Question

Miss calculate gives a test that is too hard, and decides to let students get half credit for their corrections. That is, students get half the difference between 100 and their original grade added to their original grade. Let ۼ be the original grade and let y be the new grade. a. Write an equation expressing y in terms of ۼ. Do any obvious simplification. b. What is the highest grade Make could make? c. How long should she study to make that grade? d. What grade would she make if she doesn't study at all? e. Write the special name given to this number. According to the mathematical model, is there a number of hours she could study that would give her zero for a grade? Explain why your answer is reasonable. Sketch the graph of this quadratic function. What kind of function is it in part (a)? How can you tell? Plot the graph of the function in an appropriate domain. What would the new grade be if the old grade is 48? Show this on your graph. What was the old grade if the new grade is 83? Show this on your graph. What is the lowest the new grade could be? What part of the mathematical model tells you this?

Answer 1

a. The equation y = ۼ + (100 - ۼ) / 2 represents the new grade in terms of the original grade with half credit for corrections. b. The highest grade is 100, and the student would not need to study for it. c. Studying does not affect the grade in this scenario.

Step-by-step explanation:

a. The equation expressing the new grade, y, in terms of the original grade, ۼ, is y = ۼ + (100 - ۼ) / 2. This equation represents the student getting half credit for their corrections. There are no obvious simplifications.

b. The highest grade the student could make is 100. This is because if the original grade, ۼ, is 100, then the student wouldn't need any corrections and would receive full credit.

c. Since studying doesn't affect the grading method in this scenario, the student wouldn't need to study any specific amount of time to make the highest grade of 100.

d. If the student doesn't study at all, their new grade would be ۼ + (100 - ۼ) / 2.

e. The special name given to the number ۼ in this equation is the original grade. According to the mathematical model, there is no number of hours the student could study that would give them a zero grade. This is because the lowest grade they can achieve is half the difference between their original grade and 100, added to their original grade. The graph of this quadratic function is a parabola that opens upward.

Learn more about Grading and Corrections in Math