UIL NS and Mathematics
Special Topics Session
Larry White
Box 25
Millersview, Tx 76862
325-483-5446
[email protected]
UIL State NS & Mathematics Contest Director
Be sure to ...
 sign in;
 clean up your area when
you leave;
 and
“HAVE A GREAT DAY!”
UIL NS and Mathematics
Special Topics Session
UIL Number Sense and Mathematics
Constitution and Contest Rules (C&CR)
??? Any rules need discussing or clarified ???
UIL NS and Mathematics
Special Topics Session
A Special Problem
C
Z
A
X D
Z
T
Y
B
UIL NS and Mathematics
Special Topics Session
Using A Special Theorem In Plane Geometry
C
2T
Z
T
X D
4
Y
2
2
2
4
4
= X + Y + Z
or
Z
2T
A
2
B
4
= X + Y + Z
UIL NS and Mathematics
Special Topics Session
Using A Special Theorem In Plane Geometry
C
2T
8"
T
2" D
4
6"
2
2
2
4
4
= 2 + 6 + 8
or
8"
2T
A
2
B
4
= 2 + 6 + 8
UIL NS and Mathematics
Special Topics Session
Using A Special Theorem In Plane
Geometry
Warren D. Smith - March 2012
This theorem was also used to solve a
number theory problem about
“Prouhet Tarry Excott” set pairs.
UIL NS and Mathematics
Special Topics Session
Pascal’s Triangle Clarification
row 0
row 1
1
row 2
1
row 3
row 4
(x+y)0
1
1
1
2
3
4
(x+y)1
1
3
6
(x+y)2
1
(x+y)3
1
4
1
(x+y)4
UIL NS and Mathematics
Special Topics Session
Special topics/problems/emphasis
on 2012-2013 tests
1 new mathematician added this year.
Zeno of Elea
1 new special number added this year.
Harmonic number
UIL NS and Mathematics
Special Topics Session
Emphasis this year on:
Number Theory Problems (See #23 & 25 on the SAC
test and #1, 2, & 3 on the back page of the SAC test.)
The 7 “trapezoidal” means (See #24 on the SAC test
and #4 on the back page of the SAC test.)
UIL NS and Mathematics
Special Topics Session
Trapezoidal Means
Arithmetic Mean
Geometric Mean
Harmonic Mean
Heronian Mean
Contraharmonic Mean
Root-Mean-Square
Centroidal Mean
UIL NS and Mathematics
Special Topics Session
Trapezoidal Means
UIL NS and Mathematics
Special Topics Session
If you have some questions,
I have some answers.
HAVE A
GREAT DAY!