Pre-Calculus 12 Pacing Guide - This pacing guide replaces the previous yearly plan. It has been updated to reflect removed outcomes and provide flexibility for responsive instruction.
Pre-calculus 12 Desmos Activity Collection - A collection of online student Desmos activities organized by unit.
EAL Support - Desmos offers a free suite of math software tools, including the Desmos Graphing Calculator and Scientific Calculator, as well as free digital classroom activities. Click on the globe in the tool bar to access the site in other languages.
RF 13 - It is important to note that students are not expected to determine the equation of a radical function given its graph or points on the graph, however this topic can be included as an opportunity for enrichment.
RF13 Students will be expected to graph and analyze radical functions (limited to functions involving one radical). [CN, R, T, V]
RF13.01 Sketch the graph of the function y = √ x , using a table of values, and state the domain and range.
RF13.02 Sketch the graph of the function y - k = a √(b(x - h)) by applying transformations to the graph of the function y = √ x , and state the domain and range.
RF13.03 Sketch the graph of the function y = √f(x), given the graph of the function y = f(x), and explain the strategies used.
RF13.04 Compare the domain and range of the function y = √x to the domain and range of the function y = f(x),and explain why the domains and ranges may differ.
RF13.05 Describe the relationship between the roots of a radical equation and the x-intercepts of the graph of the corresponding radical function.
RF13.06 Determine, graphically, an approximate solution of a radical equation.
Additional Resources and Activities for RF13 (graph and analyze radical functions):
Pendulum Lab - p76 Question 18 from the Precaluclus 12 textbook discusses a mini-lab using a pendulum. Sam Shah conducted a similar investigation with his students and described it on his blog. (Note that he swapped the x-y axis to model a parabola versus an Irrational function).
Trail Ratings - There is no standardized system for determining hiking trail difficulty. Most of the time, the trail rating is a nebulous qualitative combination based on an examination of the terrain, trail conditions, length, elevation gain, and the rater’s disposition. However, Shenandoah National Park has attempted to quantify this process. Their solution? The simple formula r = sqrt(2gd) where g is the elevation gain (in feet) and d is the distance (in miles). Ask students to draw an elevation map depicting a trail on which any type of hike (from easiest to very strenuous) would be possible, depending on how far a person hiked. Created by Patrick Vennebush.
Desmos Activity: Square Root of a Function - A self-checking activity where students practice graphing the square root of a function. *Updated Sept. 2025*