Applied Mathematics is basically using the maths you learn in... Show more
Irish
English
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
11
•
Updated May 1, 2026
•
Exploring Applied Mathematics: Tools for Real-World Problems
1 / 6
What is Applied Mathematics?
Ever wondered why you're learning algebra or trigonometry? Applied Mathematics is the answer - it's about taking those classroom concepts and using them to solve actual problems in the real world.
Unlike Pure Mathematics (which explores mathematical concepts just for the sake of it), applied maths has a clear goal: solve something practical. Whether it's figuring out the best angle for a football free kick or helping companies make more profit, you're always working towards a real solution.
The secret weapon in applied maths is the mathematical model - basically a simplified maths version of a complex real-world situation. Since the real world is incredibly messy and complicated, we create these models using equations and variables to make problems manageable.
Remember: Pure maths asks "What if?" whilst applied maths asks "How can we fix this?"
The Applied Mathematics Process
Solving problems with applied mathematics follows a clear cycle that you'll use again and again. It's like having a recipe for tackling any real-world challenge.
The process starts with a real-world problem and moves through several stages: making assumptions, creating a mathematical model, solving it, and interpreting your results. Think of it as translating between two languages - from real life to maths, then back to real life.
This modelling cycle is crucial because it shows that applied maths isn't just about getting the right answer. It's about understanding whether that answer actually makes sense in the original situation.
Key insight: The cycle often repeats - if your answer seems wrong, you go back and refine your model!
Breaking Down the Steps
Let's follow the mathematical modelling process with a simple example: "How high will a ball go if I throw it upwards at 10 metres per second?"
First, you identify the problem clearly. Then comes the crucial step of making assumptions - this is where you simplify reality. For our ball, we'll ignore air resistance and assume only gravity affects it.
Next, you create a mathematical model using equations. Here, we'd use physics equations like v² = u² + 2as, where the letters represent velocity, acceleration, and displacement. After solving the maths (plugging in numbers and calculating), you get a numerical answer.
The final steps are interpreting your solution and validating it . If something seems off, you might need to revisit your assumptions.
Pro tip: Always state your assumptions clearly in exams - it shows you understand that you're simplifying a complex problem!
Worked Example: Hurling Physics
Here's how applied mathematics works with a proper Irish example: A hurler strikes a sliotar with an initial vertical velocity of 19.6 m/s. How long until it reaches maximum height?
Starting with assumptions: we ignore air resistance and only consider gravity . Our mathematical model uses the equation v = u + at, where v (final velocity) = 0 at maximum height, u (initial velocity) = 19.6 m/s, and a (acceleration) = -9.8 m/s².
Solving the equation: 0 = 19.6 + (-9.8)t, which rearranges to t = 19.6/9.8 = 2. The interpretation is straightforward: the sliotar takes 2 seconds to reach its maximum height.
This demonstrates how mathematical modelling transforms a sports scenario into a solvable equation, then translates the numerical result back into practical knowledge.
Reality check: Does 2 seconds seem reasonable for a sliotar to reach its peak? Trust your instincts!
Population Growth Example
Applied mathematics also tackles biological problems brilliantly. Consider: 50 bacteria double every hour - how many after 6 hours?
Our assumptions include unlimited food, no deaths, and constant growth rate. The mathematical model for this exponential growth is P(t) = P₀ × 2ᵗ, where P₀ = 50 bacteria and t = time in hours.
Solving: P(6) = 50 × 2⁶ = 50 × 64 = 3,200 bacteria. The interpretation shows how quickly bacterial populations can explode under ideal conditions.
This example demonstrates how mathematical modelling applies across different fields - from sports physics to biological sciences. The same systematic approach works whether you're dealing with projectiles or populations.
Important: Notice how different real-world situations need completely different mathematical models!
Key Points for Success
Remember that mathematical models are never perfect - they're always simplified versions of reality. The goal is making them "good enough" to provide useful answers, not to capture every tiny detail.
Always state your assumptions clearly and draw diagrams for physics problems. Your applied mathematics solutions should pass the reality check - if a car supposedly takes 3 hours to travel 100 metres, something's gone wrong!
Applied mathematics connects directly to Physics (motion and forces), Biology (population models), Economics (financial planning), and Geography (map projections). It's the bridge between classroom maths and real-world problem-solving.
The core process remains constant: Problem → Model → Solve → Interpret. Master this cycle, and you'll be able to tackle everything from engineering challenges to environmental predictions.
Exam success tip: Always explain your final answer in the context of the original problem - numbers alone aren't enough!
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.
