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

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