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Year 10 Higher GCSE Maths Guide: Surds, Number Topics, and Edexcel Questions

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Year 10 Higher GCSE Maths Guide: Surds, Number Topics, and Edexcel Questions
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Max Taylor

@maxtaylor_mzzk

·

10 Followers

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This AQA GCSE Maths Number topic study guide PDF covers key concepts in the Number topic for Year 10 Higher GCSE Mathematics. It includes practice questions and explanations on counting outcomes, algebra, prime factors, percentages, indices, standard form, and surds.

Key points:

  • Covers GCSE Maths Number topics like place value, HCF/LCM, powers, indices, and surds
  • Provides worked examples and practice questions
  • Includes exam-style questions to prepare for GCSE Maths Number revision
  • Suitable for AQA and Edexcel GCSE Maths specifications

25/09/2022

400

Standard Form and Population Data

This final page introduces a complex problem involving standard form and real-world data:

  1. A question involving standard form calculations
  2. A table showing UK population and healthcare spending data for 2002, 2007, and 2012

Highlight: This question combines standard form calculations with interpretation of real-world data, a common feature in GCSE Maths questions and answers PDF Higher.

Vocabulary: Standard form is also known as scientific notation.

This type of question tests students' ability to apply their mathematical knowledge to practical scenarios, an important skill for higher-level GCSE Maths questions.

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

Advanced Algebraic Concepts and Surds

This page delves into more complex algebraic concepts and operations involving surds. Key areas covered include:

  1. Algebraic fractions
  2. Expanding brackets with surds
  3. Solving equations with surds
  4. Simplifying expressions with indices

Vocabulary: Surds are irrational numbers that cannot be simplified to remove a square root (or cube root, etc.).

Example: Simplify √72 Solution: √72 = √(36 × 2) = √36 × √2 = 6√2

The page provides numerous examples and practice questions on calculations with powers and surds GCSE maths questions, which are crucial for students aiming for higher grades in their GCSE Maths exam.

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

View

Indices and Standard Form

This page focuses on working with indices (powers) and standard form. Key concepts covered include:

  1. Laws of indices
  2. Negative and fractional indices
  3. Converting between standard form and ordinary numbers

Definition: Standard form is a way of writing very large or very small numbers in the form a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.

Example: Express 0.000302 in standard form Solution: 0.000302 = 3.02 × 10⁻⁴

The page provides multiple practice questions on these topics, helping students prepare for GCSE maths topic tests and exams. Understanding indices and standard form is crucial for higher-level GCSE Maths questions.

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

View

Indices and Powers Practice

This page focuses on practicing calculations involving indices and powers, including:

  1. Negative indices
  2. Fractional indices
  3. Laws of indices

Example: Simplify (27)^(-1/3) Solution: (27)^(-1/3) = 1/(27^(1/3)) = 1/3

Highlight: Understanding and applying the laws of indices is crucial for solving calculations with powers and surds GCSE maths questions.

The page provides numerous practice questions, allowing students to reinforce their understanding of these important concepts. Mastering indices is essential for success in higher-tier GCSE Maths exams.

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

View

Year 10 Higher GCSE Maths Number Topics

This page introduces the key topic areas covered in the Number section for Year 10 Higher GCSE Mathematics. The topics include:

  • Number problems and reasoning
  • Place value and estimating
  • HCF and LCM
  • Calculating with powers
  • Surds
  • Zero, negative and fractional indices
  • Powers of 10 and standard form

Highlight: This guide covers essential GCSE Maths Number topics that students need to master for the higher tier exam.

Vocabulary:

  • HCF: Highest Common Factor
  • LCM: Lowest Common Multiple

These topics form the foundation for more advanced mathematical concepts and problem-solving skills required for the GCSE Maths exam.

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

View

Algebraic Manipulation and Prime Factors

This page covers various mathematical operations and concepts, including:

  1. Algebraic manipulation
  2. Prime factorization
  3. Percentage increases
  4. Factorization of quadratic expressions
  5. Index notation simplification
  6. Evaluation of expressions
  7. Solving linear equations
  8. Simplifying surds
  9. Standard form

Example: Express 180 as a product of prime factors: 180 = 2² × 3² × 5

Definition: Standard form is a way of writing very large or very small numbers using powers of 10.

Highlight: These topics are essential for GCSE Maths questions pdf and often appear in exam questions.

