay (like compound interest or population growth), while logarithmic functions are their inverses and help solve exponential equations.
To succeed in Algebra 1, develop strong study habits. Attend every class and participate actively. Take detailed notes and review them regularly – not just before tests. Complete all homework assignments since they reinforce what you've learned.
If you're struggling with a concept, don't wait to get help. Ask your teacher, find a tutor, or form a study group with classmates. Practice regularly with problems beyond your homework, and use practice tests to prepare for exams. Take care of your physical health too – get enough sleep and eat well, especially before tests.
Success Strategy: When you make mistakes (and everyone does!), don't just look at the correct answer. Figure out exactly where your thinking went wrong so you don't repeat the same error.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Mastering High School Algebra: Expressions, Equations, and Functions
natirs
@natirs
Algebra 1 is the foundation of high school math that introduces you to working with variables, equations, and functions. This course builds essential skills that you'll use throughout high school math and beyond, focusing on everything from basic expressions to... Show more
Overview of High School Algebra
Algebra 1 introduces you to the world of abstract math through several key concepts. Instead of just working with numbers, you'll learn to use variables (letters that represent unknown values) and solve different types of equations.
The course typically covers seven main topics: variables and expressions, linear equations and inequalities, systems of equations, polynomials, factoring, quadratic equations, and functions. These concepts build on each other, so understanding earlier topics makes later ones easier.
In Unit 1, you'll start with the basics - learning what variables are, how to create expressions, and mastering the order of operations (PEMDAS). You'll also practice simplifying expressions to their clearest form.
Quick Tip: When you see an expression with multiple operations, remember "Please Excuse My Dear Aunt Sally" (PEMDAS) - Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Key Units in Algebra 1
In Unit 2, you'll tackle linear equations and inequalities. You'll learn to solve equations like 2x + 3 = 7, graph lines using the slope-intercept form , and work with inequalities that use symbols like < and >.
Unit 3 introduces systems of equations - where you'll find values that make two or more equations true at the same time. You'll learn multiple methods including elimination, substitution, and graphing to find solutions where lines intersect.
Units 4 and 5 focus on more complex expressions: polynomials and quadratic equations. You'll learn to add, subtract, multiply, divide and factor polynomials. Then you'll solve quadratic equations using methods such as factoring, completing the square, and the quadratic formula.
Unit 6 explores functions - mathematical relationships that connect inputs to outputs. You'll learn about different function types including linear, quadratic, exponential, and logarithmic functions.
Remember: When you graph a linear equation , "m" represents the slope (steepness) and "b" shows where the line crosses the y-axis.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Important Formulas and Practice
Algebra 1 introduces several formulas you'll use throughout your math career. The slope-intercept form helps you graph lines, while the quadratic formula solves quadratic equations that can't be factored easily.
Other important formulas include the distance formula for finding the distance between two points, and formulas for exponential functions and logarithmic functions , which model growth and decay.
Practice is essential for mastering algebra. Try simplifying expressions like 2x + 3y - 5x + 2y, solving equations like 2x - 5 = 7, or graphing lines like y = 3x + 1. As you progress, you'll solve more complex problems like factoring x² + 5x + 6 or finding where two lines intersect.
Challenge Yourself: When practicing, don't just solve the problem. Explain each step to yourself or a friend to make sure you truly understand the concept.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Practice Problems and Vocabulary
For systems of equations, try solving problems like "x + y = 5, 2x - y = 1" using substitution or elimination. When working with polynomials, practice multiplying expressions like and factoring quadratics like x² + 4x + 3 = 0.
Function problems might ask you to find the slope of y = 2x - 1, graph f(x) = x² + 2x - 1, or determine the domain and range of logarithmic functions. These problems build your skills gradually from simple to complex.
Understanding algebra vocabulary is crucial for success. A variable represents an unknown value, while an expression combines numbers, variables, and operations. An equation shows that two expressions are equal , but an inequality shows when one value is greater or less than another (using <, >, ≤, or ≥).
Functions create relationships between inputs (the domain) and outputs (the range), with each input giving exactly one output. The slope measures how steep a line is, while the y-intercept shows where a line crosses the y-axis.
Test Prep Tip: Make flashcards for key vocabulary terms and formulas. Review them regularly so you can quickly recall important concepts during tests.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
More Vocabulary and Study Tips
Quadratics have special terms like vertex (the highest or lowest point on a parabola) and the standard form of linear equations. You'll also use slope-intercept form for graphing lines and the quadratic formula for solving complex quadratic equations.
Exponential functions show growth or decay (like compound interest or population growth), while logarithmic functions are their inverses and help solve exponential equations.
To succeed in Algebra 1, develop strong study habits. Attend every class and participate actively. Take detailed notes and review them regularly – not just before tests. Complete all homework assignments since they reinforce what you've learned.
If you're struggling with a concept, don't wait to get help. Ask your teacher, find a tutor, or form a study group with classmates. Practice regularly with problems beyond your homework, and use practice tests to prepare for exams. Take care of your physical health too – get enough sleep and eat well, especially before tests.
Success Strategy: When you make mistakes (and everyone does!), don't just look at the correct answer. Figure out exactly where your thinking went wrong so you don't repeat the same error.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user