Subjects

Maths

Algebra

Algebraic expressions

Easy Guide: Algebra Fractions & Completing Squares for Kids

Name: Knowunity
Brand: Knowunity

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Easy Guide: Algebra Fractions & Completing Squares for Kids

Kimberley

@kimberley_ncyf

37 Followers

This comprehensive study guide covers key mathematical concepts including expanding brackets in mathematics, completing the square quadratic example, and simplifying algebraic fractions. It provides detailed explanations and examples for students learning these topics.

• The guide covers expanding brackets, factorising, completing the square, indices, surds, scientific notation, and algebraic fractions.
• Each section includes multiple worked examples to illustrate the concepts.
• Important rules and formulas are highlighted throughout the guide.
• The material progresses from simpler to more complex applications of each topic.
• Practice problems are provided to reinforce understanding of the techniques.

25/02/2023

284

Block I
Exponding Brackets
1. (200-3)²
= (2x-3)(2x-3)
= 2x (2x-3)-3(2x-3)
= 4x² - 6x-60c +9
= 4x²-12x+9
2. (2x₁-1) (2x²-3x-4)
= 20 (2xx²-3xx

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Quadratic Factorisation and Completing the Square

This section delves deeper into quadratic factorisation and introduces the method of completing the square.

Example: 3x² + 11x + 6 is factored as (3x+2)(x+3)

The page provides multiple examples of factoring quadratic expressions, including those with a coefficient other than 1 for the x² term. It then transitions to completing the square, a technique used to rewrite quadratic expressions in a specific form.

Definition: Completing the square is a method used to convert a quadratic expression into the form (x+p)² + q.

Highlight: The completing the square quadratic example with solution shown is x² + 8x - 5, which is rewritten as (x+4)² - 21.

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Indices, Expanding Brackets, and Surds

This page covers rules for indices, further examples of expanding brackets, and an introduction to surds.

Vocabulary: Indices (or exponents) are the powers to which a number or variable is raised.

The page provides examples of simplifying expressions with indices and expanding brackets with more complex terms. It also introduces the concept of surds and their simplification.

Example: 3a³ × 4a / 8a² is simplified to 3/2a²

Highlight: The section on surds introduces important rules for simplifying and rationalising expressions involving square roots.

View

Surds and Scientific Notation

This page continues with more advanced surd operations and introduces scientific notation.

Definition: A surd is a root (usually a square root) of a number that cannot be simplified to a whole or rational number.

The page provides examples of simplifying and rationalising surds, emphasizing the importance of fully simplifying expressions. It then transitions to scientific notation, demonstrating how to represent very large or small numbers.

Example: √27 + √48 - √12 is simplified to 5√3

Highlight: The scientific notation section includes practical examples, such as calculating the surface area of Jupiter relative to Earth.

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Scientific Notation and Distance Calculations

This page focuses on applying scientific notation to real-world problems, particularly in astronomy and space travel.

Vocabulary: Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

The page provides examples of using scientific notation to perform calculations involving very large distances and speeds. It demonstrates how to use the distance-speed-time formula in conjunction with scientific notation.

Example: A rocket traveling at 1.32 × 10⁵ miles per second for 4 minutes covers a distance of 3.168 × 10⁸ miles.

Highlight: This section emphasizes the practical applications of scientific notation in fields like astronomy and space exploration.

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Algebraic Fractions

The final page focuses on simplifying algebraic fractions, a crucial skill in advanced algebra.

Definition: An algebraic fraction is a fraction where the numerator, denominator, or both contain algebraic expressions.

The page provides examples of simplifying complex algebraic fractions, including those involving quadratic expressions. It demonstrates techniques for factoring and canceling common terms to simplify fractions.

Example: (b²-49) / (b²-16) is simplified to (b+7) / (b+4)

Highlight: The simplifying algebraic fractions questions and answers provided here offer valuable practice for students preparing for advanced mathematics exams.

