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1
Kat ◡̈
01/10/2025
Maths
Edexcel maths year 1 - exponential functions and logarithms notes
639
•
1 Oct 2025
•
Kat ◡̈
@katmccrindell_xoxo
Understanding exponential functions and logarithms is crucial for success in ... Show more
This page delves into logarithms, a crucial topic for A level Maths logarithms questions and answers pdf.
Logarithms are introduced as the inverse of exponential functions:
Definition: If aˣ = n, then log_a = x
The laws of logarithms are presented:
Special cases and properties of logarithms are discussed:
Highlight: log_a = 1 and log_a = 0
The page also covers the natural logarithm (ln) and provides examples of solving logarithmic equations:
Example: 3ˣ = 2ˣ⁺¹ Solution: x = ln / - ln(2)) ≈ 1.71 (3 sig figs)
These concepts are essential for Exponentials and logarithms AS Level Maths Edexcel coursework.
This final page demonstrates the practical application of exponential functions in modelling real-world phenomena, essential for Exponential Modelling A Level Maths Edexcel.
A detailed example is provided, modeling the density of a pesticide over time:
Example: P = 160e^, where P is the density of pesticide and t is time in days
The page walks through various calculations and interpretations:
Highlight: The rate of change of the pesticide density is given by dP/dt = -0.006P, indicating a decreasing density over time.
This example illustrates the power of exponential models in describing decay processes and demonstrates key skills required for A level Maths exponentials and logarithms Exam questions.
The page concludes with a discussion on interpreting the model and its limitations, providing valuable insights for students preparing for Exponentials and logarithms A Level Maths pdf assessments.
This page introduces exponential functions and their properties, essential for Edexcel year 1 maths exponential functions worksheets.
Exponential functions are defined as f = aˣ, where a is a constant. These functions have unique properties:
Highlight: All exponential functions cross the y-axis at y = 1, as any number to the power of 0 is 1.
The page also covers differentiation of exponential functions:
Example: If f = eˣ, then f' = eˣ If f = e^, then f' = ke^(kx)
Transformations of exponential functions are explored, including vertical and horizontal shifts, reflections, and stretches. Several examples are provided to illustrate these concepts:
Example: y = 10eˣ (vertical stretch) y = 3 + 4e^(2x) (combination of transformations)
The page concludes with a comparison of exponential functions and their reciprocals, such as y = 2ˣ and y = ˣ, which are reflections of each other in the y-axis.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
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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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Kat ◡̈
@katmccrindell_xoxo
Understanding exponential functions and logarithms is crucial for success in A Level Maths exponentials and logarithms Exam questions.
The study of exponential functions begins with understanding basic properties and transformations. Students learn how to manipulate expressions like ax where... Show more
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page delves into logarithms, a crucial topic for A level Maths logarithms questions and answers pdf.
Logarithms are introduced as the inverse of exponential functions:
Definition: If aˣ = n, then log_a = x
The laws of logarithms are presented:
Special cases and properties of logarithms are discussed:
Highlight: log_a = 1 and log_a = 0
The page also covers the natural logarithm (ln) and provides examples of solving logarithmic equations:
Example: 3ˣ = 2ˣ⁺¹ Solution: x = ln / - ln(2)) ≈ 1.71 (3 sig figs)
These concepts are essential for Exponentials and logarithms AS Level Maths Edexcel coursework.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This final page demonstrates the practical application of exponential functions in modelling real-world phenomena, essential for Exponential Modelling A Level Maths Edexcel.
A detailed example is provided, modeling the density of a pesticide over time:
Example: P = 160e^, where P is the density of pesticide and t is time in days
The page walks through various calculations and interpretations:
Highlight: The rate of change of the pesticide density is given by dP/dt = -0.006P, indicating a decreasing density over time.
This example illustrates the power of exponential models in describing decay processes and demonstrates key skills required for A level Maths exponentials and logarithms Exam questions.
The page concludes with a discussion on interpreting the model and its limitations, providing valuable insights for students preparing for Exponentials and logarithms A Level Maths pdf assessments.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page introduces exponential functions and their properties, essential for Edexcel year 1 maths exponential functions worksheets.
Exponential functions are defined as f = aˣ, where a is a constant. These functions have unique properties:
Highlight: All exponential functions cross the y-axis at y = 1, as any number to the power of 0 is 1.
The page also covers differentiation of exponential functions:
Example: If f = eˣ, then f' = eˣ If f = e^, then f' = ke^(kx)
Transformations of exponential functions are explored, including vertical and horizontal shifts, reflections, and stretches. Several examples are provided to illustrate these concepts:
Example: y = 10eˣ (vertical stretch) y = 3 + 4e^(2x) (combination of transformations)
The page concludes with a comparison of exponential functions and their reciprocals, such as y = 2ˣ and y = ˣ, which are reflections of each other in the y-axis.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
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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Explore key concepts of exponential and logarithmic functions, including properties, natural logarithms, and the change of base formula. This summary covers essential techniques and examples for A-Level mathematics, focusing on Edexcel syllabus requirements.
MathsExplore the step-by-step process of solving logarithmic equations, including properties of logarithms and exponential expressions. This resource covers key concepts such as the laws of logarithms, simplifying logarithmic functions, and solving quadratic equations derived from logarithmic forms. Ideal for A Level Maths students preparing for AQA exams.
MathsComprehensive overview of Year 1 AS Pure Mathematics concepts, including quadratic functions, logarithms, differentiation, and graph transformations. This resource is designed to aid students in understanding key mathematical principles and problem-solving techniques essential for exams.
MathsApp Store
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
