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1 Jan 2026

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

gracie keenan

@graciekeenan_

The CCEA GCSE Mathscurriculum covers a wide range of... Show more

$# indices $a^m \cdot a^n = a^{m+n}$ $a^{-n} = \frac{1}{a^n}$ $a^m \div a^n = a^{m-n}$ $a^{\frac{1}{2}} = \sqrt{a}$ $(a^m)^n = a^{mn}$$

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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1 Jan 2026

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1 page

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

gracie keenan

@graciekeenan_

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... Show more

$# indices $a^m \cdot a^n = a^{m+n}$ $a^{-n} = \frac{1}{a^n}$ $a^m \div a^n = a^{m-n}$ $a^{\frac{1}{2}} = \sqrt{a}$ $(a^m)^n = a^{mn}$$

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

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.

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 √ $(x₂ - x₁)² + (y₂ - y₁)²$ .