# welcome to winter break!

I just spent a very rewarding day at my daughter’s school, together with my husband, hosting their classroom holiday party! We had a lot of fun with a classroom full of 4th graders mainly just being silly and eating lots of treats! Next stop Christmas!!

My honors Geometry students have wrapped up their week with a test on the chapter regarding lines and planes in space. It’s a pretty short chapter which teaches the ways to determine a plane, how to prove that a line is perpendicular to a plane, and includes properties about parallel lines and planes. I’ve included a list of some tricky true/false questions which my students usually have trouble with.

My regular Geometry students were just tested on parallelograms. Their LEAST favorite type of problem is when they have to decide on the most descriptive name of a quadrilateral given four points on a graph. For most problems you can rely on just the slope and bypass using the distance formula…which they much prefer and it saves them a lot of time!

Stay tuned over Winter Break…I would love to answer any questions that you might have. Especially if you are like my own students and have 1st semester finals coming up in January! In the spirit of this season of giving, I would love to give out a #mathfavorsaver or two!

# one more night

I only have one more night of tutoring before I’m on Winter Break, yay! I’m going to do my best to stay focused though and help my students make it through this Thursday and Friday of tests!!

My Advanced Algebra Trig students, both honors and regular, are doing synthetic division to find the factors and zeros of polynomials. Teachers definitely vary when they teach this topic to students. Most of my students however are asked to make a list of p/q’s which tells them the possible rational zeros, and then they are allowed to look at the graph on a calculator to find a few zeros that they then use in synthetic division. At least that way they don’t have to sit there and guess and check every p/q until they find one that gives them a zero remainder, but they are still showing the work and not just writing down all of the answers straight from the graph on the calculator! Whew…it’s still a lot to understand and can for sure be confusing. Here are two examples (one of them even has imaginary zeros):

Stay tuned for Geometry tomorrow! Even though it’s my Winter Break, I’m still planning to post to my blog!!

# post office fun

I wish I was as good at using those self-service machines at the post office as I am at math! It would have saved me probably a half hour over waiting in line yesterday. I was almost late to tutor, and you probably noticed that I didn’t publish my Calculus post until midnight last night!!

Both my honors and regular Precalc students are synced up working on the chapter with trig identities right now. Both classes are solving trig equations so I created one video today showing a few examples of those. You have to be really familiar with your trig identities to make solving these equations much easier.

Have a wonderful Tuesday, and I’ll see you back here tomorrow for Advanced Algebra Trig!

# is it xmas yet?

One more week and then Winter Break! All of my students have their finals in January so this week is filled with lots of chapter tests and quizzes. I know it’s a busy time for all of you…and not just in math!

My AB Calculus students have been studying the relationship between position, velocity and acceleration. They have been working on word problems involving all three which can definitely be confusing. Hopefully this example will help you sort through similar problems. I’m planning on doing another video on this same subject next time too. It’s just too much to cover in only one video!

My BC Calculus students recently learned integration by parts. This is a method that helps you take a very difficult integral and rewrite it as a much easier one instead. I’ve shown two very frequent types of integration by parts…the tabular method where you keep taking the derivative of “u” until you get 0 and a wrap-around problem where you eventually get the same integral that you started with (which doesn’t seem like something that would be very helpful, but it is!)

Have a great week! Just keep looking forward to winter break, and I know you can make it!!

# linear programming

TGIF! To finish off the week I’ve worked through a dreaded linear programming word problem. Depending on your Algebra class, you might not have to write the inequalities yourself…which would make it MUCH easier! Just in case some of you have to do this type of problem from scratch however, I’ve shown you how I typically organize the numbers in a chart. I’ve found this makes the whole process a lot easier

I also gave out my very first #mathsaverfavor this week! It was a Statistics question from a college Statistics student which involved comparing the difference between two means by running a hypothesis test and creating a confidence interval. I didn’t make a video for it, but I’ve included the notes that I wrote out and sent to that student earlier this week! I don’t regularly post on my blog regarding Statistics questions, but I do tutor several AP Statistics students each week so those types of questions are always welcome here!!

Here’s the original question:

And here is my worked out solution: