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CCEA GCSE Maths: Indices, Trigonometry, Quadratics & Circle Theorems Notes

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CCEA GCSE Maths: Indices, Trigonometry, Quadratics & Circle Theorems Notes
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gracie keenan

@graciekeenan_

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220 Followers

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The CCEA GCSE Maths curriculum covers a wide range of mathematical concepts, including indices, trigonometry, quadratic equations, and circle theorems. This comprehensive summary provides an overview of key topics and formulas essential for success in CCEA GCSE Maths:

  • Indices and roots
  • Quadratic formula and equations
  • Trigonometric ratios and identities
  • Graph transformations
  • Circle equations and theorems
  • Inequalities and coordinate geometry
  • Binomial expansion and polynomial theorems

06/09/2022

1421

aªaªa(mm) a-"a
as. Ja
a = √√√a
a=√ am
aa" am-n)
(am) m = amn
a a
indices
a ²-1 (a/0)
serds
(√a-56) I√a+√6) = a - b
quadratic formula
-b: √b²

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Mathematical Indices, Trigonometry, and More: CCEA GCSE Maths Overview

This page provides a comprehensive overview of key mathematical concepts covered in the CCEA GCSE Maths curriculum. It serves as a quick reference guide for students preparing for exams or seeking to reinforce their understanding of fundamental principles.

The page begins with a section on indices, presenting important rules and formulas. For example, it shows that (aᵐ)ⁿ = aᵐⁿ and a^(m-n) = aᵐ/aⁿ. These rules are essential for simplifying and manipulating expressions involving exponents.

Definition: Indices, also known as exponents, indicate how many times a number is multiplied by itself.

Next, the quadratic formula is presented, which is crucial for solving quadratic equations:

Highlight: The quadratic formula is given as x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients in the quadratic equation ax² + bx + c = 0.

The page then moves on to trigonometry, introducing the basic ratios of sine, cosine, and tangent. These are fundamental for solving problems involving right-angled triangles and have numerous applications in geometry and physics.

Vocabulary: Trigonometry is the study of relationships between the sides and angles of triangles.

Graph transformations are also covered, explaining how functions can be shifted, stretched, or reflected. For instance, y = f(x) + 2 adds 2 to all y-values, shifting the graph up by 2 units.

The equation of a circle is presented as (x - a)² + (y - b)² = r², where (a, b) is the center and r is the radius. This formula is essential for problems involving circular geometry.

Example: The equation (x - 3)² + (y + 1)² = 25 represents a circle with center (3, -1) and radius 5.

The discriminant of a quadratic equation is explained, showing how it determines the number of roots:

  • When b² - 4ac > 0, there are two distinct roots
  • When b² - 4ac = 0, there is one repeated root
  • When b² - 4ac < 0, there are no real roots

Coordinate geometry concepts are also included, such as finding the gradient between two points and the distance formula.

Formula: The distance between two points (x₁, y₁) and (x₂, y₂) is given by √((x₂ - x₁)² + (y₂ - y₁)²).

The page concludes with advanced topics like the factor theorem, remainder theorem, circle theorems, and trigonometric identities. It also touches on the binomial expansion, which is crucial for higher-level mathematics.

This comprehensive overview serves as an excellent revision tool for students preparing for their CCEA GCSE Maths exams, covering a wide range of topics from basic algebra to advanced geometry and trigonometry.

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CCEA GCSE Maths: Indices, Trigonometry, Quadratics & Circle Theorems Notes

user profile picture

gracie keenan

@graciekeenan_

·

220 Followers

Follow

The CCEA GCSE Maths curriculum covers a wide range of mathematical concepts, including indices, trigonometry, quadratic equations, and circle theorems. This comprehensive summary provides an overview of key topics and formulas essential for success in CCEA GCSE Maths:

  • Indices and roots
  • Quadratic formula and equations
  • Trigonometric ratios and identities
  • Graph transformations
  • Circle equations and theorems
  • Inequalities and coordinate geometry
  • Binomial expansion and polynomial theorems

06/09/2022

1421

 

13

 

Maths

65

aªaªa(mm) a-"a
as. Ja
a = √√√a
a=√ am
aa" am-n)
(am) m = amn
a a
indices
a ²-1 (a/0)
serds
(√a-56) I√a+√6) = a - b
quadratic formula
-b: √b²

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Mathematical Indices, Trigonometry, and More: CCEA GCSE Maths Overview

This page provides a comprehensive overview of key mathematical concepts covered in the CCEA GCSE Maths curriculum. It serves as a quick reference guide for students preparing for exams or seeking to reinforce their understanding of fundamental principles.

The page begins with a section on indices, presenting important rules and formulas. For example, it shows that (aᵐ)ⁿ = aᵐⁿ and a^(m-n) = aᵐ/aⁿ. These rules are essential for simplifying and manipulating expressions involving exponents.

Definition: Indices, also known as exponents, indicate how many times a number is multiplied by itself.

Next, the quadratic formula is presented, which is crucial for solving quadratic equations:

Highlight: The quadratic formula is given as x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients in the quadratic equation ax² + bx + c = 0.

The page then moves on to trigonometry, introducing the basic ratios of sine, cosine, and tangent. These are fundamental for solving problems involving right-angled triangles and have numerous applications in geometry and physics.

Vocabulary: Trigonometry is the study of relationships between the sides and angles of triangles.

Graph transformations are also covered, explaining how functions can be shifted, stretched, or reflected. For instance, y = f(x) + 2 adds 2 to all y-values, shifting the graph up by 2 units.

The equation of a circle is presented as (x - a)² + (y - b)² = r², where (a, b) is the center and r is the radius. This formula is essential for problems involving circular geometry.

Example: The equation (x - 3)² + (y + 1)² = 25 represents a circle with center (3, -1) and radius 5.

The discriminant of a quadratic equation is explained, showing how it determines the number of roots:

  • When b² - 4ac > 0, there are two distinct roots
  • When b² - 4ac = 0, there is one repeated root
  • When b² - 4ac < 0, there are no real roots

Coordinate geometry concepts are also included, such as finding the gradient between two points and the distance formula.

Formula: The distance between two points (x₁, y₁) and (x₂, y₂) is given by √((x₂ - x₁)² + (y₂ - y₁)²).

The page concludes with advanced topics like the factor theorem, remainder theorem, circle theorems, and trigonometric identities. It also touches on the binomial expansion, which is crucial for higher-level mathematics.

This comprehensive overview serves as an excellent revision tool for students preparing for their CCEA GCSE Maths exams, covering a wide range of topics from basic algebra to advanced geometry and trigonometry.

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

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.