This topic continues from Mathematical Definitions P1, which can be found here:

Mathematical definitions are an essential component of GCSE Mathematics as they provide a precise and unambiguous way of describing mathematical concepts, properties, and relationships. So, here are some additional examples of mathematical definitions for different concepts:

**Two shapes are said to be congruent if they have the same size and shape and their corresponding sides and angles are equal. For example, two triangles are congruent if all three sides and angles of one triangle are equal to those of the other triangle.**

**Congruent:****Probability measures the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event, and 1 represents a specific event. For example, if a fair coin is tossed, the probability of getting heads is 0.5.**

**Probability:****In statistics, the mode is the value that appears most frequently in a data set. For example, in the data set {1, 2, 3, 3, 4, 5, 5, 5}, the mode is 5, which appears three times more than any other value in the set.**

**Mode:****There are several types of numbers, including natural numbers (positive integers), whole numbers (including zero), integers (positive and negative whole numbers), rational numbers (numbers that can be expressed as a fraction), and irrational numbers (numbers that cannot be expressed as a fraction).**

**Types of Numbers:****The HCF (Highest Common Factor) is the largest number that divides two or more numbers without leaving a remainder. For example, the HCF of 12 and 18 is 6, as 6 is the largest number that divides 12 and 18 without leaving a remainder.**

**HCF:****There are many types of shapes, including polygons (closed shapes with straight sides), circles (closed shapes with a curved boundary), and three-dimensional shapes such as cubes, spheres, and pyramids.**

**Shapes:**Additionally, mathematical definitions provide a common language for communicating mathematical ideas and concepts. Mathematical definitions allow mathematicians and students to communicate and work together effectively. In the context of GCSE Mathematics, clear and concise explanations are essential for students to understand the exam questions and demonstrate their understanding.

In conclusion, mathematical definitions are a critical component of GCSE Mathematics. They provide an unambiguous way of describing mathematical concepts, properties, and relationships. Furthermore, a good understanding of mathematical definitions is essential for students to develop problem-solving skills, mathematical reasoning, and logical thinking.

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