Learning Resources

Home »  » Courses » Mathematics » Advanced Mathematics 3207 (delisted) » Unit 01 » Set 05 ILO 01 » Go to Work

Lesson

The following hints and suggestions are offered to help you progress through the Case Studies and successfully complete each.

Case Study 1: Exploring Sequences

• focuses on both arithmetic and geometric sequences and series
• reviews the notion of recursion
• reviews formulas for summing arithmetic and geometric sequences

Case Study 2: Visuals and Proofs

• you will examine relationships involving triangular numbers
• be sure you understand the difference between deductive and inductive reasoning, as well as proof by induction
• examine each visual closely to for patterns of the 3 given triangular numbers. You will be looking to see how many sets of each one exists in the given visuals

Case Study 3: Oblong Numbers

• focuses on proof by induction (part c)

Case Study 4: How Far?

• remember that the area of the regions under the curve will represent the distance traveled by each car
• when approximating area under the curve, the more rectangles you use, the better the approximation.

Activity

Consultation between your teacher, class and you will determine how much of this material will be covered. However, even if not formally assigned, these parts of the chapter are very useful for review and consolidation of the topics studied in this unit. Thus, you should spend time working in this section.

Your teacher may assign these Case Studies and/or Extensions as:

• a replacement for a chapter project
• a homework assignment
• a portfolio item
• a homework project as part of an end of year review
• as a quiz item or test item

Test Yourself

There is no self test for this lesson.