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Comprehensive Maths Exam Revision Notes PDF Free Download - GCSE Algebra and Sequences

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Brand: Knowunity

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Comprehensive Maths Exam Revision Notes PDF Free Download - GCSE Algebra and Sequences

Harriet SULLIVAN

@harrietsullivan_geqk

4 Followers

Verified Study Note

This comprehensive study guide covers key topics in mathematics, including algebra, sequences, and function machines. It provides detailed explanations, examples, and practice problems to help students prepare for their GCSE Maths exams. The guide is an excellent resource for students looking for comprehensive maths exam revision notes PDF free download.

• The guide covers various mathematical concepts, including linear and non-linear sequences, algebraic expressions, and function machines.
• It includes practice problems and examples to reinforce learning.
• The content is presented in a clear, easy-to-understand format suitable for GCSE-level students.
• Visual aids such as diagrams and charts are used to illustrate key concepts.

11/06/2023

397

25/05/23
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Algebra and Equality

This page delves deeper into algebraic concepts, focusing on equations and the principle of equality.

Vocabulary: Equality refers to the state of being equal or equivalent.

The page provides examples of algebraic equations and demonstrates how to solve them using the concept of equality.

Example: In the equation 4x + 3x - 2x = 5x, like terms are combined to simplify the expression.

There are also practice problems that involve filling in missing numbers to maintain equality in equations.

Highlight: The page emphasizes the importance of grouping like terms in algebraic expressions and understanding the concept of equality in equations.

View

Shapes and Angles

This page focuses on geometric shapes and their properties, particularly squares, triangles, and quadrilaterals.

Definition: A square is a four-sided shape with all sides equal and all angles measuring 90 degrees.

Definition: A triangle is a three-sided shape with angles that add up to 180 degrees.

The page provides information on different types of triangles (equilateral, isosceles, and scalene) and their properties.

Vocabulary: Perpendicular lines meet at a right angle (90 degrees).

Highlight: The page emphasizes the importance of understanding the properties of different shapes and how angles relate to these properties.

View

Sequences

This page provides an in-depth look at sequences, offering numerous examples and practice problems.

Definition: A sequence is a series of numbers that follow a specific pattern or rule.

The page includes exercises where students are asked to identify and continue various sequences.

Example: In the sequence 3, 5, 7, 9, ..., students are asked to write down the 5th and 6th terms.

Highlight: The page emphasizes the importance of recognizing patterns in sequences and being able to continue them based on the identified rule.

View

Linear Sequences

This page focuses specifically on linear sequences, a key concept in GCSE Maths.

Definition: A linear sequence is a sequence that goes up or down by the same amount each time.

Highlight: Linear sequences give straight line graphs when plotted.

The page provides examples of how to create different linear sequences starting from the same number.

Example: Two different linear sequences starting with 20: 20, 25, 30, 35, ... and 20, 27, 34, 41, ...

Vocabulary: The term "linear" refers to the constant difference between consecutive terms in the sequence.

View

Geometric Sequences

This page introduces geometric sequences, another important concept in GCSE Maths.

Definition: A geometric sequence is a sequence where each term is found by multiplying or dividing the previous term by a constant.

The page provides several examples of geometric sequences.

Example: 2, 6, 18, 54, ... is a geometric sequence where each term is multiplied by 3 to get the next term.

Highlight: The page emphasizes the difference between linear sequences (which involve addition or subtraction) and geometric sequences (which involve multiplication or division).

View

Inverse Operations

This page focuses on inverse operations, a crucial concept in algebra and problem-solving.

Definition: Inverse operations are operations that undo each other.

The page illustrates how addition and subtraction are inverse operations, as are multiplication and division.

Example: If you add 5 to a number and then subtract 5, you end up with the original number.

Highlight: Understanding inverse operations is crucial for solving equations and manipulating algebraic expressions.

View

Function Machines

This page introduces the concept of function machines, a key topic in algebra sequences and function machines study guide PDF.

