Subjects

Maths

Algebra

Algebraic expressions

Factorising quadratics when the coefficient of x squared ≠ 1 - higher

Fun with BODMAS and Trigonometry: Cool Worksheets for Kids

Name: Knowunity
Brand: Knowunity

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Fun with BODMAS and Trigonometry: Cool Worksheets for Kids

Sofia Gibson

@sofiagibson_japn

1 Follower

This transcript covers various mathematical topics including multiplying and simplifying expressions, solving equations, factoring, and trigonometry. Here's a summary incorporating the guidelines:

A comprehensive guide to essential math concepts for students, covering multiplying and simplifying BODMAS steps, solving trigonometry with right-angled triangles, and factorising trinomials with examples. Key topics include:

Expanding and simplifying algebraic expressions
Multiplying brackets and factoring
Solving equations using BODMAS
Pythagoras theorem and trigonometry basics
Factorising trinomials and quadratic expressions

16/11/2022

122

3(x-2)
= 3x-6
-2 Cy+4)
-24-8
=
x (x + 4)
x² + 4x
multiplying brackets
Single brackets
5(x + 7)
-5x+35
-7(m-3)
=-7m+24
y (2y-m)
= 2y²-ym
x-n-

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Factoring Trinomials

This page focuses on factoring trinomials, particularly quadratic expressions.

Definition: A trinomial is an algebraic expression consisting of three terms, often in the form ax² + bx + c.

The page provides several examples of factoring trinomials:

Example: x² + 7x + 10 = (x + 2)(x + 5)

Example: a² + 3a + 2 = (a + 1)(a + 2)

Highlight: When factoring trinomials, look for two numbers that multiply to give the constant term and add to give the coefficient of x.

The page also covers the special case of perfect square trinomials:

Example: x² + 2x + 1 = (x + 1)(x + 1) = (x + 1)²

It concludes with a method for checking factorization by expanding the factors:

Example: For (x + 2)(x + 5): 2 + 5 = 7 (coefficient of x) 2 × 5 = 10 (constant term)

This method provides a quick way to verify if the factorization is correct.

View

Multiplying and Simplifying Algebraic Expressions

This page focuses on multiplying and simplifying algebraic expressions using the BODMAS rule. It covers single brackets, multiple brackets, and more complex expressions.

Definition: BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, Subtraction. It defines the order of operations in mathematical expressions.

The page provides numerous examples of multiplying brackets and simplifying expressions, such as:

Example: 3(x-2) = 3x-6

Example: x(x+4) = x² + 4x

It also demonstrates how to handle expressions with multiple terms and brackets:

Example: 3(x+4) - 5(x-3) = 3x+12 - 5x+15 = -2x+27

Highlight: When simplifying expressions with multiple terms, it's crucial to combine like terms and follow the BODMAS rule.

View

Pythagoras Theorem and Trigonometry

This page compares and contrasts the Pythagorean theorem with trigonometric methods for solving trigonometry with right-angled triangles.

Definition: The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides: a² = b² + c².

Highlight: Both Pythagoras theorem and trigonometry involve right-angled triangles and finding lengths or angles within these triangles.

Key differences:

Pythagoras theorem requires two sides to find the third side
Trigonometry needs one side and one angle to find another side
Trigonometry can also be used to find angles when two sides are known

Example: Using Pythagoras theorem: a² = b² + c² Using trigonometry: sin θ = opposite / hypotenuse, cos θ = adjacent / hypotenuse, tan θ = opposite / adjacent

The page also briefly touches on factoring, including common factor factorization:

Example: 6y² - 12y = 6y(y - 2)

View

Expanding Higher Degree Polynomials

This page focuses on expanding higher degree polynomials, including cubic expressions and more complex algebraic terms.

Vocabulary: A cubic expression is an algebraic expression of the third degree, typically in the form ax³ + bx² + cx + d.

The page provides several examples of expanding higher degree polynomials:

Example: (x+2)(x² + 5x + 4) = x³ + 5x² + 4x + 2x² + 10x + 8 = x³ + 7x² + 14x + 8

It also covers expanding the square of a binomial with a coefficient:

Example: (2x + 3)² = 4x² + 12x + 9

Highlight: When expanding (ax + b)², remember the formula a²x² + 2abx + b². This is a generalization of the (x + a)² formula.