The page provides a mix of questions and solutions, allowing students to practice different mathematical skills required for the GCSE Maths exam. It's particularly useful for students preparing for AQA topic tests Maths answers.

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

View

Counting Outcomes in GCSE Maths

This page focuses on counting outcomes, an important concept in GCSE Maths Number revision. It provides several examples to illustrate how to calculate the number of possible outcomes in different scenarios.

Key points:

  • Calculating combinations for card distributions
  • Determining menu combinations
  • Counting possible sports uniform combinations
  • Calculating PIN code possibilities

Example: For a 4-digit PIN code using digits 0-9:

  • With repetition allowed: 10 x 10 x 10 x 10 = 10,000 possible codes
  • Without repetition: 10 x 9 x 8 x 7 = 5,040 possible codes

Highlight: Understanding counting outcomes is crucial for solving probability questions in GCSE Maths questions and answers PDF Higher.

The page concludes with a more complex problem involving selecting a number with specific constraints, demonstrating the application of counting principles in more challenging scenarios.

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

View

Homework Outcomes and Extension Questions

This page presents a summary of homework outcomes and extension questions covering various GCSE Maths topics:

  1. Factorizing and solving quadratic equations
  2. Trigonometric ratios
  3. Area of sectors
  4. Product rule for counting outcomes
  5. Limits of accuracy in calculations

Highlight: The extension questions provide challenging problems that test students' understanding of multiple concepts simultaneously.

Example: "Jacob picks a 5-digit even number. The first digit is a prime number. The third digit is odd. The fourth digit is 8. How many different 5-digit numbers could he pick?"

This page is excellent for students looking for Year 10 higher GCSE maths number problems with answers, as it provides a mix of questions and solutions across different topic areas.

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

View

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

View

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

View

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

View

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

View

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

View

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

View

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Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

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Knowunity is the #1 education app in five European countries

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iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.

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

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the #1 education app in five European countries

4.9+

Average app rating

13 M

Pupils love Knowunity

#1

In education app charts in 11 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.

Subjects

/

Maths

/

Number

/

Surds

/

Multiplying and dividing surds

/

Year 10 Higher GCSE Maths Guide: Surds, Number Topics, and Edexcel Questions

View

Year 10 Higher GCSE Maths Guide: Surds, Number Topics, and Edexcel Questions
user profile picture

Max Taylor

@maxtaylor_mzzk

·

10 Followers

Follow

Year 10 Higher GCSE Maths Guide: Surds, Number Topics, and Edexcel Questions

This AQA GCSE Maths Number topic study guide PDF covers key concepts in the Number topic for Year 10 Higher GCSE Mathematics. It includes practice questions and explanations on counting outcomes, algebra, prime factors, percentages, indices, standard form, and surds.

Key points:

  • Covers GCSE Maths Number topics like place value, HCF/LCM, powers, indices, and surds
  • Provides worked examples and practice questions
  • Includes exam-style questions to prepare for GCSE Maths Number revision
  • Suitable for AQA and Edexcel GCSE Maths specifications

25/09/2022

400

Standard Form and Population Data

This final page introduces a complex problem involving standard form and real-world data:

  1. A question involving standard form calculations
  2. A table showing UK population and healthcare spending data for 2002, 2007, and 2012

Highlight: This question combines standard form calculations with interpretation of real-world data, a common feature in GCSE Maths questions and answers PDF Higher.

Vocabulary: Standard form is also known as scientific notation.

This type of question tests students' ability to apply their mathematical knowledge to practical scenarios, an important skill for higher-level GCSE Maths questions.

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Advanced Algebraic Concepts and Surds

This page delves into more complex algebraic concepts and operations involving surds. Key areas covered include:

  1. Algebraic fractions
  2. Expanding brackets with surds
  3. Solving equations with surds
  4. Simplifying expressions with indices

Vocabulary: Surds are irrational numbers that cannot be simplified to remove a square root (or cube root, etc.).

Example: Simplify √72 Solution: √72 = √(36 × 2) = √36 × √2 = 6√2

The page provides numerous examples and practice questions on calculations with powers and surds GCSE maths questions, which are crucial for students aiming for higher grades in their GCSE Maths exam.

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Indices and Standard Form

This page focuses on working with indices (powers) and standard form. Key concepts covered include:

  1. Laws of indices
  2. Negative and fractional indices
  3. Converting between standard form and ordinary numbers

Definition: Standard form is a way of writing very large or very small numbers in the form a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.