Definition: A function machine is a diagram that shows how a number (input) is changed according to certain rules to produce a result (output).

The page provides examples of function machines and how to use them.

Example: If the input is 4 and the function machine multiplies by 2 and then adds 6, the output would be 14.

Highlight: Function machines are a visual way to represent mathematical operations and can help in understanding more complex algebraic concepts.

View

Function Machines Practice

This page provides additional practice with function machines, reinforcing the concepts introduced in the previous page.

The page includes several examples of function machines with different operations.

Example: A function machine that multiplies the input by 3 and then adds 5.

Highlight: The page emphasizes the importance of understanding both the input and output of function machines, as well as the operations performed within the machine.

View

Multiplying Algebraic Expressions

This page focuses on multiplying algebraic expressions, an important skill in algebra.

Definition: When multiplying algebraic expressions, we multiply the coefficients and combine like terms.

The page provides examples of how to multiply algebraic expressions.

Example: 5x × 5x = 25x²

Vocabulary: Coefficients are the numerical factors of algebraic terms.

The page also introduces the concept of substitution in algebra.

Definition: Substitution in algebra involves replacing variables with specific values.

Example: If x = 5, then 3x + 2 would become 3(5) + 2 = 17

View

Algebraic Substitution Practice

This page provides further practice with algebraic substitution, building on the concepts introduced in the previous page.

The page includes several examples where students are asked to substitute given values into algebraic expressions.

Example: If x = 10, what is the value of 3x + 2?

Highlight: The page emphasizes the importance of following the order of operations when performing substitutions.

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.

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Download in

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Knowunity is the #1 education app in five European countries

4.9+

Average app rating

15 M

Pupils love Knowunity

#1

In education app charts in 12 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

Fractions

Comprehensive Maths Exam Revision Notes PDF Free Download - GCSE Algebra and Sequences

Harriet SULLIVAN

@harrietsullivan_geqk

4 Followers

Verified Study Note

11/06/2023

397

Maths

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Algebra and Equality

This page delves deeper into algebraic concepts, focusing on equations and the principle of equality.

Vocabulary: Equality refers to the state of being equal or equivalent.

The page provides examples of algebraic equations and demonstrates how to solve them using the concept of equality.

Example: In the equation 4x + 3x - 2x = 5x, like terms are combined to simplify the expression.

There are also practice problems that involve filling in missing numbers to maintain equality in equations.

Highlight: The page emphasizes the importance of grouping like terms in algebraic expressions and understanding the concept of equality in equations.

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Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Shapes and Angles

This page focuses on geometric shapes and their properties, particularly squares, triangles, and quadrilaterals.

Definition: A square is a four-sided shape with all sides equal and all angles measuring 90 degrees.

Definition: A triangle is a three-sided shape with angles that add up to 180 degrees.

The page provides information on different types of triangles (equilateral, isosceles, and scalene) and their properties.

Vocabulary: Perpendicular lines meet at a right angle (90 degrees).

Highlight: The page emphasizes the importance of understanding the properties of different shapes and how angles relate to these properties.

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Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Sequences

This page provides an in-depth look at sequences, offering numerous examples and practice problems.

Definition: A sequence is a series of numbers that follow a specific pattern or rule.

The page includes exercises where students are asked to identify and continue various sequences.

Example: In the sequence 3, 5, 7, 9, ..., students are asked to write down the 5th and 6th terms.

Highlight: The page emphasizes the importance of recognizing patterns in sequences and being able to continue them based on the identified rule.

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Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Linear Sequences

This page focuses specifically on linear sequences, a key concept in GCSE Maths.

Definition: A linear sequence is a sequence that goes up or down by the same amount each time.

Highlight: Linear sequences give straight line graphs when plotted.

The page provides examples of how to create different linear sequences starting from the same number.

Example: Two different linear sequences starting with 20: 20, 25, 30, 35, ... and 20, 27, 34, 41, ...

