 ## Introduction

As we all know, the Abitur exam is one of the most challenging exams that students face in Germany. The Abitur exam covers a wide range of subjects, including mathematics. In 2015, the Mathe Abitur exam in NRW was particularly difficult. However, with the help of the solutions provided in this article, students can gain a deeper understanding of the exam questions.

## Overview of the Exam

The Mathe Abitur 2015 NRW exam consisted of three parts. The first part was an analysis, the second part was a geometry, and the third part was a stochastics. Each part had three tasks, and each task had multiple sub-tasks. The exam lasted for a total of 300 minutes.

## Analysis

The first part of the exam focused on analysis. The first task was about the derivation of a function, and the second task was about finding the maximum and minimum of a function. The third task was about finding the area under a curve. The solutions for these tasks can be found on various online platforms, and students can use these solutions to improve their understanding of analysis.

## Geometry

The second part of the exam focused on geometry. The first task was about the calculation of the volume of a pyramid, and the second task was about the calculation of the surface area of a sphere. The third task was about the calculation of the distance between two points in three-dimensional space. The solutions for these tasks can also be found on various online platforms, and students can use these solutions to improve their understanding of geometry.

## Stochastics

The third and final part of the exam focused on stochastics. The first task was about the calculation of the probability of an event, and the second task was about the calculation of the expectation value of a random variable. The third task was about the calculation of the variance of a random variable. The solutions for these tasks can also be found on various online platforms, and students can use these solutions to improve their understanding of stochastics.

## Conclusion

In conclusion, the Mathe Abitur 2015 NRW exam was a challenging exam that required a deep understanding of mathematics. However, with the help of the solutions provided in this article, students can gain a deeper understanding of the exam questions. It is important to note that these solutions are not a substitute for studying, but rather a tool to help students improve their understanding of mathematics. With hard work and dedication, students can achieve success in the Abitur exam and beyond.