Fächer

Mathe

Funktionen und analysis

Kurvendiskussion einzelschritte

Grenzwert

Zentrale Klausur EF NRW 2023-2025: Mathe, Deutsch und mehr!

Name: Knowunity
Brand: Knowunity

MindGame

@mindgame_wyud

166 Follower

Klassenbester Student

7.6.2021

14274

-
Hilfsmittelfreier Teil:
m =
А^)
a) Sekante durch die Punkte A (-110) und 8(216)
42)
tentrale Ulausue 2021
b) f(x)= x³
J.
3
36
4
6-0
2-(-1)

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.

Öffnen

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.

Öffnen

Page 4: Advanced Function Analysis

This page delves deeper into function analysis for the Zentrale Klausur EF NRW 2024, covering:

Finding critical points using the first derivative
Applying the second derivative test for extrema
Analyzing function behavior at infinity

Definition: Critical points are points where the first derivative of a function equals zero or is undefined.

Highlight: The page demonstrates the use of both analytical methods and graphing calculator techniques to solve complex problems, a key skill tested in the Zentrale Klausur EF NRW 2024 Lösungen.

The analysis also includes finding intersection points between the original function and a linear function, showcasing the exam's focus on comprehensive function analysis.

Öffnen

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.

Öffnen

Page 6: Environmental Policy Analysis

The final page of the Zentrale Klausur EF NRW 2024 sample continues the air pollution problem, focusing on:

Calculating percentage exceedances of pollution limits
Determining time intervals when pollution exceeds set thresholds
Analyzing the effects of different pollution reduction measures

Example: The problem calculates that the pollution level exceeds the threshold by 44.7%, demonstrating the application of percentage calculations in environmental analysis.

Highlight: This page showcases the exam's interdisciplinary approach, combining mathematical analysis with environmental policy considerations, preparing students for real-world applications of mathematics.

The problem concludes with a comparison of two pollution reduction strategies, emphasizing critical thinking and data interpretation skills crucial for success in the Zentrale Klausur EF NRW 2024.

Öffnen

Page 1: Calculator-Free Section

This page introduces the calculator-free portion of the Zentrale Klausur EF NRW 2024. It covers several mathematical concepts:

Calculating the slope of a secant line between two points
Finding the equation of a cubic function
Solving quadratic equations

Example: For the secant line through points A(-1,0) and B(2,6), the slope is calculated as (6-0)/(2-(-1)) = 2.

Highlight: The page demonstrates step-by-step solutions for each problem, providing a clear guide for students preparing for the Zentrale Klausur EF NRW 2024 Lösungen.

The page also includes a probability calculation involving dice rolls, illustrating the exam's coverage of various mathematical domains.