View

Expanding Brackets and Factorising

This page covers techniques for expanding brackets and factorising expressions. It provides several examples to illustrate these important algebraic skills.

Example: (2x-3)² is expanded as 4x²-12x+9

The page demonstrates the step-by-step process of expanding squared terms and multiplying two binomials. It also covers factorising techniques, including the difference of two squares and quadratic expressions.

Highlight: Factorising quadratic expressions is a crucial skill in algebra, often used in solving equations and simplifying complex expressions.

Vocabulary: Difference of two squares - a special case in algebra where an expression can be factored into the product of two binomials.

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

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.

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Subjects

Maths

Algebra

Algebraic expressions

Easy Guide: Algebra Fractions & Completing Squares for Kids

Kimberley

@kimberley_ncyf

37 Followers

25/02/2023

284

S3/S4

Maths

Quadratic Factorisation and Completing the Square

This section delves deeper into quadratic factorisation and introduces the method of completing the square.

Example: 3x² + 11x + 6 is factored as (3x+2)(x+3)

Definition: Completing the square is a method used to convert a quadratic expression into the form (x+p)² + q.

Highlight: The completing the square quadratic example with solution shown is x² + 8x - 5, which is rewritten as (x+4)² - 21.

Indices, Expanding Brackets, and Surds

This page covers rules for indices, further examples of expanding brackets, and an introduction to surds.

Vocabulary: Indices (or exponents) are the powers to which a number or variable is raised.

The page provides examples of simplifying expressions with indices and expanding brackets with more complex terms. It also introduces the concept of surds and their simplification.

Example: 3a³ × 4a / 8a² is simplified to 3/2a²

Highlight: The section on surds introduces important rules for simplifying and rationalising expressions involving square roots.

Surds and Scientific Notation

This page continues with more advanced surd operations and introduces scientific notation.

Definition: A surd is a root (usually a square root) of a number that cannot be simplified to a whole or rational number.

Example: √27 + √48 - √12 is simplified to 5√3

Highlight: The scientific notation section includes practical examples, such as calculating the surface area of Jupiter relative to Earth.

Scientific Notation and Distance Calculations

This page focuses on applying scientific notation to real-world problems, particularly in astronomy and space travel.

Vocabulary: Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

Example: A rocket traveling at 1.32 × 10⁵ miles per second for 4 minutes covers a distance of 3.168 × 10⁸ miles.

Highlight: This section emphasizes the practical applications of scientific notation in fields like astronomy and space exploration.

Algebraic Fractions

The final page focuses on simplifying algebraic fractions, a crucial skill in advanced algebra.

Definition: An algebraic fraction is a fraction where the numerator, denominator, or both contain algebraic expressions.

Example: (b²-49) / (b²-16) is simplified to (b+7) / (b+4)

Highlight: The simplifying algebraic fractions questions and answers provided here offer valuable practice for students preparing for advanced mathematics exams.

Expanding Brackets and Factorising

This page covers techniques for expanding brackets and factorising expressions. It provides several examples to illustrate these important algebraic skills.

Example: (2x-3)² is expanded as 4x²-12x+9

Highlight: Factorising quadratic expressions is a crucial skill in algebra, often used in solving equations and simplifying complex expressions.

Vocabulary: Difference of two squares - a special case in algebra where an expression can be factored into the product of two binomials.

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

Easy Guide: Algebra Fractions & Completing Squares for Kids

Quadratic Factorisation and Completing the Square

Indices, Expanding Brackets, and Surds

Surds and Scientific Notation

Scientific Notation and Distance Calculations

Algebraic Fractions

Expanding Brackets and Factorising

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.

Easy Guide: Algebra Fractions & Completing Squares for Kids

Quadratic Factorisation and Completing the Square

Indices, Expanding Brackets, and Surds

Surds and Scientific Notation

Scientific Notation and Distance Calculations

Algebraic Fractions

Expanding Brackets and Factorising

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.