# November 2015

Here is the list of “November Topics,” that is what AP classes usually consider from mid-November into December. There has been a lot of discussion about inverses this month at the AP Calculus Community. While not the most read on this blog, the series on inverses may be helpful in considering all the ins and…

# The Old Pump

A tank is being filled with water using a pump that is old, and slows down as it runs. The table below gives the rate at which the pump pumps at ten-minute intervals. If the tank initially has 570 gallons of water in it, approximately how much water is in the tank after 90 minutes?…

# Speed

Speed is the absolute value of velocity: speed =  . This is the definition of speed, but hardly enough to be sure students know about speed and its relationship to velocity and acceleration. Velocity is a vector quantity; that is, it had both a direction and a magnitude. The magnitude of velocity vector is the speed.…

# Motion Problems: Same Thing, Different Context

Calculus is about things that are changing. Certainly, things that move are changing, changing their position, velocity and acceleration. Most calculus textbooks deal with thing being dropped or thrown up into the air. This is called as uniformly accelerated motion since  the acceleration is due to gravity and is a constant. While this is a good place…

# Open or Closed?

About this time of year you find someone, hopefully one of your students, asking, “If I’m finding where a function is increasing, is the interval open or closed?” Do you have an answer? This is a good time to teach some things about definitions and theorems. The place to start is to ask what it…