Calculus 12 - Curriculum Document
Calculus 12 - Outcomes At-a-Glance
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.
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.
B15 demonstrate an understanding of critical points and absolute extreme values of a function
B16 find the intervals on which a function is increasing or decreasing
C5 apply the First and Second Derivative Tests to determine the local extreme values of a function
C6 determine the concavity of a function and locate the points of inflection by analyzing the second derivative
B17 solve application problems involving maximum or minimum values of a function
Additional Resources and Activities for Unit 3 (curve sketching and optimization)
Functions and Their Derivatives Desmos activity - In this activity, students will practice matching a function to its first and second derivatives. Then they'll create their own function and after successfully matching it to its derivatives, submit it into the gallery as a challenge for their classmates to solve.
Maximum and Minimum Points Fill in the Blanks - Students fill in all the missing blanks with information about each function and its max and min points (Answers). From Dr. Austin Maths.
Concavity and Points of Inflection (video) - A very well produced video from Brightstorm.
Filling the Vase - Have students study inflection points by analyzing the graph made from filling an oddly shaped vase. Pour in water 50 mL at a time to simulate a constant rate. Have students graph the depth as a function of time. Discuss concavity and points of inflection and how they relate to the vase. from Liana Dawson
Curve Sketching with Derivatives (video) - Another great video from Brightstorm.
Curve Sketching Math Menu - In a menu task, students are given a list of specifications and are asked to create functions that satisfy these specifications. It would be a fairly straightforward task for students to create a different function for each single specification (e.g. create a function that has a positive y-intercept). Students are challenged by asking them to use as few functions as possible to satisfy all the specifications in a list (in whatever combinations they desire). Google slides for this activity.
Functions on the Floor - An activity for small groups of students to understand first and second derivatives. Create an x and y axis on the floor with painters tape. Provide students with a collection of conditions on derivatives and second derivatives. Give students a piece of rope (or perhaps a jump rope) to create a graph with the given conditions. You could make this a series of stations around the room to work through.
WODB for First Derivative Test - This WOBD prompt can be used as a warm up after curve sketching is introduced. from Caitlyn Gironda
Jumping Rope to Understand Rolle's Theorem and Mean Value Theorem - An activity that gets students skipping! Relating a jump rope to Rolle's Theorem and then to the Mean Value Theorem. Inspired by Jeannette Cleveland.
SSDD Rectangle Problems - "Same Surface, Different Deep" structure math problems. Four problems involving a rectangle that look similar but require different strategies to solve (related rates, optimization, number theory).
Unit 3 Cumulative Review
Roller Coaster Design Project - Students design a roller coast and calculate the value of its "thrill". Students create a piecewise function to form a smoothly traveling roller coaster (differentiable everywhere on its domain).