Question Details and Solutions
This page provides detailed solutions for the first four questions of the exam.
Question 1 focuses on determining the Definitionsmenge Wurzeln (definition set for roots). The solutions show that for √(7x-1), the definition set is x ≥ 1/7, while for √(-4x-6), it's x ≤ -1.5.
Question 2 involves simplifying root expressions and rationalizing denominators. Notable solutions include:
- √225x² simplified to 15√x²
- √7p² √49p² √7p simplified to 14p√p
Example: For rationalizing the denominator of 3/(√6 - √2), the solution multiplies both numerator and denominator by (√6 + √2), resulting in 3(√6 + √2)/(6 - 2) = 3(√6 + √2)/4.
Question 3 requires students to identify a quadratic equation from a graph, with the solution given as x² + 0.5x - 2 = 0.
Question 4 involves solving a quadratic equation using the completing the square method. The equation 2x² - 4.8x + 0.88 = 0 is solved step-by-step, resulting in solutions x = 0.2 and x = 2.2.