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Free Higher Maths Guides & Worksheets - 100 Questions on Quadratics & More!

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O

Olaoluwa Erinfolami

16/10/2022

Maths

Revision Questions Mathematics

Free Higher Maths Guides & Worksheets - 100 Questions on Quadratics & More!

Mathematics revision resources and study materials are essential tools for mastering key concepts in Higher Maths and preparing for examinations.

The fundamentals of solving quadratic equations involve understanding various methods like factorization, completing the square, and using the quadratic formula. When factorising quadratics, students learn to identify patterns and break down complex expressions into simpler terms. This process is crucial for solving equations and finding roots. Students can practice with factorising quadratic equations worksheets that provide step-by-step solutions and multiple examples to reinforce learning.

Statistical concepts like standard deviation form another critical area of mathematics study. Standard deviation measures the spread of data points from the mean, helping students understand variation in datasets. Practice materials including standard deviation questions and answers PDF resources offer comprehensive coverage of both theoretical concepts and practical applications. These materials often include real-world examples and exam-style questions that help students develop problem-solving skills. The combination of theory guides and practice questions allows students to build confidence in handling complex mathematical problems. For example, when working with standard deviation Nat 5 questions, students learn to calculate measures of spread, interpret results, and apply statistical concepts to various scenarios. Similarly, resources like factorisation questions and answers PDF provide structured learning paths that progress from basic to advanced problems, ensuring thorough understanding of mathematical principles.

These educational materials, particularly theory guides for mathematics revision, are designed to support different learning styles and ability levels. They typically include detailed explanations, worked examples, and practice exercises that help students master mathematical concepts systematically. Whether studying quadratic equations, statistical analysis, or other mathematical topics, having access to quality revision materials significantly enhances learning outcomes and exam preparation. The availability of free theory guides for mathematics revision makes these resources accessible to all students, supporting inclusive education and academic success.

...

16/10/2022

834

1125
100 Quick Questions
Theory Guides Question
1.
Evaluate
3.
4.
2.
Find the equation of the line
5.
Solve
Y
1
18
Express
Solve
1
(6,4)
WIT

View

Comprehensive Mathematics Theory Guide: Essential Topics and Solutions

Mathematics learning becomes more manageable when broken down into clear, structured components. This comprehensive guide covers fundamental topics in Higher Maths with detailed explanations and practical examples.

Definition: Theory guides are structured learning materials that break down complex mathematical concepts into understandable segments, providing step-by-step explanations and practice problems.

Understanding mathematical concepts requires both theoretical knowledge and practical application. These theory guides for mathematics revision cover essential topics from basic arithmetic to advanced calculus, ensuring thorough comprehension at every level.

The guide includes detailed explanations of Higher Maths topics such as quadratic equations, trigonometry, and standard deviation, with comprehensive examples and solutions that help reinforce learning concepts.

1125
100 Quick Questions
Theory Guides Question
1.
Evaluate
3.
4.
2.
Find the equation of the line
5.
Solve
Y
1
18
Express
Solve
1
(6,4)
WIT

View

Advanced Mathematical Concepts: From Linear Equations to Trigonometry

When working with linear equations and trigonometric functions, understanding the fundamental principles is crucial. This section explores key concepts in solving quadratic equations and trigonometric problems.

Example: For the equation 4sinx = 2 (where 0° < x < 360°), the solution process involves:

  1. Isolating sinx: sinx = 1/2
  2. Finding angles: x = 30° or 150°

The guide provides extensive practice with factorising quadratics, including step-by-step solutions and multiple approaches to problem-solving. Each concept builds upon previous knowledge, creating a solid foundation for advanced mathematics.

1125
100 Quick Questions
Theory Guides Question
1.
Evaluate
3.
4.
2.
Find the equation of the line
5.
Solve
Y
1
18
Express
Solve
1
(6,4)
WIT

View

Statistical Analysis and Quadratic Functions

Understanding standard deviation and quadratic functions forms a crucial part of higher mathematics. This section provides comprehensive coverage of these essential topics with practical applications.

Highlight: When calculating standard deviation, remember to:

  • List all values
  • Find the mean
  • Calculate deviations from the mean
  • Square the deviations
  • Find the average of squared deviations
  • Take the square root

The guide includes numerous factorisation questions and answers PDF style problems, helping students master these crucial concepts through repeated practice and detailed explanations.

