M ATH 532, 736I: M ODERN G EOMETRY
Test 1, Spring 2011
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Instructions: Put your name at the top of this page and at the top of the rst page of the packet
of blank paper given to you. Work each problem on the paper provided, using a separa
M ATH 532, 736I: M ODERN G EOMETRY
Test 1, Spring 2013
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Instructions: This test consists of 3 pages of problems. Put your name at the top of this page and
at the top of the rst page of the packet of blank paper given to you. Work each pr
M ATH 532, 736I: M ODERN G EOMETRY
Test 1, Spring 2012
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Instructions: This test consists of 3 pages of problems. Put your name at the top of this page and
at the top of the rst page of the packet of blank paper given to you. Work each pr
Solutions for Part I
(1) Axiom P1: There exist at least four points, no three of which are collinear.
Axiom P2: There is at least one line that passes through exactly n+1 points.
Axiom P3: For any two points, there is exactly one line that passes through
M ATH 532, 736I: M ODERN G EOMETRY
Test 2, Spring 2012
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Instructions: This test consists of 4 pages (one is an information page). Put your name at the top
of this page and at the top of the rst page of the packet of blank paper given to
1. Using Theorem 1 with t = 1/10 we see that C = (1-t) A + t B
2. Using the rules we get a shape that looks like this!
A
C
( )! = ( )! | = |
( )! = ( )! | = |
( )( ) = 0
( )( ) = 0
B
D
Math 532, 736I: Modern Geometry
Test 1, Spring 2013 ( Solutions): Provided by Jeff Collins and Anil Patel
Part 1:
1. Axioms for a finite AFFINE plane of order n.
AA1: There exist at least 4 points, no 3 of wh
M ATH 532, 736I: M ODERN G EOMETRY
Test #2 (2011)
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Instructions: There are 100 points possible on the test. The value of each problem appears to the
left of each problem number. If there are boxes with these test questions, ll them in ap
M ATH 532, 736I: M ODERN G EOMETRY
Test 2, Spring 2013
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Instructions: This test consists of 5 pages (one is an information page). Put your name at the top
of this page and at the top of the rst page of the packet of blank paper given to
M AT H 5 32 , 7 36I : M ODER N GEOMETRY
Test 2 Solutions
Test #2 (2011)
1) Theorems are listed on the last page of this test. They may or may not have the numbering
that you are accustomed to them having from class. Prove Theorem 2 using Theorem 1 (but
no
M AT H 5 32 , 7 36I : M ODER N GEOMETRY
Test 1 Solutions
Test 1 (2011):
Part I:
(1) Axioms for a finite AFFINE plane of order n
Axiom A1: There exist at least 4 distinct points no 3 of which are collinear.
Axiom A2: There exists at least 1 line with exact