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 amⁿ = 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 = fx + 2 adds 2 to all y-values, shifting the graph up by 2 units.
The equation of a circle is presented as x−a² + y−b² = 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−3² + y+1² = 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−x1² + y2−y1²).
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.