1125
100 Quick Questions
Theory Guides Question
1.
Evaluate
3.
4.
2.
Find the equation of the line
5.
Solve
Y
1
18
Express
Solve
1
(6,4)
WIT

View

Advanced Mathematical Operations and Graphical Analysis

This section focuses on complex mathematical operations including surds, trigonometric graphs, and formula manipulation. These concepts are fundamental for Higher Maths Past papers success.

Vocabulary:

  • Surds: Numbers expressed with square roots that cannot be simplified to whole numbers
  • BODMAS: Bracket, Order, Division, Multiplication, Addition, Subtraction
  • Rationalising the denominator: The process of eliminating square roots from the denominator of a fraction

The guide provides extensive practice with graphical analysis, including trigonometric functions and their transformations. Understanding these concepts is essential for success in Higher Maths 2024 Solutions and beyond.

1125
100 Quick Questions
Theory Guides Question
1.
Evaluate
3.
4.
2.
Find the equation of the line
5.
Solve
Y
1
18
Express
Solve
1
(6,4)
WIT

View

Mastering Advanced Mathematics: Quadratic Equations and Geometric Problem-Solving

Understanding quadratic equations and their applications forms a crucial foundation in Higher Maths. When solving quadratic equations like 2x² + 4x - 9 = 0, students must apply the quadratic formula methodically to find solutions to one decimal place.

Definition: The quadratic formula states that for an equation ax² + bx + c = 0, x = [-b ± √(b² - 4ac)] / 2a

Factorization represents another essential technique in solving quadratic equations. For expressions like 2x² + 7x - 15, breaking them down into their factor form (2x - 3)(x + 5) helps identify roots and understand the equation's structure. This method is particularly useful when dealing with factorising quadratics problems in examinations.

Real-world applications demonstrate the practical value of these mathematical concepts. For instance, calculating discounted prices using percentages (like finding the original price of a £297.50 laptop after a 15% discount) shows how algebra connects to everyday scenarios. Similarly, geometric problems involving circles and depth calculations utilize both algebraic and geometric principles.

1125
100 Quick Questions
Theory Guides Question
1.
Evaluate
3.
4.
2.
Find the equation of the line
5.
Solve
Y
1
18
Express
Solve
1
(6,4)
WIT

View

Advanced Geometry and Vector Analysis in Mathematics

Three-dimensional geometry and vector analysis represent sophisticated topics in Higher Maths topics. When working with coordinates like (5,3,1), students must understand spatial relationships and distance calculations using vector methods.

Linear equations and parallel lines form another crucial area of study. Finding equations of lines parallel to y = 3x - 5 passing through specific points requires understanding slope concepts and parallel line properties.

Example: To find a parallel line equation:

  1. Identify the slope of the given line (3)
  2. Use point-slope form with the new point
  3. Derive the new equation y = 3x - 11

Mathematical manipulation skills come into play when simplifying expressions and solving equations. Problems involving indices, linear equations, and trigonometric graphs require systematic approaches and clear understanding of fundamental principles.

1125
100 Quick Questions
Theory Guides Question
1.
Evaluate
3.
4.
2.
Find the equation of the line
5.
Solve
Y
1
18
Express
Solve
1
(6,4)
WIT

View

Trigonometry and Volume Calculations in Advanced Mathematics

Volume calculations and trigonometric concepts form essential components of Higher Maths. When calculating sphere volumes or using trigonometric ratios, precision and proper application of formulas are crucial.

Highlight: The volume of a sphere is given by V = 4/3πr³, where r is the radius

Algebraic manipulation skills become particularly important when dealing with expressions like (2x + 2)² - 2(x² − 2). Understanding how to expand brackets and combine like terms leads to accurate simplification.

Financial mathematics applications, such as depreciation calculations, demonstrate practical uses of compound interest formulas. For example, calculating a motorbike's value after 7 years of 5.5% annual depreciation requires systematic application of compound interest principles.

1125
100 Quick Questions
Theory Guides Question
1.
Evaluate
3.
4.
2.
Find the equation of the line
5.
Solve
Y
1
18
Express
Solve
1
(6,4)
WIT

View

Advanced Problem-Solving in Mathematics: From BODMAS to Trigonometric Graphs

Mathematical problem-solving requires mastery of various concepts from basic arithmetic to advanced trigonometry. Understanding BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) helps in evaluating complex expressions without calculators.

