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ava๐ชฑ
02/12/2025
Maths
National 5 Apps of Maths - Pay
465
โข
2 Dec 2025
โข
Understanding Pay Concepts in National 5 Applications of Maths
ava๐ชฑ
@avasnotes
1 / 10
Key Pay Skills Overview
You'll need to master several important pay calculations that apply to virtually every job. These include working out basic wages, understanding overtime rates, and calculating bonuses and commission.
The main areas you'll cover are gross versus net pay (what you earn vs. what you keep), income tax calculations, and pension contributions. These skills are essential for managing your finances and understanding job offers.
Quick Tip: Remember that your payslip will always show both gross pay (before deductions) and net pay .
Basic Pay Calculations
Pay rates can be expressed in three main ways: hourly, monthly, or annually. To convert between them, remember that 1 year = 12 months = 52 weeks.
For hourly calculations, simply multiply hours worked by the hourly rate. For example, 8 hours at ยฃ7.20 per hour = 8 ร ยฃ7.20 = ยฃ57.60.
Converting between pay periods is straightforward: divide annual salary by 12 for monthly pay, or by 52 for weekly pay. If someone earns ยฃ32,000 annually, their monthly salary is ยฃ32,000 รท 12 = ยฃ2,666.67.
Remember: Always round money calculations to 2 decimal places (pence).
Overtime Pay
Overtime pay kicks in when you work undesirable hours or exceed your contracted hours. Employers must pay higher rates for this extra work.
The three main overtime rates are time and a half (hourly rate ร 1.5), double time (hourly rate ร 2), and treble time (hourly rate ร 3). These rates compensate you fairly for working outside normal hours.
For example, if your standard rate is ยฃ8.50 per hour, double time would be ยฃ8.50 ร 2 = ยฃ17.00 per hour. Working 6 hours at this rate gives you ยฃ17.00 ร 6 = ยฃ102.
Pro Tip: Weekend work often qualifies for time and a half or double time rates.
Complex Pay Calculations
Real-world pay calculations often combine regular hours with overtime. You need to calculate each part separately, then add them together.
For weekday hours, use the standard rate. For weekend or overtime hours, apply the appropriate multiplier (usually time and a half). Always identify which hours qualify for overtime before starting your calculations.
In the example with Saran, her weekday total was 24 hours at ยฃ9.20 = ยฃ220.80, plus 4 Sunday hours at time and a half (ยฃ13.80) = ยฃ55.20, giving a total weekly wage of ยฃ276.
Strategy: Break complex problems into smaller steps - calculate standard pay and overtime separately.
Commission and Bonuses
Commission is extra money earned as a percentage of sales, designed to motivate employees to work harder. It's particularly common in sales jobs like estate agents or car dealers.
To calculate commission, find the percentage of the sale value. If Jordan sells a ยฃ650,000 house with 3% commission, she earns 1% = ยฃ6,500, so 3% = ยฃ6,500 ร 3 = ยฃ19,500.
Some commission structures only apply to sales above a certain threshold. For example, earning 2.5% commission only on sales over ยฃ20,000 means you calculate the percentage on the amount exceeding that threshold.
Key Point: Commission can significantly boost your income, but it depends on your performance and sales success.
Daily Wages and Piece Rates
Some jobs pay a daily rate plus extra money for completing specific tasks. This combination gives you a guaranteed minimum with potential for additional earnings.
In the joiner example, they earn ยฃ120 per day regardless of work completed, plus ยฃ1.40 for each door they hang. This piece rate system rewards productivity while ensuring basic income security.
For 5 working days plus 40 doors: daily wage = ยฃ120 ร 5 = ยฃ600, bonus = ยฃ1.40 ร 40 = ยฃ56, total = ยฃ656.
Remember: Always identify the different components of pay before calculating the total.
Gross Pay vs Net Pay
Gross pay is what your employer says you'll earn, while net pay is what actually lands in your bank account. The difference comes from various deductions that are automatically taken out.
Common deductions include income tax, National Insurance (NI), and pension contributions. These are legal requirements that fund public services and your future retirement.
The formula is simple: Net Pay = Gross Pay - Total Deductions. If you earn ยฃ1,800 gross but pay ยฃ617 in total deductions, your take-home pay is ยฃ1,183.
