Learning Resources

Outcomes

In this lesson you will

• Review and apply all the concepts and skills learned in Unit 04.

There are no new outcomes for this section. The outcomes for this section are as stated in Section 01 to Section 05 and are copied here again for your convenience.

• Apply inductive reasoning to make conjectures in geometric situations.
• Apply properties of circles.

• Demonstrate an understanding of the concept of converse.
• Demonstrate an understanding of the transformational relationship between a circle and an ellipse.
• Develop and apply formulas for distance and midpoint.
• Develop and apply formulas for distance and midpoint. Analyze and translate between symbolic, graphic, and written representations of circles and ellipses.
• Investigate, and make and prove conjectures associated with angle relationships in circles.
• Solve problems involving the equations and characteristics of circles and ellipses.
• Demonstrate an understanding of the relationship between angle rotation and the coordinates of a rotating point.
• Solve problems involving the equations and characteristics of circles and ellipses.
• Translate between different forms of equations of circles and ellipses.

• Write proofs using various axiomatic systems and assess the validity of deductive arguments.
• Write the equations of circles and ellipses in transformational form and as mapping rules to visualize and sketch graphs.

Introduction

This section is a review of the work covered in Unit 04. Be sure to read through the Key Terms and Summary of Key Concepts on pages 280 - 293 before you do some extra practice. 

The Summary of Key Concepts not only summarizes what you should have discovered in the Investigations in this Unit, but also provides worked examples of the type of problems you are expected to be able to do. It is an excellent summary and source of review.

The Practice exercises on pages 294 -298 are just that - extra practice. There are no new concepts here. If you can follow the examples in the Summary of Key Concepts and do the exercises in the Practice you should do well on any quiz or major test on this unit. 

No time is suggested for the lesson. The time you take at this section is entirely dependent on how well you know the material in the section and how much extra practice you wish to do. That is up to you. Be sure to contact your teacher about any concept or problem that causes difficulty.

Prerequisites

To be successful in this lesson, it would be helpful to know the following:

• The concepts and skills presented in Sections 01 - 05 in Unit 04.