# Calculus

### student activities on the TI-Nspire: Calculus syllabus topic

Click on the name of an activity in the list below to move directly to the teacher video and TI-Nspire file download for that activity - or simply scroll through the activities/teacher videos below the list. There is a very brief description for each activity, but the best way to gain some insight into the activity is to watch the teacher video. Although the 'type' of each TI-Nspire file is a TI-Nspire CAS Teacher Software Document, it will run on both the CAS and non-CAS version of the handheld device or computer software. If you wish to download all eight of the TI-Nspire activities relevant for the Calculus syllabus topic in Math SL & HL in one zipped file, you can do that by clicking here.

Secant Line to Tangent Line - TI-Nspire Activity
dynamic graphs showing line through two points on a curve (secant line) approaching line tangent to the curve at a single point; first steps leading to defining derivative of a function at a point (‘first principles’); Secant Line to Tangent Line - Teacher Video below
download TI-Nspire file: Secant Line to Tangent Line.tns

Gradient-Slope Explorer - TI-Nspire Activity
dynamic graphs illustrating gradient of linear functions; and non-linear functions where tangent line can be moved along curve showing how value of gradient (slope) changes; Gradient-Slope Explorer - Teacher Video below

Linear Motion - TI-Nspire Activity
interactive activity where one can move a dot along a line to generate in real time a graph of time versus displacement, distance, velocity, speed or acceleration; can replay motion and also try to match a variety of different functions; Linear Motion - Teacher Video below

Differentiation Rule Recognition - TI-Nspire Activity
series of interactive quizzes that tests a student’s ability to recognize which differentiation rule to use for a given function; wide variety of functions appear in the quizzes; Differentiation Rule Recognition - Teacher Video below

Find the Function 1 - TI-Nspire Activity
series of interactive problems where a student is challenged to determine the algebraic connection (function) between two quantities (independent & dependent variables); each problem shows a diagram of the physical context and a graph displaying a point that traces out the function for the two variables; first two problems show sine and cosine curves generated from unit circle, and other problems are good introduction to understanding optimization tasks; Find the Function 1 - Teacher Video below
download TI-Nspire file: Find the Function 1.tns

Find the Function 2 - TI-Nspire Activity
a continuation of Set 1 where a student is to figure out the algebraic connection (function) between two quantities (independent & dependent variables); Find the Function 2 - Teacher Video below
download TI-Nspire file: Find the Function 2.tns

Find the Function 3 - TI-Nspire Activity
a continuation of Sets 1 & 2 but with the addition that there is a constraint such that a third related quantity is fixed; Find the Function 3 - Teacher Video below
download TI-Nspire file: Find the Function 3.tns

Maximum Volume of a Box - TI-Nspire Activity
classic open-top box problem is presented in three representations – 2D square from which the corners (h by h) are removed, the resulting 3D box, and a graph of h versus volume. The value of h (side of square corner removed from square) can be changed which dynamically changes the 3D box and can display either trace point of the function of volume in terms of h, or the full graph of the function; Maximum Volume of a Box - Teacher Video below
download TI-Nspire file: Maximum Volume of a Box.tns

Maximum Volume of a Cone - TI-Nspire Activity
optimization problem where a sector of a certain angle is cut out from a circle and formed into a cone; interactively change sector angle showing resulting 3D cone and traces out a point on the graph of the function of cone volume in terms of sector angle; Maximum Volume of a Cone - Teacher Video below
download TI-Nspire file: Maximum Volume of a Cone.tns

Definite Integral Intro - TI-Nspire Activity
interactive exploration of area under a curve approximated by rectangles whose widths can be changed; also shows definite integrals with calculations for different rectangle widths; Definite Integral Intro - Teacher Video below

Area Between Two Curves - TI-Nspire Activity
interactive graph with an animation option that illustrates the equivalence between two different approaches with definite integrals to compute the area between two curves; Area Between Two Curves - Teacher Video below
download TI-Nspire file: Area Between Two Curves.tns

Modelling Linear Motion - TI-Nspire Activity
explores linear motion by means of an editable displacement function which determines the animated motion of a dot along a vertical line; Modelling Linear Motion - Teacher Video below