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AP Microeconomics

Nov 26, 2025

11

5 pages

Understanding Supply and Demand in AP Microeconomics Unit 2

user profile picture

Cassandra @caska

Dive into the world of economics where we explore how markets work through supply, demand, and elasticity. These... Show more

Law of Demand
is inverse
- On
Demand is
Unit 2 Supply & Demand.
the curve the relationship between price and quantity.
when someone is willi

Supply, Demand, and Market Equilibrium

The Law of Demand shows an inverse relationship between price and quantity - when prices go up, people buy less. Remember, demand means being both willing AND able to purchase something. For example, Mr. Stirn might be able to afford milk but isn't willing to buy it because he's lactose intolerant.

Only price changes move us along the demand curve. Meanwhile, the Law of Supply shows a direct relationship between price and quantity - when prices rise, producers supply more. Five key factors can shift the entire demand curve taste preferences, related goods, income levels, number of buyers, and expectations of future prices.

Supply curves shift due to six factors resource costs, other outputs, technology improvements, taxes and subsidies, expectations, and number of suppliers. When both supply and demand shift simultaneously, either the new price or quantity must be indeterminate - we call this the Double Shift Rule.

Real-world connection Price controls are government tools that manipulate market prices. Price ceilings (maximum prices) set below equilibrium create shortages - think of rent control in expensive cities where apartments become scarce!

Law of Demand
is inverse
- On
Demand is
Unit 2 Supply & Demand.
the curve the relationship between price and quantity.
when someone is willi

Price Elasticity and Market Responsiveness

Elasticity measures how sensitive buyers and sellers are to price changes. Price elasticity of demand specifically shows how much quantity demanded changes when price changes. The formula is percent change in quantity divided by percent change in price.

Inelastic demand means quantity barely responds to price changes - the demand curve looks steep like the letter "I." Products with inelastic demand include necessities like gasoline, milk, and diapers. Inelastic goods typically have few substitutes, represent a small portion of income, and are necessities people can't delay purchasing.

Elastic demand means quantity is highly responsive to price changes - the demand curve is relatively flat. Products like soda, pizza, and beef tend to be elastic. Elastic goods usually have many substitutes, are considered luxuries rather than necessities, and take up a large portion of income.

Test tip For elasticity calculations, if the coefficient is less than 1, demand is inelastic. If greater than 1, it's elastic. Remember that necessities tend to be inelastic while luxury items are usually elastic!

Law of Demand
is inverse
- On
Demand is
Unit 2 Supply & Demand.
the curve the relationship between price and quantity.
when someone is willi

Understanding Different Types of Elasticity

The elasticity coefficient tells us exactly how responsive quantity is to price changes. Perfectly inelastic goods coefficient=0coefficient = 0 don't change quantity at all when price changes. Relatively inelastic goods (coefficient < 1) change quantity slightly with price changes.

Unit elastic goods coefficient=1coefficient = 1 have proportional changes in quantity and price. Relatively elastic goods (coefficient > 1) show larger quantity changes than price changes. Perfectly elastic goods coefficient=coefficient = ∞ mean buyers will purchase unlimited amounts at one price and none at any higher price.

Price elasticity of supply works similarly but focuses on producers' responsiveness. Supply elasticity depends largely on time - in the short run, most goods have inelastic supply because producers need time to adjust. In the long run, supply becomes more elastic as producers can fully respond to price incentives.

Study hack Visualize elasticity by thinking about time constraints. Could you quickly produce more if prices rose? Supply is usually inelastic in the short-run (steep curve) but elastic in the long-run (flat curve) as producers adapt.

Law of Demand
is inverse
- On
Demand is
Unit 2 Supply & Demand.
the curve the relationship between price and quantity.
when someone is willi

Total Revenue and Cross-Price Elasticity

The Total Revenue Test helps determine elasticity by examining what happens to total revenue (price × quantity) when price changes. For inelastic goods, price increases cause total revenue to increase, while price decreases cause revenue to decrease. The opposite happens with elastic goods.

