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25 Oct 2023

2 pages

Free PDF: GCSE Higher Maths Formulas and Examples

user profile picture

eshal

@eshal_usjl

This GCSE Maths formula sheet provides essential formulas for higher-level... Show more

Formul
Comuca sheet gisk
• Area of a Trapezirem = 1½/2 (a+b)h
• volume
section x
of a prisim = area of cross
tengon
20x15=300
volume=
300cm³

Trigonometric Functions and Their Applications

This page delves deeper into trigonometric functions, providing a visual representation of a right-angled triangle and the relationships between its sides and angles.

The page is dominated by a large diagram of a right-angled triangle, clearly labeling the opposite side OO, adjacent side AA, and hypotenuse HH. This visual aid is crucial for understanding the fundamental concepts of trigonometry.

Highlight: The mnemonic device "SOH CAH TOA" is prominently displayed, serving as a memory aid for students to recall the trigonometric ratios.

The trigonometric ratios are broken down as follows:

  1. Sine SINSIN: Opposite / Hypotenuse
  2. Cosine COSCOS: Adjacent / Hypotenuse
  3. Tangent TANTAN: Opposite / Adjacent

Example: The formula sheet provides practical applications, such as finding the opposite side using sine: opposite side = sin X × hypotenuse.

The page emphasizes the importance of correctly labeling the sides of the triangle in relation to the angle in question. This is a critical step in solving trigonometric problems accurately.

Vocabulary: Hypotenuse refers to the longest side of a right-angled triangle, opposite the right angle.

At the bottom of the page, there's a reminder to only label the two sides involved in the question, which is a helpful tip for students when approaching trigonometry problems in their GCSE Maths formula sheet Edexcel exams.

Highlight: This detailed breakdown of trigonometric functions is essential for students tackling GCSE trigonometry and probability formulas with examples in their higher-level mathematics coursework.

Formul
Comuca sheet gisk
• Area of a Trapezirem = 1½/2 (a+b)h
• volume
section x
of a prisim = area of cross
tengon
20x15=300
volume=
300cm³

Comprehensive GCSE Higher Maths Formula Sheet

This page presents a wide array of GCSE higher maths formulas essential for success in mathematics examinations. The formulas cover various topics, including geometry, trigonometry, algebra, and probability.

Highlight: The formula sheet includes key equations for area and volume calculations, which are crucial for solving geometry problems in the GCSE Maths exam.

The page begins with area formulas, notably the area of a trapezium: 1/2a+ba+bh. It then moves on to volume calculations, providing the formula for the volume of a prism: area of cross-section × length.

Example: A practical application of the volume formula is demonstrated with a prism measuring 20cm × 15cm, resulting in a volume of 300cm³.

Circular geometry is addressed with formulas for the area πr2πr² and circumference 2πrorπd2πr or πd of a circle. The sheet also includes the quadratic formula for solving equations in the form ax² + bx + c = 0.

Definition: The quadratic formula, x = b±(b24ac)-b ± √(b²-4ac) / 2a, is used to find the roots of a quadratic equation.

Trigonometric ratios sine,cosine,tangentsine, cosine, tangent are presented, along with the Pythagorean theorem a2+b2=c2a²+b²=c² for right-angled triangles. The sine and cosine rules for non-right-angled triangles are also provided.

Vocabulary: Trigonometry involves the study of relationships between the sides and angles of triangles.

The page concludes with probability formulas, including those for compound events: PAorBA or B = PAA + PBB - PAandBA and B, and conditional probability: PAandBA and B = PAgivenBA given B × PBB.

Highlight: These probability formulas GCSE Maths are crucial for solving complex probability problems in the exam.



Can't find what you're looking for? Explore other subjects.

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4.9/5

App Store

4.8/5

Google Play

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

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

 

Maths

2,351

25 Oct 2023

2 pages

Free PDF: GCSE Higher Maths Formulas and Examples

user profile picture

eshal

@eshal_usjl

This GCSE Maths formula sheet provides essential formulas for higher-level mathematics, covering areas such as geometry, trigonometry, and probability. It serves as a comprehensive reference for students preparing for their GCSE exams, offering key equations and concepts in a concise... Show more

Formul
Comuca sheet gisk
• Area of a Trapezirem = 1½/2 (a+b)h
• volume
section x
of a prisim = area of cross
tengon
20x15=300
volume=
300cm³

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

Trigonometric Functions and Their Applications

This page delves deeper into trigonometric functions, providing a visual representation of a right-angled triangle and the relationships between its sides and angles.

The page is dominated by a large diagram of a right-angled triangle, clearly labeling the opposite side OO, adjacent side AA, and hypotenuse HH. This visual aid is crucial for understanding the fundamental concepts of trigonometry.

Highlight: The mnemonic device "SOH CAH TOA" is prominently displayed, serving as a memory aid for students to recall the trigonometric ratios.

The trigonometric ratios are broken down as follows:

  1. Sine SINSIN: Opposite / Hypotenuse
  2. Cosine COSCOS: Adjacent / Hypotenuse
  3. Tangent TANTAN: Opposite / Adjacent

Example: The formula sheet provides practical applications, such as finding the opposite side using sine: opposite side = sin X × hypotenuse.

The page emphasizes the importance of correctly labeling the sides of the triangle in relation to the angle in question. This is a critical step in solving trigonometric problems accurately.

Vocabulary: Hypotenuse refers to the longest side of a right-angled triangle, opposite the right angle.

At the bottom of the page, there's a reminder to only label the two sides involved in the question, which is a helpful tip for students when approaching trigonometry problems in their GCSE Maths formula sheet Edexcel exams.

Highlight: This detailed breakdown of trigonometric functions is essential for students tackling GCSE trigonometry and probability formulas with examples in their higher-level mathematics coursework.

Formul
Comuca sheet gisk
• Area of a Trapezirem = 1½/2 (a+b)h
• volume
section x
of a prisim = area of cross
tengon
20x15=300
volume=
300cm³

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

Comprehensive GCSE Higher Maths Formula Sheet

This page presents a wide array of GCSE higher maths formulas essential for success in mathematics examinations. The formulas cover various topics, including geometry, trigonometry, algebra, and probability.

Highlight: The formula sheet includes key equations for area and volume calculations, which are crucial for solving geometry problems in the GCSE Maths exam.

The page begins with area formulas, notably the area of a trapezium: 1/2a+ba+bh. It then moves on to volume calculations, providing the formula for the volume of a prism: area of cross-section × length.

Example: A practical application of the volume formula is demonstrated with a prism measuring 20cm × 15cm, resulting in a volume of 300cm³.

Circular geometry is addressed with formulas for the area πr2πr² and circumference 2πrorπd2πr or πd of a circle. The sheet also includes the quadratic formula for solving equations in the form ax² + bx + c = 0.

Definition: The quadratic formula, x = b±(b24ac)-b ± √(b²-4ac) / 2a, is used to find the roots of a quadratic equation.

Trigonometric ratios sine,cosine,tangentsine, cosine, tangent are presented, along with the Pythagorean theorem a2+b2=c2a²+b²=c² for right-angled triangles. The sine and cosine rules for non-right-angled triangles are also provided.

Vocabulary: Trigonometry involves the study of relationships between the sides and angles of triangles.

The page concludes with probability formulas, including those for compound events: PAorBA or B = PAA + PBB - PAandBA and B, and conditional probability: PAandBA and B = PAgivenBA given B × PBB.

Highlight: These probability formulas GCSE Maths are crucial for solving complex probability problems in the exam.

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

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