Example: Express 0.000302 in standard form Solution: 0.000302 = 3.02 × 10⁻⁴

The page provides multiple practice questions on these topics, helping students prepare for GCSE maths topic tests and exams. Understanding indices and standard form is crucial for higher-level GCSE Maths questions.

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Indices and Powers Practice

This page focuses on practicing calculations involving indices and powers, including:

  1. Negative indices
  2. Fractional indices
  3. Laws of indices

Example: Simplify (27)^(-1/3) Solution: (27)^(-1/3) = 1/(27^(1/3)) = 1/3

Highlight: Understanding and applying the laws of indices is crucial for solving calculations with powers and surds GCSE maths questions.

The page provides numerous practice questions, allowing students to reinforce their understanding of these important concepts. Mastering indices is essential for success in higher-tier GCSE Maths exams.

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Year 10 Higher GCSE Maths Number Topics

This page introduces the key topic areas covered in the Number section for Year 10 Higher GCSE Mathematics. The topics include:

  • Number problems and reasoning
  • Place value and estimating
  • HCF and LCM
  • Calculating with powers
  • Surds
  • Zero, negative and fractional indices
  • Powers of 10 and standard form

Highlight: This guide covers essential GCSE Maths Number topics that students need to master for the higher tier exam.

Vocabulary:

  • HCF: Highest Common Factor
  • LCM: Lowest Common Multiple

These topics form the foundation for more advanced mathematical concepts and problem-solving skills required for the GCSE Maths exam.

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Algebraic Manipulation and Prime Factors

This page covers various mathematical operations and concepts, including:

  1. Algebraic manipulation
  2. Prime factorization
  3. Percentage increases
  4. Factorization of quadratic expressions
  5. Index notation simplification
  6. Evaluation of expressions
  7. Solving linear equations
  8. Simplifying surds
  9. Standard form

Example: Express 180 as a product of prime factors: 180 = 2² × 3² × 5

Definition: Standard form is a way of writing very large or very small numbers using powers of 10.

Highlight: These topics are essential for GCSE Maths questions pdf and often appear in exam questions.

The page provides a mix of questions and solutions, allowing students to practice different mathematical skills required for the GCSE Maths exam. It's particularly useful for students preparing for AQA topic tests Maths answers.

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Counting Outcomes in GCSE Maths

This page focuses on counting outcomes, an important concept in GCSE Maths Number revision. It provides several examples to illustrate how to calculate the number of possible outcomes in different scenarios.

Key points:

  • Calculating combinations for card distributions
  • Determining menu combinations
  • Counting possible sports uniform combinations
  • Calculating PIN code possibilities

Example: For a 4-digit PIN code using digits 0-9:

  • With repetition allowed: 10 x 10 x 10 x 10 = 10,000 possible codes
  • Without repetition: 10 x 9 x 8 x 7 = 5,040 possible codes

Highlight: Understanding counting outcomes is crucial for solving probability questions in GCSE Maths questions and answers PDF Higher.

The page concludes with a more complex problem involving selecting a number with specific constraints, demonstrating the application of counting principles in more challenging scenarios.

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Homework Outcomes and Extension Questions

This page presents a summary of homework outcomes and extension questions covering various GCSE Maths topics:

  1. Factorizing and solving quadratic equations
  2. Trigonometric ratios
  3. Area of sectors
  4. Product rule for counting outcomes
  5. Limits of accuracy in calculations

Highlight: The extension questions provide challenging problems that test students' understanding of multiple concepts simultaneously.

Example: "Jacob picks a 5-digit even number. The first digit is a prime number. The third digit is odd. The fourth digit is 8. How many different 5-digit numbers could he pick?"

This page is excellent for students looking for Year 10 higher GCSE maths number problems with answers, as it provides a mix of questions and solutions across different topic areas.

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

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By signing up you accept Terms of Service and Privacy Policy

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

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By signing up you accept Terms of Service and Privacy Policy

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

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By signing up you accept Terms of Service and Privacy Policy

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

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By signing up you accept Terms of Service and Privacy Policy

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

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By signing up you accept Terms of Service and Privacy Policy

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Year 10 Higher 31. Number Topic Areas 31.1 Number problems and reasoning 31.2 Place value and estimating 31.3 HCF and LCM 31.4 Calculating w

Register

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Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

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Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the #1 education app in five European countries

4.9+

Average app rating

13 M

Pupils love Knowunity

#1

In education app charts in 11 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.