Unit 3 Practice Quiz

Unit 3 Practice Quiz Pascal’s Triangle Questions

1. What is the 4th term in the expansion of (a + b)9? 1. ______

2. What is the coefficient of the 4th term in the expansion of (a + b)9? 2. ______

3. What are the variables of the 4th term in the expansion of (a + b)9? 3. ______

4. What is the 3rd term in the expansion of (3a + 2b)5? 4. ______

5. What is the coefficient of the 10th term in the expansion of (a + b)9? 5. ______

6. What are the variables of the 34th term in the expansion of (a + b)95? 6. ______

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. ______

8. Using the same bag as in 7, what are the odds of drawing a red, white, or blue

from the bag? 8. ______

Fano’s Geometry

9. How many Axioms are in the geometry? 9. ______

10. How many lines are in the geometry? 10. ______

11. Do the lines in the geometry have to be straight? 11. ______

12. Are there any parallel lines in the geometry? 12. ______

13. Draw a representation of the geometry. 13. ______

Given the following: 14. a.______ There exists exactly three distinct points in the geometry.  Two distinct points are on exactly one line. b.______ Not all the points of the geometry are on the same line.  Two distinct lines are on at least one point. c.______14. Rewrite the above using tree for point, row for line, and forest for geometry. d.______15. What does QED mean? 15. ______Patty Paper Geometry

16. How many lines can be constructed through one point? 16. ______

17. How many lines can be constructed through two points? 17. ______

18. Construct a perpendicular bisector for any random but fixed line segment. 18. ______

19. Construct the angle bisector for any random but fixed angle. 19. ______

20. Construct the Centroid for any random but fixed triangle. 20. ______

21. Construct the Circumcenter for any random but fixed triangle. 21. ______

22. Construct the Incenter for any random but fixed triangle. 22. ______

Invariants

23. The diagonal of a rectangle inscribed in a circle is always a ______. 23. ______

24. The diagonals of any quadrilateral ABCD intersect at E so that AE(EC) 24. ______has what relationship to DE(EB)?

25. A triangle inscribe inside a semi-circle is always what kind of triangle? 25. ______

26. The medians of a triangle form a point of concurrency called ______. 26. ______

27. The altitudes of a triangle form a point of concurrency called ______. 27. ______

28. The perpendicular bisectors of a triangle form a point of concurrency called ______. 28. ______

29. The angle bisectors of a triangle form a point of concurrency called ______. 29. ______30. Which of the four points of triangle concurrency are NOT on Euler’s line? 30. ______What’s My Angle

31. What is the sum of the interior angles of a triangle? 31. ______

32. What is the sum of the interior angles of a hexagon? 32. ______

33. What is the sum of the interior angles of an n-gon? 33. ______

34. What is the sum of the exterior angles of an octagon? 34. ______

35. What is the sum of the exterior angles of an n-gon? 35. ______

36. If I can make 3 triangles inside a figure connecting vertices, how many sides does it have? 36. ______

37. If I can make 7 triangles inside a figure connecting vertices, how many sides does it have? 37. ______

38. If I can make n triangles inside a figure connecting vertices, how many sides does it have? 38. ______Cross Words

39. Rotate the following 90o counter-clockwise:  39. ______

o 40. ______40. Rotate the following 90 clockwise: ↯ 41. ______41. Rotate the following 180o counter-clockwise:  42. ______42. Rotate the following 180o clockwise: ↯ 43. ______43. Rotate the following 270o counter-clockwise:  44. ______44. Rotate the following 270o clockwise: ↯ 45. ______45. Reflect the following vertically:  46. ______46. Reflect the following horizontally: ↯ 47. ______47. Reflect the following diagonally (y = x):  48. ______

48. Reflect the following diagonally (y = -x): ↯

Taxicab Geometry 49. ______

49. What does a circle look like in taxicab geometry? 50. ______

50. If I am at 300 South 900 West, how far away is my hotel at 200 North 500 East?