Page 2: Probability Calculations

This page continues the probability problem from Page 1, focusing on calculating the probability of specific dice roll outcomes. The solution demonstrates:

• Calculating individual probabilities for different dice combinations
• Adding probabilities for multiple favorable outcomes
• Simplifying fractions to find the final probability

Example: The probability of rolling a sum of 6 with two dice is calculated as (1/36 + 2/36 + 3/36) = 1/6.

Highlight: This problem showcases the exam's emphasis on practical applications of probability, a key topic in the Zentrale Klausur EF NRW 2024.

Page 3: Calculator Section - Function Analysis

This page marks the beginning of the calculator-allowed section of the Zentrale Klausur EF NRW 2024. It focuses on analyzing a complex polynomial function:

• Finding the derivative of the given function
• Calculating function values at specific points
• Determining the equation of a tangent line

Vocabulary: Tangent line - A line that touches a curve at a single point without crossing it.

Highlight: The use of a graphing calculator (GTR) is introduced here, demonstrating the integration of technology in solving complex mathematical problems.

The page also includes graphing the original function and its tangent line, emphasizing visual representation in mathematical analysis.

Page 5: Applied Mathematics - Air Pollution Analysis

This page presents a real-world application problem for the Zentrale Klausur EF NRW 2024, focusing on analyzing air pollution data:

• Interpreting a polynomial function modeling particulate matter concentration
• Calculating average rates of change
• Finding and classifying extrema of the pollution function

Vocabulary: Particulate matter - Tiny particles or droplets in the air that can cause health problems.

Highlight: This problem demonstrates the exam's emphasis on applying mathematical concepts to real-world scenarios, a crucial skill for students preparing for the Zentrale Klausur EF NRW 2024.

The page includes detailed calculations and interpretations of the pollution data, showcasing the integration of calculus concepts in environmental analysis.