4.6/5
App Store
4.7/5
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 Knowunity AI. 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 Knowunity AI. 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
Exploring Applied Mathematics: Tools for Real-World Problems
Applied Mathematics is basically using the maths you learn in class to solve real-world problems - from designing rollercoasters to predicting weather patterns. Think of it as being a detective where your main tool is maths instead of a magnifying... Show more
What is Applied Mathematics?
Ever wondered why you're learning algebra or trigonometry? Applied Mathematics is the answer - it's about taking those classroom concepts and using them to solve actual problems in the real world.
Unlike Pure Mathematics (which explores mathematical concepts just for the sake of it), applied maths has a clear goal: solve something practical. Whether it's figuring out the best angle for a football free kick or helping companies make more profit, you're always working towards a real solution.
The secret weapon in applied maths is the mathematical model - basically a simplified maths version of a complex real-world situation. Since the real world is incredibly messy and complicated, we create these models using equations and variables to make problems manageable.
Remember: Pure maths asks "What if?" whilst applied maths asks "How can we fix this?"
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
The Applied Mathematics Process
Solving problems with applied mathematics follows a clear cycle that you'll use again and again. It's like having a recipe for tackling any real-world challenge.
The process starts with a real-world problem and moves through several stages: making assumptions, creating a mathematical model, solving it, and interpreting your results. Think of it as translating between two languages - from real life to maths, then back to real life.
This modelling cycle is crucial because it shows that applied maths isn't just about getting the right answer. It's about understanding whether that answer actually makes sense in the original situation.
Key insight: The cycle often repeats - if your answer seems wrong, you go back and refine your model!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Breaking Down the Steps
Let's follow the mathematical modelling process with a simple example: "How high will a ball go if I throw it upwards at 10 metres per second?"
First, you identify the problem clearly. Then comes the crucial step of making assumptions - this is where you simplify reality. For our ball, we'll ignore air resistance and assume only gravity affects it.
Next, you create a mathematical model using equations. Here, we'd use physics equations like v² = u² + 2as, where the letters represent velocity, acceleration, and displacement. After solving the maths (plugging in numbers and calculating), you get a numerical answer.
The final steps are interpreting your solution and validating it . If something seems off, you might need to revisit your assumptions.
Pro tip: Always state your assumptions clearly in exams - it shows you understand that you're simplifying a complex problem!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Worked Example: Hurling Physics
Here's how applied mathematics works with a proper Irish example: A hurler strikes a sliotar with an initial vertical velocity of 19.6 m/s. How long until it reaches maximum height?
Starting with assumptions: we ignore air resistance and only consider gravity . Our mathematical model uses the equation v = u + at, where v (final velocity) = 0 at maximum height, u (initial velocity) = 19.6 m/s, and a (acceleration) = -9.8 m/s².
Solving the equation: 0 = 19.6 + (-9.8)t, which rearranges to t = 19.6/9.8 = 2. The interpretation is straightforward: the sliotar takes 2 seconds to reach its maximum height.
This demonstrates how mathematical modelling transforms a sports scenario into a solvable equation, then translates the numerical result back into practical knowledge.
Reality check: Does 2 seconds seem reasonable for a sliotar to reach its peak? Trust your instincts!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Population Growth Example
Applied mathematics also tackles biological problems brilliantly. Consider: 50 bacteria double every hour - how many after 6 hours?
Our assumptions include unlimited food, no deaths, and constant growth rate. The mathematical model for this exponential growth is P(t) = P₀ × 2ᵗ, where P₀ = 50 bacteria and t = time in hours.
Solving: P(6) = 50 × 2⁶ = 50 × 64 = 3,200 bacteria. The interpretation shows how quickly bacterial populations can explode under ideal conditions.
This example demonstrates how mathematical modelling applies across different fields - from sports physics to biological sciences. The same systematic approach works whether you're dealing with projectiles or populations.
Important: Notice how different real-world situations need completely different mathematical models!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Key Points for Success
Remember that mathematical models are never perfect - they're always simplified versions of reality. The goal is making them "good enough" to provide useful answers, not to capture every tiny detail.
Always state your assumptions clearly and draw diagrams for physics problems. Your applied mathematics solutions should pass the reality check - if a car supposedly takes 3 hours to travel 100 metres, something's gone wrong!
Applied mathematics connects directly to Physics (motion and forces), Biology (population models), Economics (financial planning), and Geography (map projections). It's the bridge between classroom maths and real-world problem-solving.
The core process remains constant: Problem → Model → Solve → Interpret. Master this cycle, and you'll be able to tackle everything from engineering challenges to environmental predictions.
Exam success tip: Always explain your final answer in the context of the original problem - numbers alone aren't enough!
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.
1
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Practice Test ✓ Essay Outlines
Practice Test
Quiz
Flashcards
Essay
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
4.7/5
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 Knowunity AI. 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 Knowunity AI. 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