北京 景山 学校 数学系
Elective / Pre-Calculus @ MATHEMATICS @ Junior 8.5  。2010-11
jiguanglaoshi@gmail.com

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[2] May
[updated : 2011/06/02]
Date
 Activities / Objectives
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Wednesday

May 04

16:00 -17:00
  • FORMAL ARITHMETIC :
    • Correction of exercises
    • New exercises on GCD & LCM
      • Bézout
      • Gauss
    • Diophantines equations
      • more complicated than the previous one ...

  • AMC sample problems :
    • Correction of exercises #2
    • New Exercises


Class of next Werdnesday
changed to Next Monday 9th
from 4:45 to 5:30
(Leave of absence)

MEMO / DEMO of Formal ARITHMETIC

Monday

May 09

16:00 -17:30
ARITHMETIC


Exercises on Euclidian Division
  • N = a(a2 – 1) is a multiple of 6

  • if the quotient q of the Euclidian division of a by b is not 0, then a is larger than the double of the rest of the division of a by b.

  • Find (x;y) such that    x2 –  y2 = 13



Exercises on Euclidian Division




Monday

May 16

16:00 -17:00

ARITHMETIC

More exercises on the Euclidian division

  • 2n + 1 = 2(n – 3) + 7.
    Find the values of n such that
    (n – 3) is a factor of (2n + 1)

  • n2 – n + 3 = (n – 2)(n + 1) + 5.
    Find the values of n such that
    (n + 1) is a factor of (n2 – n + 3)

  • Find the values of n such that the fraction fract can be simplified into an Integer.




More on the Euclidian division
Wednesday

May 18

16:00 -17:00
AMC Problems

Solutions & Answers :
  • End of sheet # 2 of April

  • New sheet of AMC problems # 3


Prepare solution of  problem #5
on sheet # 3



AMC PROBLEMS #3
Monday

May 23

16:00 -17:00
ARITHMETIC
  • Congruences :
    • definition in Z :
      cong
    • properties of Add° and Mult.°
    • classes : definition of Z/nZ
    • Addition Table in Z/5Z and Z/6Z
    • Multiplication Table in Z/5Z & Z/6Z
  • Typical Exercise : in Z/6Z
    solve the system :    syst
Addition table in Z/6Z
+
 0
 1
 2
 3
 4
 5
0
 0
 1
 2
 3
 4
 5
1
 1
 2
 3
 4
 5
 0
2
 2
 3
 4
 5
 0
 1
3
 3
 4
 5
 0
 1
 2
4
 4
 5
 0
 1
 2
 3
5
 5
 0
 1
 2
 3
 4


Multiplication table in Z/6Z
X
 0
 1
 2
 3
 4
 5
0
 0
 0
 0
 0
 0
 0
1
 0
 1
 2
 3
 4
 5
2
 0
 2
 4
 0 2
 4
3
 0
 3
 0 3
 0 3
4
 0
 4
 2
 0 4
 2
5
 0
 5
 4
 3
 2
 1




Memo on CONGRUENCES


Exercises on Congruences



Wednesday

May 25

16:00 -17:00		 End problem on congruences
(system of equations in Z/6Z)
syst

Answer to AMC problems (#3)
Handout AMC Problems (#4)
 Exercise in class :
Other example of system in Z/6Z
S2
  • Prepare AMC Problems (#4)
Missing Registration forms !!!

The following students will not be accepted in next class without it !
  • "Dicky"
  • "Totti"
  • "Angelina"
  • "Heavenly"
  • "John"


AMC PROBLEMS #4



Monday

May 30

16:00 -17:00

Answers and correction of
AMC Problems :
  • Problem # 5 of sheet # 3

  • Problem # 1 & # 2 of sheet # 4
  • How many pairs of positive intergers (a;b) are such that a and b have no common
    factor greater than 1
    and [a/b + 14a/9b] is an integer.

  • Let a and b the roots of the equation
    x2 – mx + 2 = 0.
    Suppose that (a+1/b) and (b +1/a)
    are the roots of the equation
    x2 – px + q = 0
    What is q ?
    The Dunbar family consists of a mother, a father and some children. The average age of the members of the family is 20, the fatther is 48 years old, and the average age of the mother and the children is 16.
How many children are in the family ?

============

NO Class on Monday 6th
(Dragon's day)


AMC PROBLEMS #3

AMC PROBLEMS #4