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Unit 3 Practice Quiz
Pascal’s Triangle Questions
1. What is the 4th term in the expansion of (a + b)9?
1. 84a6b3
2. What is the coefficient of the 4th term in the expansion of (a + b)9?
2. 84
3. What are the variables of the 4th term in the expansion of (a + b)9?
3. a6b3
4. What is the 3rd term in the expansion of (3a + 2b)5?
4. 1080a3b2
5. What is the coefficient of the 10th term in the expansion of (a + b)9?
5. 1
6. What are the variables of the 34th term in the expansion of (a + b)95?
6. a62b33
Odds Questions
7. There are 12 marbles in a bag: 2 blue, 3 white, 6 yellow, 1 red. What are the
odds of drawing a white or yellow ball from the bag?
7. 3:1
8. Using the same bag as in 7, what are the odds of drawing a red, white, or blue
from the bag?
8. 1:1
Fano’s Geometry
9. How many Axioms are in the geometry?
9. 4
10. How many lines are in the geometry?
10. 3
11. Do the lines in the geometry have to be straight?
11. no
12. Are there any parallel lines in the geometry?
12. no
13. Draw a representation of the geometry.
13. answers will vary
Given the following:
 There exists exactly three distinct points in the geometry.
 Two distinct points are on exactly one line.
 Not all the points of the geometry are on the same line.
 Two distinct lines are on at least one point.
14. Rewrite the above using tree for point, row for line, and forest for geometry.
14. a. There exists exactly three
distinct trees in the forest.
b. Two distinct trees are in
exactly one row.
c. Not all the trees in the forest
are in the same row.
d. Two distinct rows contain at
least one tree.
15. Quid Errata Demonstratum
15. What does QED mean?
Patty Paper Geometry
16. How many lines can be constructed through one point?
16. infinitely many
17. How many lines can be constructed through two points?
17. exactly one
18. Construct a perpendicular bisector for any random but fixed line segment.
18. patty paper - awv
19. Construct the angle bisector for any random but fixed angle.
19. patty paper - awv
20. Construct the Centroid for any random but fixed triangle.
20. patty paper - awv
21. Construct the Circumcenter for any random but fixed triangle.
21. patty paper - awv
22. Construct the Incenter for any random but fixed triangle.
22. patty paper - awv
Invariants
23. The diagonal of a rectangle inscribed in a circle is always a __________.
23. diameter
24. The diagonals of any quadrilateral ABCD intersect at E so that AE(EC)
has what relationship to DE(EB)?
24. they are always equal
25. A triangle inscribe inside a semi-circle is always what kind of triangle?
25. a right triangle
26. The medians of a triangle form a point of concurrency called __________ . 26. the Centroid
27. The altitudes of a triangle form a point of concurrency called __________ . 27. the Orthocenter
28. The perpendicular bisectors of a triangle form a point of concurrency called __________ .
28. the Circumcenter
29. The angle bisectors of a triangle form a point of concurrency called __________ .
29. the Incenter
30. Which of the four points of triangle concurrency are NOT on Euler’s line?
30. the Incenter
What’s My Angle
31. What is the sum of the interior angles of a triangle?
31. 180o
32. What is the sum of the interior angles of a hexagon?
32. 720o
33. What is the sum of the interior angles of an n-gon?
33. (n – 2)180o
34. What is the sum of the exterior angles of an octagon?
34. 360o
35. What is the sum of the exterior angles of an n-gon?
35. 360o
36. If I can make 3 triangles inside a figure connecting vertices, how many sides does it have?
36. 5
37. If I can make 7 triangles inside a figure connecting vertices, how many sides does it have? 37. 9
38. If I can make n triangles inside a figure connecting vertices, how many sides does it have? 38. n + 2
Cross Words
39. Rotate the following 90o counter-clockwise: 
39. 
40. Rotate the following 90o clockwise: 
40. 
41. Rotate the following 180o counter-clockwise: 
41. 
42. Rotate the following 180o clockwise: 
42. 
43. Rotate the following 270o counter-clockwise: 
43. 
44. Rotate the following 270o clockwise: 
44. 
45. Reflect the following vertically: 
45. 
46. Reflect the following horizontally: 
46. 
47. Reflect the following diagonally (y = x): 
47. 
48. Reflect the following diagonally (y = -x): 
48. 
Taxicab Geometry
49. What does a circle look like in taxicab geometry?
50. If I am at 300 South 900 West, how far away is my hotel at 200 North 500 East?
49. square
50. 19 blocks