Education Technology

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