Reality Check: Your net pay is typically 70-80% of your gross pay, depending on your income level and deductions.
Complex Deduction Calculations
Real payslips often combine overtime calculations with percentage-based deductions. Start by calculating total gross pay, then work out each deduction separately.
In Alex's case: 37 standard hours (ยฃ355.20) + 7 overtime hours at time and a half (ยฃ100.80) = ยฃ456 gross pay. Then calculate 5% pension (ยฃ22.80), 12% tax (ยฃ54.72), plus ยฃ74 NI = ยฃ151.52 total deductions.
Final take-home pay: ยฃ456 - ยฃ151.52 = ยฃ304.48. This shows how deductions can significantly reduce your actual income compared to gross pay.
Important: Always check your payslip calculations - employers sometimes make mistakes with deductions.
Income Tax Basics
Income tax in the UK starts with a personal allowance of ยฃ12,500 - you pay no tax on earnings up to this amount. Above this threshold, you typically pay 20% on additional income.
To calculate tax: subtract ยฃ12,500 from annual salary, then take 20% of the remainder. Someone earning ยฃ20,000 pays tax on ยฃ7,500 (ยฃ20,000 - ยฃ12,500), which equals ยฃ1,500 in tax.
For monthly salaries, convert to annual first, then follow the same process. ยฃ2,400 monthly = ยฃ28,800 annually, minus ยฃ12,500 = ยฃ16,300 taxable income = ยฃ3,260 tax.
Key Fact: The personal allowance means part-time workers often pay very little or no income tax.
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Best app on earth! no words because itโs 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
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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 didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm 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 ๐๐๐ฒ๐ค๐โจ๐๐ฎ
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 itโs 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 didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm 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 ๐๐๐ฒ๐ค๐โจ๐๐ฎ
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
Understanding Pay Concepts in National 5 Applications of Maths
ava๐ชฑ
@avasnotes
Understanding how pay works is crucial for your future career and financial planning. This topic covers everything from calculating basic wages to understanding the difference between what you earn and what you actually take home after deductions.
Key Pay Skills Overview
You'll need to master several important pay calculations that apply to virtually every job. These include working out basic wages, understanding overtime rates, and calculating bonuses and commission.
The main areas you'll cover are gross versus net pay (what you earn vs. what you keep), income tax calculations, and pension contributions. These skills are essential for managing your finances and understanding job offers.
Quick Tip: Remember that your payslip will always show both gross pay (before deductions) and net pay .
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By signing up you accept Terms of Service and Privacy Policy
Basic Pay Calculations
Pay rates can be expressed in three main ways: hourly, monthly, or annually. To convert between them, remember that 1 year = 12 months = 52 weeks.
For hourly calculations, simply multiply hours worked by the hourly rate. For example, 8 hours at ยฃ7.20 per hour = 8 ร ยฃ7.20 = ยฃ57.60.
Converting between pay periods is straightforward: divide annual salary by 12 for monthly pay, or by 52 for weekly pay. If someone earns ยฃ32,000 annually, their monthly salary is ยฃ32,000 รท 12 = ยฃ2,666.67.
Remember: Always round money calculations to 2 decimal places (pence).
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Overtime Pay
Overtime pay kicks in when you work undesirable hours or exceed your contracted hours. Employers must pay higher rates for this extra work.
The three main overtime rates are time and a half (hourly rate ร 1.5), double time (hourly rate ร 2), and treble time (hourly rate ร 3). These rates compensate you fairly for working outside normal hours.
For example, if your standard rate is ยฃ8.50 per hour, double time would be ยฃ8.50 ร 2 = ยฃ17.00 per hour. Working 6 hours at this rate gives you ยฃ17.00 ร 6 = ยฃ102.
Pro Tip: Weekend work often qualifies for time and a half or double time rates.
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Improve your grades
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Complex Pay Calculations
Real-world pay calculations often combine regular hours with overtime. You need to calculate each part separately, then add them together.
For weekday hours, use the standard rate. For weekend or overtime hours, apply the appropriate multiplier (usually time and a half). Always identify which hours qualify for overtime before starting your calculations.