Cross-price elasticity of demand reveals how the quantity demanded of one product responds to price changes in another product. The formula divides percent change in quantity of product B by percent change in price of product A. A positive coefficient means the goods are substitutes (like Coke and Pepsi), while a negative coefficient indicates complements (like hot dogs and hot dog buns).

Income elasticity of demand shows how sensitive demand is to changes in consumer income. When the coefficient is positive, we're dealing with a normal good (demand increases with income). A negative coefficient identifies an inferior good (demand decreases as income rises).

Real-world application Companies use elasticity data to set prices strategically. If they sell products with inelastic demand, they can raise prices to increase revenue. For elastic goods, lowering prices might actually bring in more total revenue!

Law of Demand
is inverse
- On
Demand is
Unit 2 Supply & Demand.
the curve the relationship between price and quantity.
when someone is willi

Taxation and Market Efficiency

When governments implement taxes, they create a gap between what buyers pay and what sellers receive. On a supply and demand graph, this shifts the supply curve upward by the amount of the tax, creating a new equilibrium with higher prices and lower quantity.

The tax burden is shared between consumers and producers, with consumer surplus decreasing, producer surplus decreasing, and government collecting tax revenue. However, taxes also create a deadweight loss - a reduction in total market efficiency represented by the triangle of lost trades that would have happened without the tax.

The size of this deadweight loss depends on the elasticity of supply and demand. More elastic markets experience larger efficiency losses from taxation because participants more readily change their behavior in response to price changes.

Connect the concepts Remember that the more inelastic the demand, the more consumers bear the tax burden. This is why governments often tax goods with inelastic demand (like cigarettes and gasoline) - consumers will still buy them even at higher prices!

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?

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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

 

AP Microeconomics

11

Nov 26, 2025

5 pages

Understanding Supply and Demand in AP Microeconomics Unit 2

user profile picture

Cassandra

@caska

Dive into the world of economics where we explore how markets work through supply, demand, and elasticity. These fundamental concepts explain why prices change, how buyers and sellers interact, and what happens when governments intervene in markets.

Law of Demand
is inverse
- On
Demand is
Unit 2 Supply & Demand.
the curve the relationship between price and quantity.
when someone is willi

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

Supply, Demand, and Market Equilibrium

The Law of Demand shows an inverse relationship between price and quantity - when prices go up, people buy less. Remember, demand means being both willing AND able to purchase something. For example, Mr. Stirn might be able to afford milk but isn't willing to buy it because he's lactose intolerant.

Only price changes move us along the demand curve. Meanwhile, the Law of Supply shows a direct relationship between price and quantity - when prices rise, producers supply more. Five key factors can shift the entire demand curve: taste preferences, related goods, income levels, number of buyers, and expectations of future prices.

Supply curves shift due to six factors: resource costs, other outputs, technology improvements, taxes and subsidies, expectations, and number of suppliers. When both supply and demand shift simultaneously, either the new price or quantity must be indeterminate - we call this the Double Shift Rule.

Real-world connection: Price controls are government tools that manipulate market prices. Price ceilings (maximum prices) set below equilibrium create shortages - think of rent control in expensive cities where apartments become scarce!

Law of Demand
is inverse
- On
Demand is
Unit 2 Supply & Demand.
the curve the relationship between price and quantity.
when someone is willi

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

Price Elasticity and Market Responsiveness

Elasticity measures how sensitive buyers and sellers are to price changes. Price elasticity of demand specifically shows how much quantity demanded changes when price changes. The formula is percent change in quantity divided by percent change in price.

Inelastic demand means quantity barely responds to price changes - the demand curve looks steep like the letter "I." Products with inelastic demand include necessities like gasoline, milk, and diapers. Inelastic goods typically have few substitutes, represent a small portion of income, and are necessities people can't delay purchasing.

