splitting the middle term : how kids can see a connection in precalc and calculus

If students will hear me out, I usually show them how to factor quadratics that have a leading coefficient by splitting the middle term (instead of using other tricks). I’ve noticed that it introduces them to the idea that a GCF doesn’t only have to be a monomial but that it can be a binomial quantity, which in turn helps them with more difficult factoring in Precalculus and also with simplifying derivatives in Calculus!

 

This was just an extra post today in addition to my daily posts for you students! See you tomorrow!

sunshine!

It’s so nice to see the sun out today! I think it’s been almost a full week of rain throughout our travels for Thanksgiving. Rain just makes it that much harder to get up and at ’em.

 

My regular Precalc students are just beginning to simplify trig expressions using all of the different trig identities. I’ve found that students either LOVE these (it’s like solving a puzzle!) or HATE them (why isn’t there just a formula to follow for each one??) I’m sure I’ll be posting a few more videos in the upcoming weeks to show all of the different types because they usually teach you one group of formulas at a time (double angles, half angles, sum and difference, etc). These examples just show the beginning basics including the pythagorean identities.

 

 

My honors Precalc students are working with the law of sines and law of cosines. The most challenging problems are the applications which involve navigation and surveying. I’ve worked through a surveying example which I hope will help you “navigate” your way through all of these types of word problems 😉

 

 

Until tomorrow…let’s hope this sunshine continues!!

stay healthy during this busy week

It was only a matter of time…I have my first cold of the Fall season. I’m sure plenty of you have been struggling to stay healthy too with the colder weather and your busy schedules! I usually lose my voice when I get sick since I spend so many hours each day talking so hopefully my videos later this week will still sound semi-normal!!

 

 

My honors Precalc students are preparing for a quiz this Friday which includes doing arc length and area of sectors. I’ve picked out two of the more challenging problems to show how to apply these formulas. The first deals with the apparent size of a planet when you view it from the Earth. And the other is the “famous” tethered cow problem! I think many of you will have seen it in class or in your books.

 

 

My regular Precalc students are wrapping up their trig chapter by solving inverse trig functions using the unit circle. I’ve explained how to solve what is called the “principle” values of those functions which is what you’re finding when they write uppercase Sin inverse.

 

 

See you tomorrow for Advanced Algebra Trig!

Our favorite precalc word problems

My students have a lot of tests this week including both my regular and honors Precalc students. Most of them have the day off tomorrow for Veteran’s Day so all their tests have been crammed onto Monday or Tuesday! Their books typically save the word problems for the end of the chapter so that is what they’ve been doing a LOT of lately. And I know students usually have the most trouble with word problems so let’s dive right in!

 

My regular Precalc students are finishing off the trig chapter that has been mainly graphing sin, cos, and tan curves. The chapter ends with word problems like ferris wheels, high tide/low tide, heartbeats…basically anything that can be modeled by a sin or cos curve. Here are two of the most common examples…

 

 

My honors Precalc students are finishing of the logarithm chapter. It has a big section with exponential word problems like half-life, continuous compounding of money, population growth, etc. I’ve worked out and explained a few common, but difficult examples…

 

 

Best of luck if you have tests this week too! And have a great day off tomorrow if your school observes the holiday!

Precalculus Tuesday!

Good morning everyone! Precalculus…I sometimes think it is even harder than Calculus because of the way you jump from one chapter to the next completely unrelated chapter. At least with Calculus it continuously builds on itself throughout the whole year!

 

I have students in both Regular Precalc and Honors Precalc so I will include videos for both (since they move at a different pace those students are very rarely learning the same thing at the same time of year).

 

My Regular Precalc students are wrapping up their unit on sketching trig graphs (sin, cos, tan, csc, sec, cot). That’s all of those “fun” equations with amplitude, period, shifting, etc! Here are two videos. The first demonstrates a sine graph and the second is tangent. In my opinion, tangent graphs are the trickiest because they are sketched much differently than all of the other graphs.

 

Here’s the sin graph

 

And here’s the tan graph

 

 

My Honors Precalc students are in the middle of logarithms and exponential functions. This video has three examples of solving these types of equations…

 

 

Check back again next Tuesday for some more Precalculus! Tomorrow we will take on Advanced Algebra Trig!!