The page concludes with more complex examples involving negative terms and higher powers:

Example: (x-2)(x²-7x+3x-21) = x³ - 7x² + 3x² - 21x - 2x² + 14x - 6x + 42 = x³ - 6x² - 13x + 42

View

Distance, Speed, and Time Problems

This page focuses on solving problems involving distance, speed, and time using the formula D = S × T.

Definition: The formula D = S × T relates Distance (D), Speed (S), and Time (T). Distance is typically measured in kilometers or miles, speed in km/h or mph, and time in hours.

The page provides several examples of solving problems using this formula:

Example: If D = 50km and S = 20km/h, find T: T = D ÷ S = 50 ÷ 20 = 2.5 hours = 2 hours 30 minutes

Example: If D = 100 miles and T = 1 hour 25 minutes, find S: S = D ÷ T = 100 ÷ 1.416 ≈ 71 mph

Highlight: When solving these problems, it's crucial to ensure all units are consistent. Convert minutes to hours when necessary.

The page also introduces the concept of BEDO FORTS, which appears to be a mnemonic device for remembering formulas or steps in problem-solving, though its specific meaning is not explained in the given transcript.

View

Expanding and Simplifying Quadratic Expressions

This page delves into expanding and simplifying quadratic expressions, focusing on multiplying two binomials and squaring binomials.

Vocabulary: A quadratic expression is an algebraic expression of the second degree, typically in the form ax² + bx + c.

The page provides several examples of expanding binomial products:

Example: (x+3)(x+7) = x² + 7x + 3x + 21 = x² + 10x + 21

It also covers the special case of squaring binomials:

Example: (a-b)² = a² - 2ab + b²

Highlight: When expanding (a+b)², remember the formula a² + 2ab + b². This is different from (a+b)², which equals a² + b².

The page concludes with more complex examples involving algebraic terms:

Example: (x+y)(x-m) = x² - xm + yx - ym

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

13 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

Algebra

Algebraic expressions

Factorising quadratics when the coefficient of x squared ≠ 1 - higher

Fun with BODMAS and Trigonometry: Cool Worksheets for Kids

Sofia Gibson

@sofiagibson_japn

1 Follower

This transcript covers various mathematical topics including multiplying and simplifying expressions, solving equations, factoring, and trigonometry. Here's a summary incorporating the guidelines:

Expanding and simplifying algebraic expressions
Multiplying brackets and factoring
Solving equations using BODMAS
Pythagoras theorem and trigonometry basics
Factorising trinomials and quadratic expressions

16/11/2022

122

Maths

Factoring Trinomials

This page focuses on factoring trinomials, particularly quadratic expressions.

Definition: A trinomial is an algebraic expression consisting of three terms, often in the form ax² + bx + c.

The page provides several examples of factoring trinomials:

Example: x² + 7x + 10 = (x + 2)(x + 5)

Example: a² + 3a + 2 = (a + 1)(a + 2)

Highlight: When factoring trinomials, look for two numbers that multiply to give the constant term and add to give the coefficient of x.

The page also covers the special case of perfect square trinomials:

Example: x² + 2x + 1 = (x + 1)(x + 1) = (x + 1)²

It concludes with a method for checking factorization by expanding the factors:

Example: For (x + 2)(x + 5): 2 + 5 = 7 (coefficient of x) 2 × 5 = 10 (constant term)

This method provides a quick way to verify if the factorization is correct.

Multiplying and Simplifying Algebraic Expressions

This page focuses on multiplying and simplifying algebraic expressions using the BODMAS rule. It covers single brackets, multiple brackets, and more complex expressions.

Definition: BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, Subtraction. It defines the order of operations in mathematical expressions.

The page provides numerous examples of multiplying brackets and simplifying expressions, such as:

Example: 3(x-2) = 3x-6

Example: x(x+4) = x² + 4x

It also demonstrates how to handle expressions with multiple terms and brackets:

Example: 3(x+4) - 5(x-3) = 3x+12 - 5x+15 = -2x+27

Highlight: When simplifying expressions with multiple terms, it's crucial to combine like terms and follow the BODMAS rule.

