Maybe I shouldn't have started this blog now, not with everything that's been going on.

It was the last day of my lecture classes yesterday.

In Trig I just went for review questions on the previous topics that are included in the finals, such as getting the exact values of the trigonometric functions of the sum to product and product to sum identities, which a lot of them still floundered over.

After that were the numeric properties of the graphs of the trigonometric functions. I hope it’s clear to them now how to get the minimum and maximum values of the equations, based on the constants given, which are either multiplied or added to the function. It certainly tested my limit when up to now they were still asking how to compute for the y-intercept of the equation.

I also had to list down again the special angles that we have been using: 30, 45, 60, 90, 180, 270 and 360 degrees, and their respective functions, which I said we have been assuming for so long that they can derive early on.

Lastly, based on the board work that we had, I also listed down their most common mistakes in the exams, which usually involves the incorrect operations of numbers inside and outside the trigonometric function.

Surprisingly, it was also the only time that they were in complete attendance, discounting one student who, through word of mouth I have been told is on leave of absence following his family’s financial difficulties. The student I mentioned yesterday even showed up, if only in the last quarter of the class period.

In my mechanics classes we had only three problems on collisions for the review. The first problem was in one dimension, and used the equation for law of conservation of momentum to find one final velocity.

The second problem was in two dimensions, with the x and y components of the initial and final velocity of the first mass given, as well as those of the initial velocity of the second mass. They were supposed to get the resultant velocity and direction of the final velocity of the second mass. So they had to apply the same equation from the first problem twice, one for each axis.

The third problem had very few given: the mass of the first object, that the initial velocities are similar in magnitude but opposite in direction, and that the first mass was stationary after the collision. They were supposed to look for the mass of the second object.

This is what occupied the majority of the class time, at least for the person on the board solving and the others diligent enough to work on the problem in their seats and try to assist him.

They ended up with three unknowns and two equations, but as I said at the start, they could manipulate the resulting equation with two unknowns so that one of the variables disappears, and only one variable remains.

The first attempt ended up with a quadratic equation that had both roots positive. The second attempt had a positive and a negative root, and we thought the positive root was the correct answer (because the mass cannot be negative). It was then that those who tried to analyze the solution while copying saw that a corrected error in computation led to a shorter and simpler answer. I guess we all learned.