Vocabulary: The term "linear" refers to the constant difference between consecutive terms in the sequence.

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By signing up you accept Terms of Service and Privacy Policy

Geometric Sequences

This page introduces geometric sequences, another important concept in GCSE Maths.

Definition: A geometric sequence is a sequence where each term is found by multiplying or dividing the previous term by a constant.

The page provides several examples of geometric sequences.

Example: 2, 6, 18, 54, ... is a geometric sequence where each term is multiplied by 3 to get the next term.

Highlight: The page emphasizes the difference between linear sequences (which involve addition or subtraction) and geometric sequences (which involve multiplication or division).

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Inverse Operations

This page focuses on inverse operations, a crucial concept in algebra and problem-solving.

Definition: Inverse operations are operations that undo each other.

The page illustrates how addition and subtraction are inverse operations, as are multiplication and division.

Example: If you add 5 to a number and then subtract 5, you end up with the original number.

Highlight: Understanding inverse operations is crucial for solving equations and manipulating algebraic expressions.

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Function Machines

This page introduces the concept of function machines, a key topic in algebra sequences and function machines study guide PDF.

Definition: A function machine is a diagram that shows how a number (input) is changed according to certain rules to produce a result (output).

The page provides examples of function machines and how to use them.

Example: If the input is 4 and the function machine multiplies by 2 and then adds 6, the output would be 14.

Highlight: Function machines are a visual way to represent mathematical operations and can help in understanding more complex algebraic concepts.

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Function Machines Practice

This page provides additional practice with function machines, reinforcing the concepts introduced in the previous page.

The page includes several examples of function machines with different operations.

Example: A function machine that multiplies the input by 3 and then adds 5.

Highlight: The page emphasizes the importance of understanding both the input and output of function machines, as well as the operations performed within the machine.

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Multiplying Algebraic Expressions

This page focuses on multiplying algebraic expressions, an important skill in algebra.

Definition: When multiplying algebraic expressions, we multiply the coefficients and combine like terms.

The page provides examples of how to multiply algebraic expressions.

Example: 5x × 5x = 25x²

Vocabulary: Coefficients are the numerical factors of algebraic terms.

The page also introduces the concept of substitution in algebra.

Definition: Substitution in algebra involves replacing variables with specific values.

Example: If x = 5, then 3x + 2 would become 3(5) + 2 = 17

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Algebraic Substitution Practice

This page provides further practice with algebraic substitution, building on the concepts introduced in the previous page.

The page includes several examples where students are asked to substitute given values into algebraic expressions.

Example: If x = 10, what is the value of 3x + 2?

Highlight: The page emphasizes the importance of following the order of operations when performing substitutions.

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.

Download in

Google Play

Download in

App Store

4.9+

Average app rating

15 M

Pupils love Knowunity

#1

In education app charts in 12 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

Comprehensive Maths Exam Revision Notes PDF Free Download - GCSE Algebra and Sequences

Algebra and Equality

Shapes and Angles

Sequences

Linear Sequences

Geometric Sequences

Inverse Operations

Function Machines

Function Machines Practice

Multiplying Algebraic Expressions

Algebraic Substitution Practice

Similar content

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.

4.9+

15 M

#1

950 K+

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

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

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

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

Comprehensive Maths Exam Revision Notes PDF Free Download - GCSE Algebra and Sequences

Sign up to see the content. It's free!

Algebra and Equality

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Shapes and Angles

Sign up to see the content. It's free!

Sequences

Sign up to see the content. It's free!

Linear Sequences

Sign up to see the content. It's free!

Geometric Sequences

Sign up to see the content. It's free!

Inverse Operations

Sign up to see the content. It's free!

Function Machines

Sign up to see the content. It's free!

Function Machines Practice

Sign up to see the content. It's free!

Multiplying Algebraic Expressions

Sign up to see the content. It's free!

Algebraic Substitution Practice

Similar content

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.

4.9+

15 M

#1

950 K+

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

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

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

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