Vocabulary: BODMAS - the order of operations in mathematics:

  • Brackets first
  • Orders (powers/indices)
  • Division and Multiplication (left to right)
  • Addition and Subtraction (left to right)

Working with surds and algebraic expressions requires careful attention to simplification rules. Problems involving √40 + 4√10 + √90 demonstrate the importance of recognizing common factors and simplifying radical expressions.

Graphing skills, particularly with trigonometric functions like y = 3sin(0.5x), require understanding period, amplitude, and phase shifts. These concepts are fundamental in Higher Maths Past papers and examinations.

1125
100 Quick Questions
Theory Guides Question
1.
Evaluate
3.
4.
2.
Find the equation of the line
5.
Solve
Y
1
18
Express
Solve
1
(6,4)
WIT

View

Comprehensive Mathematics Theory Guide: Vectors, Lines, Pythagoras, and Trigonometry

Understanding fundamental mathematical concepts is crucial for success in Higher Maths. This detailed exploration covers essential topics including vector operations, straight-line equations, Pythagorean theorem with surds, and trigonometric equations.

Definition: Vectors represent quantities with both magnitude and direction, commonly used to describe journeys and movements in mathematical space. When working with vectors like RP, we express them in terms of component vectors (f, g, h) to analyze complex spatial relationships.

The study of straight lines forms a cornerstone of coordinate geometry. When analyzing linear graphs, understanding the relationship between gradient and y-intercept is essential for solving quadratic equations. The equation y = 2x - 1 represents a line with a positive gradient of 2 and a y-intercept of -1, demonstrating how algebraic expressions translate into geometric representations.

Pythagorean theorem applications involving surds require careful manipulation of irrational numbers. In right-angled triangles, the longest side (hypotenuse) can be calculated using the square root relationship, often resulting in surd expressions. This connects directly to Higher Maths topics involving rational and irrational numbers.

Example: In a right-angled triangle with sides 1m and 7m, the hypotenuse can be calculated as 5√2m using the Pythagorean theorem: 1² + 7² = hypotenuse².

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Maths

834

16 Oct 2022

21 pages

Free Higher Maths Guides & Worksheets - 100 Questions on Quadratics & More!

O

Olaoluwa Erinfolami

@olaoluwaerinfolami_pbuj

Mathematics revision resources and study materials are essential tools for mastering key concepts in Higher Maths and preparing for examinations.

The fundamentals of solving quadratic equationsinvolve understanding various methods like factorization, completing the square, and using the quadratic formula.... Show more

1125
100 Quick Questions
Theory Guides Question
1.
Evaluate
3.
4.
2.
Find the equation of the line
5.
Solve
Y
1
18
Express
Solve
1
(6,4)
WIT

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 Mathematics Theory Guide: Essential Topics and Solutions

Mathematics learning becomes more manageable when broken down into clear, structured components. This comprehensive guide covers fundamental topics in Higher Maths with detailed explanations and practical examples.

Definition: Theory guides are structured learning materials that break down complex mathematical concepts into understandable segments, providing step-by-step explanations and practice problems.

Understanding mathematical concepts requires both theoretical knowledge and practical application. These theory guides for mathematics revision cover essential topics from basic arithmetic to advanced calculus, ensuring thorough comprehension at every level.

The guide includes detailed explanations of Higher Maths topics such as quadratic equations, trigonometry, and standard deviation, with comprehensive examples and solutions that help reinforce learning concepts.

1125
100 Quick Questions
Theory Guides Question
1.
Evaluate
3.
4.
2.
Find the equation of the line
5.
Solve
Y
1
18
Express
Solve
1
(6,4)
WIT

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

Advanced Mathematical Concepts: From Linear Equations to Trigonometry

When working with linear equations and trigonometric functions, understanding the fundamental principles is crucial. This section explores key concepts in solving quadratic equations and trigonometric problems.

Example: For the equation 4sinx = 2 (where 0° < x < 360°), the solution process involves:

  1. Isolating sinx: sinx = 1/2
  2. Finding angles: x = 30° or 150°

The guide provides extensive practice with factorising quadratics, including step-by-step solutions and multiple approaches to problem-solving. Each concept builds upon previous knowledge, creating a solid foundation for advanced mathematics.

