# Activities

• • • ##### Subject Area

• Math: Math General: General
• Math: Statistics: Statistical Inference

• ##### Author 9-12

60 Minutes

Derive™ 6

## 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
• Re-teach concepts as necessary