Elastic demand means quantity is highly responsive to price changes - the demand curve is relatively flat. Products like soda, pizza, and beef tend to be elastic. Elastic goods usually have many substitutes, are considered luxuries rather than necessities, and take up a large portion of income.

Test tip: For elasticity calculations, if the coefficient is less than 1, demand is inelastic. If greater than 1, it's elastic. Remember that necessities tend to be inelastic while luxury items are usually elastic!

Law of Demand
is inverse
- On
Demand is
Unit 2 Supply & Demand.
the curve the relationship between price and quantity.
when someone is willi

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

Understanding Different Types of Elasticity

The elasticity coefficient tells us exactly how responsive quantity is to price changes. Perfectly inelastic goods coefficient=0coefficient = 0 don't change quantity at all when price changes. Relatively inelastic goods (coefficient < 1) change quantity slightly with price changes.

Unit elastic goods coefficient=1coefficient = 1 have proportional changes in quantity and price. Relatively elastic goods (coefficient > 1) show larger quantity changes than price changes. Perfectly elastic goods coefficient=coefficient = ∞ mean buyers will purchase unlimited amounts at one price and none at any higher price.

Price elasticity of supply works similarly but focuses on producers' responsiveness. Supply elasticity depends largely on time - in the short run, most goods have inelastic supply because producers need time to adjust. In the long run, supply becomes more elastic as producers can fully respond to price incentives.

Study hack: Visualize elasticity by thinking about time constraints. Could you quickly produce more if prices rose? Supply is usually inelastic in the short-run (steep curve) but elastic in the long-run (flat curve) as producers adapt.

Law of Demand
is inverse
- On
Demand is
Unit 2 Supply & Demand.
the curve the relationship between price and quantity.
when someone is willi

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

Total Revenue and Cross-Price Elasticity

The Total Revenue Test helps determine elasticity by examining what happens to total revenue (price × quantity) when price changes. For inelastic goods, price increases cause total revenue to increase, while price decreases cause revenue to decrease. The opposite happens with elastic goods.

Cross-price elasticity of demand reveals how the quantity demanded of one product responds to price changes in another product. The formula divides percent change in quantity of product B by percent change in price of product A. A positive coefficient means the goods are substitutes (like Coke and Pepsi), while a negative coefficient indicates complements (like hot dogs and hot dog buns).

Income elasticity of demand shows how sensitive demand is to changes in consumer income. When the coefficient is positive, we're dealing with a normal good (demand increases with income). A negative coefficient identifies an inferior good (demand decreases as income rises).

Real-world application: Companies use elasticity data to set prices strategically. If they sell products with inelastic demand, they can raise prices to increase revenue. For elastic goods, lowering prices might actually bring in more total revenue!

Law of Demand
is inverse
- On
Demand is
Unit 2 Supply & Demand.
the curve the relationship between price and quantity.
when someone is willi

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

Taxation and Market Efficiency

When governments implement taxes, they create a gap between what buyers pay and what sellers receive. On a supply and demand graph, this shifts the supply curve upward by the amount of the tax, creating a new equilibrium with higher prices and lower quantity.

The tax burden is shared between consumers and producers, with consumer surplus decreasing, producer surplus decreasing, and government collecting tax revenue. However, taxes also create a deadweight loss - a reduction in total market efficiency represented by the triangle of lost trades that would have happened without the tax.

The size of this deadweight loss depends on the elasticity of supply and demand. More elastic markets experience larger efficiency losses from taxation because participants more readily change their behavior in response to price changes.

Connect the concepts: Remember that the more inelastic the demand, the more consumers bear the tax burden. This is why governments often tax goods with inelastic demand (like cigarettes and gasoline) - consumers will still buy them even at higher prices!

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.

0

Smart Tools NEW

Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines

Mock Exam
Quiz
Flashcards
Essay

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