Education Technology

MM CAS 2002 Exam 1 Part 1 : Sample Solutions Q14 & Q27

Published on 07/23/2005

Activity Overview

This activity, which acts as a learning review, is a solution of the questions 14 - 27 of the MM CAS 2002 Exam 1 Part 1. 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 printed pages to the class.

In this activity, students will:

  • Calculate the derivative of the function
  • Apply the chain rule pattern to the composite function

  • Calculate the gradient of each option
  • Realize that the normal is a linear function
  • Find the gradient of the normal

  • Eliminate options which do not have correct locations for stationary points
  • Recognize the fact that all graphs include required zeros of the function

  • Determine the derivative of the given composite exponential function
  • Anti-differentiate the derivative and identify the function

  • Evaluate the anti-derivative, and include an arbitrary constant to find the correct alternative

  • Observe the graph of the function over the interval, and note that the values are positive
  • Use the definite integral (without partitioning the interval) to model the distance traveled

  • Understand that when a function changes sign over an interval, the definite integral does not give the area between the function and the x-axis
  • Evaluate the definite integral from a to b, and add it to the negative integral from b to c, to compute the area

  • Solve two simultaneous equations in n and p
  • Use the Mean and Variance to solve for p

  • Understand the transformation between the Standard Normal Distribution, some other Normal Distribution, and the Symmetry of a Normal Distribution
  • After the Activity

    Review student results:

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