In the example with Saran, her weekday total was 24 hours at ยฃ9.20 = ยฃ220.80, plus 4 Sunday hours at time and a half (ยฃ13.80) = ยฃ55.20, giving a total weekly wage of ยฃ276.
Strategy: Break complex problems into smaller steps - calculate standard pay and overtime separately.
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Improve your grades
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By signing up you accept Terms of Service and Privacy Policy
Commission and Bonuses
Commission is extra money earned as a percentage of sales, designed to motivate employees to work harder. It's particularly common in sales jobs like estate agents or car dealers.
To calculate commission, find the percentage of the sale value. If Jordan sells a ยฃ650,000 house with 3% commission, she earns 1% = ยฃ6,500, so 3% = ยฃ6,500 ร 3 = ยฃ19,500.
Some commission structures only apply to sales above a certain threshold. For example, earning 2.5% commission only on sales over ยฃ20,000 means you calculate the percentage on the amount exceeding that threshold.
Key Point: Commission can significantly boost your income, but it depends on your performance and sales success.
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Daily Wages and Piece Rates
Some jobs pay a daily rate plus extra money for completing specific tasks. This combination gives you a guaranteed minimum with potential for additional earnings.
In the joiner example, they earn ยฃ120 per day regardless of work completed, plus ยฃ1.40 for each door they hang. This piece rate system rewards productivity while ensuring basic income security.
For 5 working days plus 40 doors: daily wage = ยฃ120 ร 5 = ยฃ600, bonus = ยฃ1.40 ร 40 = ยฃ56, total = ยฃ656.
Remember: Always identify the different components of pay before calculating the total.
Sign up to see the contentIt's free!
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Improve your grades
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By signing up you accept Terms of Service and Privacy Policy
Gross Pay vs Net Pay
Gross pay is what your employer says you'll earn, while net pay is what actually lands in your bank account. The difference comes from various deductions that are automatically taken out.
Common deductions include income tax, National Insurance (NI), and pension contributions. These are legal requirements that fund public services and your future retirement.
The formula is simple: Net Pay = Gross Pay - Total Deductions. If you earn ยฃ1,800 gross but pay ยฃ617 in total deductions, your take-home pay is ยฃ1,183.
Reality Check: Your net pay is typically 70-80% of your gross pay, depending on your income level and deductions.
Sign up to see the contentIt's free!
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Complex Deduction Calculations
Real payslips often combine overtime calculations with percentage-based deductions. Start by calculating total gross pay, then work out each deduction separately.
In Alex's case: 37 standard hours (ยฃ355.20) + 7 overtime hours at time and a half (ยฃ100.80) = ยฃ456 gross pay. Then calculate 5% pension (ยฃ22.80), 12% tax (ยฃ54.72), plus ยฃ74 NI = ยฃ151.52 total deductions.
Final take-home pay: ยฃ456 - ยฃ151.52 = ยฃ304.48. This shows how deductions can significantly reduce your actual income compared to gross pay.
Important: Always check your payslip calculations - employers sometimes make mistakes with deductions.
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
Income Tax Basics
Income tax in the UK starts with a personal allowance of ยฃ12,500 - you pay no tax on earnings up to this amount. Above this threshold, you typically pay 20% on additional income.
To calculate tax: subtract ยฃ12,500 from annual salary, then take 20% of the remainder. Someone earning ยฃ20,000 pays tax on ยฃ7,500 (ยฃ20,000 - ยฃ12,500), which equals ยฃ1,500 in tax.
For monthly salaries, convert to annual first, then follow the same process. ยฃ2,400 monthly = ยฃ28,800 annually, minus ยฃ12,500 = ยฃ16,300 taxable income = ยฃ3,260 tax.
Key Fact: The personal allowance means part-time workers often pay very little or no income tax.
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
We thought youโd never ask...
What is the Knowunity AI companion?
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.
Where can I download the Knowunity app?
You can download the app from Google Play Store and 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 โ all at your fingertips.
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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 itโs 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 didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm 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 ๐๐๐ฒ๐ค๐โจ๐๐ฎ
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 itโs 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 didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm 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 ๐๐๐ฒ๐ค๐โจ๐๐ฎ
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