Friday, April 10, 2015

Chapter 10 Test (Day 144)

Here is the Chapter 10 Test. Let me include the answers as well as the rationale for including some of the questions that I did.

1. 4.
2. 24 square units.
3. 9pi cubic units.
4. sqrt(82) * pi square units, 3pi cubic units.
5. 48,000 cubic units.
6. 98 square units.
7. 28,224pi square units, 790,272 cubic units.
8. 5.5. Section 10-3 of the U of Chicago text asks the students to estimate cube roots. If one prefers to make it a volume question, simply change it to: The volume of a cube is 165 cubic units. What is the length of its sides to the nearest tenth?
9. Its volume is multiplied by 343. This is a big PARCC question!
10. Its volume is multiplied by 25 -- not 125 because only two of the dimensions are being multiplied by 5, not the thickness.
11. The volume of Neptune is 64 times that of Earth.
12. A ring -- specifically the area between the the circular cross section of the cylinder and the circular cross section of the cone. This is Cavalieri's Principle -- recall the comments I made about Dr. Beals?
13. 3pi cubic centimeters -- or, if you prefer, 3pi milliliters.
14. 22,000 cubic cubits -- a sort of tongue twister.
15. l^2 + lw + w^2. This area question comes from Section 10-4 of the U of Chicago text, and this specific question was used by Dr. M in his derivation of the rectangle area formula.

The last five questions come from Sections 11-3 and 15-3, our two circle sections.

16. a. (0, 0) b. sqrt(65) c. Answers may vary. There are many different possible answers that one may choose here, not just intercepts like (sqrt(65), 0), but also lattice points such as (8, 1) or even (7, 6) -- not to mention points in other quadrants.
17. A circle centered at (3, 3) of radius 3. The graphs appear to stop at 5, but it may be convenient to graph points involving 6, such as (6, 3).
18. A circle centered at (3, 0) of radius 3. This requires completing the square -- big for PARCC!
19. 178 degrees -- which is double 89.
20. 52 degrees. One needs to know that angles of a triangle add up to 180, or that arcs of a circle add up to 360, since the arc the students need isn't given!

Have a nice weekend!

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