Tuesday, May 23, 2017

Review for Chapter 15 Test (Day 160)

This is what Theoni Pappas writes on page 143 of her Magic of Mathematics -- a table of contents for the new Chapter 6, "Mathematical Magic From the Past":

-- Babylonians & Square Roots
-- The Chinese Method of Piling Squares
-- The Ladder That Inches on the sqrt(2)
-- Early Random Number Generators
-- Egyptian Multiplication
-- The First Scientific Laboratory
-- Plato Doubles the Square
-- The Romans & the Area of a Circle
-- How the Gnomon Trisects an Angle
-- Unsolved Mathematical Mysteries
-- Fermat's Last Theorem
-- Galileo & Proportion
-- Mathematics & Containers
-- Geometries -- Old & New
-- What's in a Name?
-- Euler's Magic Formula -- F + V - E = 2

There are many fascinating things for Pappas to discuss in this chapter -- and I definitely look forward to writing about them.

Let's get to today's Geometry lesson. Notice that Chapter 15 contains nine sections, so normally we'd have to squeeze in the Chapter 15 test today (Day 160) so we could begin Lesson 16-1 tomorrow (which is Day 161). But notice that Chapter 15 is the last of the U of Chicago text. Since there is no Chapter 16, we can take our time and review today for the test tomorrow.

Last year I wrote a "Chapter 15 Test." But last year I didn't cover Chapter 15 as a whole -- instead it was a general "circles and spheres" test with questions from five different chapters. This year we covered Chapter 15 straight through, so I could post a genuine Chapter 15 test today.

I decided to take last year's test and create a new first page, since all of the Chapter 15 questions are included on the second page. My new first page includes two questions each from Lessons 15-3 and 15-4 and one each from 15-1, 15-5, 15-6, and 15-7.

Last year's Page 2 contains some questions from Lessons 15-3 and 15-8. But there are also some questions from different sections.

Questions 9 through 11 are on the equation of a circle, Questions 14 and 16 are on the volume/surface area of a sphere, Question 15 is on the Pythagorean Theorem, and Question 17 is on the relationship between radius and tangent.

The new version of the test still contains these questions from four other chapters, but now most of the questions are from Chapter 15.

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