1125
100 Quick Questions
Theory Guides Question
1.
Evaluate
3.
4.
2.
Find the equation of the line
5.
Solve
Y
1
18
Express
Solve
1
(6,4)
WIT

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

Statistical Analysis and Quadratic Functions

Understanding standard deviation and quadratic functions forms a crucial part of higher mathematics. This section provides comprehensive coverage of these essential topics with practical applications.

Highlight: When calculating standard deviation, remember to:

  • List all values
  • Find the mean
  • Calculate deviations from the mean
  • Square the deviations
  • Find the average of squared deviations
  • Take the square root

The guide includes numerous factorisation questions and answers PDF style problems, helping students master these crucial concepts through repeated practice and detailed explanations.

1125
100 Quick Questions
Theory Guides Question
1.
Evaluate
3.
4.
2.
Find the equation of the line
5.
Solve
Y
1
18
Express
Solve
1
(6,4)
WIT

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

Advanced Mathematical Operations and Graphical Analysis

This section focuses on complex mathematical operations including surds, trigonometric graphs, and formula manipulation. These concepts are fundamental for Higher Maths Past papers success.

Vocabulary:

  • Surds: Numbers expressed with square roots that cannot be simplified to whole numbers
  • BODMAS: Bracket, Order, Division, Multiplication, Addition, Subtraction
  • Rationalising the denominator: The process of eliminating square roots from the denominator of a fraction

The guide provides extensive practice with graphical analysis, including trigonometric functions and their transformations. Understanding these concepts is essential for success in Higher Maths 2024 Solutions and beyond.

1125
100 Quick Questions
Theory Guides Question
1.
Evaluate
3.
4.
2.
Find the equation of the line
5.
Solve
Y
1
18
Express
Solve
1
(6,4)
WIT

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

Mastering Advanced Mathematics: Quadratic Equations and Geometric Problem-Solving

Understanding quadratic equations and their applications forms a crucial foundation in Higher Maths. When solving quadratic equations like 2x² + 4x - 9 = 0, students must apply the quadratic formula methodically to find solutions to one decimal place.

Definition: The quadratic formula states that for an equation ax² + bx + c = 0, x = [-b ± √(b² - 4ac)] / 2a

Factorization represents another essential technique in solving quadratic equations. For expressions like 2x² + 7x - 15, breaking them down into their factor form (2x - 3)(x + 5) helps identify roots and understand the equation's structure. This method is particularly useful when dealing with factorising quadratics problems in examinations.

Real-world applications demonstrate the practical value of these mathematical concepts. For instance, calculating discounted prices using percentages (like finding the original price of a £297.50 laptop after a 15% discount) shows how algebra connects to everyday scenarios. Similarly, geometric problems involving circles and depth calculations utilize both algebraic and geometric principles.

1125
100 Quick Questions
Theory Guides Question
1.
Evaluate
3.
4.
2.
Find the equation of the line
5.
Solve
Y
1
18
Express
Solve
1
(6,4)
WIT

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

Advanced Geometry and Vector Analysis in Mathematics

Three-dimensional geometry and vector analysis represent sophisticated topics in Higher Maths topics. When working with coordinates like (5,3,1), students must understand spatial relationships and distance calculations using vector methods.

Linear equations and parallel lines form another crucial area of study. Finding equations of lines parallel to y = 3x - 5 passing through specific points requires understanding slope concepts and parallel line properties.

Example: To find a parallel line equation:

  1. Identify the slope of the given line (3)
  2. Use point-slope form with the new point
  3. Derive the new equation y = 3x - 11

Mathematical manipulation skills come into play when simplifying expressions and solving equations. Problems involving indices, linear equations, and trigonometric graphs require systematic approaches and clear understanding of fundamental principles.

1125
100 Quick Questions
Theory Guides Question
1.
Evaluate
3.
4.
2.
Find the equation of the line
5.
Solve
Y
1
18
Express
Solve
1
(6,4)
WIT

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

Trigonometry and Volume Calculations in Advanced Mathematics

Volume calculations and trigonometric concepts form essential components of Higher Maths. When calculating sphere volumes or using trigonometric ratios, precision and proper application of formulas are crucial.

