Do you use a calendar or "to do" list to organize upcoming activities, events and assignments? If not, what is an alternative method that you use to keep track of academic/extracurricular responsibilities?
This will vary by student. As a tutor, I can propose additional or alternative tools to help students best manage their responsibilities. These tools might include computer applications (e.g. Todoist, Reminders, Notes, Google Calendar), agenda planners and more. By outlining these responsibilities, I can also help students realize when they will have time to study such that we can set tangible goals for each of their study sessions (and set these sessions far enough in advanced based on their availability). I always find it helpful to leave an extra day or two (again this will vary based on the amount of material on an exam or quiz) to re-study material that I have a harder time understanding and/or remembering.
What does 20*(54+8) simplify to?
There are several ways that you can consider this multiplication problem. a) 20*(54+8) = 20*62...Since 54+8 is included in parentheses, these two values can be added (by the order of operations) and then multiplied by 20. Now that we have the problem reduced to 20*62, we can also look as this as 20*(60+2) to reduce the difficulty of the mental multiplication. This expands to 20*60 + 20*2 = 1200+40 = 1240. b) Similarly, 20*(54+8) = 20*54+20*8. For mental math purposes, we can further decompose this to 20*(50+4) + 20*8 = 20*50+20*4+20*8 = 1000+80+160 = 1240.
What is the derivative of 2x*e^x?
The product rule states that the derivative of h(x) = g(x)*f(x) = g'(x)*f(x) + f'(x)*g(x). In this case, let 2x = g(x) and e^x = f(x). Since g'(x) = g'(2x) = 2 and f'(x) = f'(e^x), the derivative = 2*e^x + 2x*e^x = 2*e^x(1+x)