Pythagoras Theorem and Trigonometry

This page compares and contrasts the Pythagorean theorem with trigonometric methods for solving trigonometry with right-angled triangles.

Definition: The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides: a² = b² + c².

Highlight: Both Pythagoras theorem and trigonometry involve right-angled triangles and finding lengths or angles within these triangles.

Key differences:

Pythagoras theorem requires two sides to find the third side
Trigonometry needs one side and one angle to find another side
Trigonometry can also be used to find angles when two sides are known

Example: Using Pythagoras theorem: a² = b² + c² Using trigonometry: sin θ = opposite / hypotenuse, cos θ = adjacent / hypotenuse, tan θ = opposite / adjacent

The page also briefly touches on factoring, including common factor factorization:

Example: 6y² - 12y = 6y(y - 2)

Expanding Higher Degree Polynomials

This page focuses on expanding higher degree polynomials, including cubic expressions and more complex algebraic terms.

Vocabulary: A cubic expression is an algebraic expression of the third degree, typically in the form ax³ + bx² + cx + d.

The page provides several examples of expanding higher degree polynomials:

Example: (x+2)(x² + 5x + 4) = x³ + 5x² + 4x + 2x² + 10x + 8 = x³ + 7x² + 14x + 8

It also covers expanding the square of a binomial with a coefficient:

Example: (2x + 3)² = 4x² + 12x + 9

Highlight: When expanding (ax + b)², remember the formula a²x² + 2abx + b². This is a generalization of the (x + a)² formula.

The page concludes with more complex examples involving negative terms and higher powers:

Example: (x-2)(x²-7x+3x-21) = x³ - 7x² + 3x² - 21x - 2x² + 14x - 6x + 42 = x³ - 6x² - 13x + 42

Distance, Speed, and Time Problems

This page focuses on solving problems involving distance, speed, and time using the formula D = S × T.

Definition: The formula D = S × T relates Distance (D), Speed (S), and Time (T). Distance is typically measured in kilometers or miles, speed in km/h or mph, and time in hours.

The page provides several examples of solving problems using this formula:

Example: If D = 50km and S = 20km/h, find T: T = D ÷ S = 50 ÷ 20 = 2.5 hours = 2 hours 30 minutes

Example: If D = 100 miles and T = 1 hour 25 minutes, find S: S = D ÷ T = 100 ÷ 1.416 ≈ 71 mph

Highlight: When solving these problems, it's crucial to ensure all units are consistent. Convert minutes to hours when necessary.

Expanding and Simplifying Quadratic Expressions

This page delves into expanding and simplifying quadratic expressions, focusing on multiplying two binomials and squaring binomials.

Vocabulary: A quadratic expression is an algebraic expression of the second degree, typically in the form ax² + bx + c.

The page provides several examples of expanding binomial products:

Example: (x+3)(x+7) = x² + 7x + 3x + 21 = x² + 10x + 21

It also covers the special case of squaring binomials:

Example: (a-b)² = a² - 2ab + b²

Highlight: When expanding (a+b)², remember the formula a² + 2ab + b². This is different from (a+b)², which equals a² + b².

The page concludes with more complex examples involving algebraic terms:

Example: (x+y)(x-m) = x² - xm + yx - ym

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

13 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

Fun with BODMAS and Trigonometry: Cool Worksheets for Kids

Factoring Trinomials

Multiplying and Simplifying Algebraic Expressions

Pythagoras Theorem and Trigonometry

Expanding Higher Degree Polynomials

Distance, Speed, and Time Problems

Expanding and Simplifying Quadratic Expressions

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+

13 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.

Fun with BODMAS and Trigonometry: Cool Worksheets for Kids

Factoring Trinomials

Multiplying and Simplifying Algebraic Expressions

Pythagoras Theorem and Trigonometry

Expanding Higher Degree Polynomials

Distance, Speed, and Time Problems

Expanding and Simplifying Quadratic Expressions

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+

13 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.