Education Technology

# Activities

• ##### Subject Area

• Math: Math General: General

9-12

60 Minutes

Derive™ 6

## MM CAS 2003 Exam 1 Part 2 : Sample Solutions

#### Activity Overview

This activity, which acts as a learning review, is a solution of the questions of the MM CAS 2003 Exam 1 Part 2. Students use the Derive software to solve problems.

#### Before the Activity

• See the attached PDF / DFW file for solutions to the questions, and print the file for the class
• #### During the Activity

Distribute the pages to the class.

In this activity, students will:

• Define a function and write down the equations involving values of the function and its derivative
• Solve the equations by expressing two variables in terms of the third

• Graph the given curves, and determine the range of the intersection point
• Observe the period for each curve, and understand that the period + solution will also be a solution

• Define a function, graph it, and find the intercepts
• Specify the equation parametrically, and obtain the asymptote on the graph

• Enter the expressions separately and combine later
• Set bounds for the numerical solver
• Determine the value of the integral
• Calculate the area of the shaded region

• Use Derive to define a function, ignoring the scale factor, and interpret the absolute value part of the function
• Use embedded IF statements to obtain an appropriate graph
• Insert labels on the axes
• Plot the four line segments and determine where the line cuts the y-axis
• Observe that the region under the curve is triangular, and calculate the area
• Integrate the density function and solve for the variable

• Use transition matrices to solve the probability problem
• #### After the Activity

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary