What i didn't do well on- This quiz was designed with care to challenge our knowledge of logarithms and how they are applied to calculate squares and simplify mathematical expressions. Although I usually had an elementary understanding of the concepts—knowing, for example, that division of squares is subtraction and multiplication is addition—there were some areas where I might have done better. In the first question, for instance, I omitted the logarithmic function logm - logn from my answer. By doing so, this mistake was pivotal because it revealed a gap in my ability to integrate the relevant mathematical principles in that context. By leaving out this significant element, my answer was not only lacking but also far too shallow and incorrect to properly solve the question. Reflecting on my performance, I acknowledge that while I have a solid conceptual understanding of logarithmic functions and their application, rigid control over detail is essential. Small oversights like the one I committed have a strong impact on the clarity and comprehensiveness of my answers. Being more meticulous and precise in my response, I feel that my results could see considerable improvement in future tests.

What i did will on- I performed well on the recent test focused on exponential functions and graphing. The exam required evaluating and simplifying equations, and I excelled in graphing and solving word problems. The formula (a * b^x) is key for exponential functions, where 'a' is the initial value, 'b' is the growth or decay factor, and 'x' is the exponent. If 'b' is greater than 1, it indicates growth; if it's between 0 and 1, it indicates decay. I learned important rules about exponents: when multiplying with the same base, add the exponents; when dividing, subtract them. A negative exponent represents the reciprocal of the base raised to the positive exponent. I also found that square roots can be converted into exponential forms, which helps in simplifying answers. Overall, I grasped most concepts, preparing me for future math topics.

GRADE- 65

The assignment emphasizes the importance of understanding the fundamental concepts of the unit circle rather than simply memorizing facts. The unit circle, which has a radius of one unit and is centered at the origin (0,0) on a coordinate plane, is crucial for enhancing our comprehension of pre-calculus. It serves as a valuable tool in trigonometry, illustrating the relationships between angles and the sine, cosine, and tangent values. Reflecting on my experiences with the unit circle, I recognize that I could have improved my understanding by studying more diligently, especially given the opportunities provided to enhance my grasp of how these functions behave. Overall, I have identified areas for improvement in my understanding of this concept.

GRADE- 90%

In this quiz, we explored trigonometric functions such as sine, cosine, and tangent, which are defined using the unit circle—a circle with a radius of 1. The unit circle helps establish relationships between angles and the coordinates of points on the circle. For any angle θ, we can identify its terminal side on the unit circle, forming a right triangle with the x-axis. The x-coordinate of the intersection point is cos(θ), while the y-coordinate is sin(θ).

For example, when we draw a 30-degree angle in standard position, with its vertex at the origin and its initial side on the positive x-axis, the terminal side intersects the unit circle at the point (√3/2, 1/2). This means that cos(30°) is √3/2 and sin(30°) is 1/2. Additionally, we can determine the tangent of 30 degrees using the ratio of sine to cosine: tan(30°) = sin(30°)/cos(30°) = (1/2) / (√3/2) = 1/√3, which simplifies to √3/3.

Overall, the quiz served as a useful reminder of how the unit circle is applied in trigonometry and also something im glad i had a good grade on.