PreCalculus

/PreCalculus

Polar Coordinates and Graphs

I remember being frightened by the polar coordinate system and graphing equations using it when I was in my students' seats many years ago. With graphing calculators, this doesn't have to be intimidating. I started the unit with an introduction to the polar coordinate system and reminded my students about how intimately familiar they are [...]

Conics!

It's conic section time in Pre-Calculus. Learning from last year, I added a section on circles. I polled my students prior to spring break and they didn't recall the equation of a circle in standard form. To dust off the rust and get into completing the square mode, I created some doodle notes and a [...]

Sequences, Series, & Probability

Based on feedback from my geometry students, I've created some doodle notes for my pre-calculus classes as well. Sequences and Series This notes sheet can be used to help explain the the vocabulary involved withe sequences and series - explicit, recursive, summation, factorial, etc. It helps prepare students for Arithmetic and Geometric Sequences. Arithmetic Sequences [...]

Equations from Data

When businesses, governments and other policy makers prepare to make decisions, they often look at data to find trends. In this activity, we will use data and a graphing calculator, Desmos, or Geogebra to find an equation that best fits the data points. Statista has Global Apple iPod sales (in million units). Plot the data [...]

Find an equation of best fit in Geogebra

Go to Geogebra.org. Click on Geogebra Math Apps. Choose Spreadsheet. Enter your data in the spreadsheet. Click in the graph area, then right click and choose Graphics. In the Basic tab, change your x- and y- mins and maxes to represent your data points. Click on the Grid tab and Show Grid if you want. [...]

Functions and their Graphs

Reviewing Parent Functions In Pre-Calculus class we dove right in and reviewed five of our parent functions. Screen shots of Reviewing Parent Functions Geogebra Activity are shown below. I will likely rework it next year to include a slider for a variable "b" that reflects across the y-axis and horizontally stretches/shrinks the graph. I made [...]

Polynomial and Rational Functions

Polynomial Functions Pre-Calculus has a heavy emphasis on learning how to graph various functions. The Polynomial Functions Exploration is one strategy for learning how various functions behave based on the sign of their leading coefficient and the highest power of the polynomial. I find that my students remember functions ending behavior better when they discover [...]

Graphing Polar Equations

We have spent some time learning how to graph circles, limacons, rose curves, and lemniscates on the polar coordinate plane. The material you see below is borrowed heavily from Yosh's Graphing Polar Equations part 1, part 2, and part 3. I have included a link to the Word document instead of a pdf of the [...]

Trigonometry

The start of the second semester has me teaching both Algebra II and Pre-Calculus trigonometry simultaneously. My initial plan is to post material for both classes here. It it becomes confusing or too cumbersome, I'll split the two classes. Algebra II Right Triangle Trigonometry A foldable on trig concepts seems in order given the amount [...]