Highlight: The volume of a sphere is given by V = 4/3πr³, where r is the radius

Algebraic manipulation skills become particularly important when dealing with expressions like (2x + 2)² - 2(x² − 2). Understanding how to expand brackets and combine like terms leads to accurate simplification.

Financial mathematics applications, such as depreciation calculations, demonstrate practical uses of compound interest formulas. For example, calculating a motorbike's value after 7 years of 5.5% annual depreciation requires systematic application of compound interest principles.

1125
100 Quick Questions
Theory Guides Question
1.
Evaluate
3.
4.
2.
Find the equation of the line
5.
Solve
Y
1
18
Express
Solve
1
(6,4)
WIT

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

Advanced Problem-Solving in Mathematics: From BODMAS to Trigonometric Graphs

Mathematical problem-solving requires mastery of various concepts from basic arithmetic to advanced trigonometry. Understanding BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) helps in evaluating complex expressions without calculators.

Vocabulary: BODMAS - the order of operations in mathematics:

  • Brackets first
  • Orders (powers/indices)
  • Division and Multiplication (left to right)
  • Addition and Subtraction (left to right)

Working with surds and algebraic expressions requires careful attention to simplification rules. Problems involving √40 + 4√10 + √90 demonstrate the importance of recognizing common factors and simplifying radical expressions.

Graphing skills, particularly with trigonometric functions like y = 3sin(0.5x), require understanding period, amplitude, and phase shifts. These concepts are fundamental in Higher Maths Past papers and examinations.

1125
100 Quick Questions
Theory Guides Question
1.
Evaluate
3.
4.
2.
Find the equation of the line
5.
Solve
Y
1
18
Express
Solve
1
(6,4)
WIT

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 Mathematics Theory Guide: Vectors, Lines, Pythagoras, and Trigonometry

Understanding fundamental mathematical concepts is crucial for success in Higher Maths. This detailed exploration covers essential topics including vector operations, straight-line equations, Pythagorean theorem with surds, and trigonometric equations.

Definition: Vectors represent quantities with both magnitude and direction, commonly used to describe journeys and movements in mathematical space. When working with vectors like RP, we express them in terms of component vectors (f, g, h) to analyze complex spatial relationships.

The study of straight lines forms a cornerstone of coordinate geometry. When analyzing linear graphs, understanding the relationship between gradient and y-intercept is essential for solving quadratic equations. The equation y = 2x - 1 represents a line with a positive gradient of 2 and a y-intercept of -1, demonstrating how algebraic expressions translate into geometric representations.

Pythagorean theorem applications involving surds require careful manipulation of irrational numbers. In right-angled triangles, the longest side (hypotenuse) can be calculated using the square root relationship, often resulting in surd expressions. This connects directly to Higher Maths topics involving rational and irrational numbers.

Example: In a right-angled triangle with sides 1m and 7m, the hypotenuse can be calculated as 5√2m using the Pythagorean theorem: 1² + 7² = hypotenuse².

1125
100 Quick Questions
Theory Guides Question
1.
Evaluate
3.
4.
2.
Find the equation of the line
5.
Solve
Y
1
18
Express
Solve
1
(6,4)
WIT

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

Advanced Mathematical Problem-Solving: Inequalities and Trigonometric Equations

Mastering inequalities and trigonometric equations is fundamental for Higher Maths Past papers success. These topics frequently appear in examinations and require systematic problem-solving approaches.

Linear inequalities like 112(1 + 3x) < 39 demand careful algebraic manipulation while maintaining the inequality direction. The solution process involves distributing terms, collecting like terms, and isolating the variable to determine the solution interval. This connects to real-world applications where constraints need to be expressed mathematically.

Highlight: When solving trigonometric equations such as 2tanx + 5 = -4, remember to consider all solutions within the specified interval. For 0° < x < 180°, multiple solutions may exist due to the periodic nature of trigonometric functions.

Trigonometric equations combine algebraic manipulation with understanding of trigonometric relationships. The solution process requires isolating the trigonometric term, solving for the basic angle, and then determining all applicable angles within the given interval. This demonstrates the interconnection between algebra and trigonometry in Higher Maths 2024 Solutions.

Vocabulary: Key terms include vectors, linear equations, Pythagorean theorem, surds, inequalities, and trigonometric equations - all essential components of Standard deviation and factorisation exam questions.

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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

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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