Do you know how to solve for simple logarithmic equations?
Logs are essentially a way to write a number into the power of another number. The number 4 can be written as 2^2, therefore log base 2 of 4 is 2. The number 100 can be written as 10^2, therefore log base 10 of 100 is 2. Logs grab the power that number is raised to. Log base 2 of 8 is 3. Log base 2 of 1 is 0 because 2^0 is equal to 1. Same thing for log base 10 of 1, it is equal to 0. Log2 of 1 = 0 Log2 of 2 = 1 Log2 of 4 = 2 Log2 of 8 = 3 Log3 of 1 = 0 Log3 of 3 = 1 Log3 of 9 = 2 and so on.
Do you understand what the difference between the secant line and tangent line is?
The secant equation is a way to get the average rate of change between two points, whereas the tangent line gives the rate of change of a single point on a graph. The tangent line is equal to the secant line when "delta x" or "h" goes to 0. Take for example, the equation y = x^2. The secant equation is dy/dx = 2x + h. If I wanted to know the average rate of change between point x = 4 from x = 2. I plug in h = 2. My average rate of change is 6. We can check this is correct by doing (y2-y1)/(x2-x1), which is (16-4)/(4-2) and it is equal to 6 as well. When we set h = 0, we are able to find the slope/tangent line of only that point because you're no longer comparing two points.
What is your most difficult issue: answering questions or figuring out how you're supposed to answer a question?
If the former, then I would have the student rate their strength per each algebra subject. I will then begin on the worst subjects and work our way to the top. If the latter, then I would work with students on giving them a variety of questions and build their intuition to figure out what to solve for.